diff --git a/docs/amg4psblas_1.0-guide.pdf b/docs/amg4psblas_1.0-guide.pdf new file mode 100644 index 00000000..65f5f8d7 Binary files /dev/null and b/docs/amg4psblas_1.0-guide.pdf differ diff --git a/docs/html/amg4psblaslibrary.png b/docs/html/amg4psblaslibrary.png new file mode 100644 index 00000000..604d1a53 Binary files /dev/null and b/docs/html/amg4psblaslibrary.png differ diff --git a/docs/html/index.html b/docs/html/index.html index b7b34168..ae4a08ca 100644 --- a/docs/html/index.html +++ b/docs/html/index.html @@ -71,7 +71,7 @@ class="cmr-12">Contributors
3 Configuring and Building MLD2P4 +class="cmr-12">Configuring and Building AMG4PSBLAS
 3.1 Auxiliary Methods
7 Adding new smoother and solver objects to MLD2P4 +class="cmr-12">Adding new smoother and solver objects to AMG4PSBLAS
8 Contributors
3 Configuring and Building MLD2P4 +class="cmr-12">Configuring and Building AMG4PSBLAS
 3.1 Auxiliary Methods
7 Adding new smoother and solver objects to MLD2P4 +class="cmr-12">Adding new smoother and solver objects to AMG4PSBLAS
8 Abstract

MLD2P4 (MuAMG4PSBLAS (AltiLevgel Dombrain Decomposic Multion PaiGrallel Pid Preconers -Ps Packsed on PSBLAS) is a package of parallel algebraic multilevel +class="small-caps">n +PSBLAS) is a package of parallel algebraic multilevel preconditioners included in the +PSCToolkit (Parallel Sparse Computation Toolkit) software framework. It is a progress +of a software development project started in 2007, named MLD2P4, which +implemented a multilevel version of some domain decomposition preconditioners of +additive-Schwarz type and was based on a parallel decoupled version of the well known +smoothed aggregation method to generate the multilevel hierarchy of coarser +matrices. In the last years, within the context of the EU-H2020 EoCoE project +(Energy Oriented Center of Excellence), the package was extended including +new algorithms and functionalities for setup and application of new AMG +preconditioners with the final aims of improving efficiency and scalability when tens of preconditioners. The first release of MLD2P4 made available multilevel additive and +class="cmr-12">thousands cores are used and of boosting reliability in dealing with general hybrid Schwarz preconditioners, as well as one-level additive Schwarz preconditioners. +class="cmr-12">symmetric positive definite linear systems. Due to the significant number The package has been extended to include further multilevel cycles and smoothers +class="cmr-12">of changes and the increase in scope, we decided to rename the package as widely used in multigrid methods. In the multilevel case, a purely algebraic approach is +class="cmr-12">AMG4PSBLAS. +

AMG4PSBLAS has been designed to provide scalable and easy-to-use applied to generate coarse-level corrections, so that no geometric background is needed +class="cmr-12">preconditioners in the context of the PSBLAS (Parallel Sparse Basic Linear Algebra concerning the matrix to be preconditioned. The matrix is assumed to be square, real +class="cmr-12">Subprograms) computational framework and can be used in conjuction with the Krylov or complex. -

MLD2P4 has been designed to provide scalable and easy-to-use preconditioners in +class="cmr-12">solvers available in this framework. Our package is based on a completely algebraic the context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms) +class="cmr-12">approach and users level interfaces assume that the system matrix and preconditioners computational framework and can be used in conjuction with the Krylov solvers +class="cmr-12">are represented as PSBLAS distributed sparse matrices. AMG4PSBLAS enables the available in this framework. MLD2P4 enables the user to easily specify different +class="cmr-12">user to easily specify different features of an algebraic multilevel preconditioner, thus features of an algebraic multilevel preconditioner, thus allowing to search for the “best” +class="cmr-12">allowing to experiment with different preconditioners for the problem and parallel preconditioner for the problem at hand. +class="cmr-12">computers at hand.

The package employs object-oriented design techniques in Fortran 2003, with @@ -136,7 +137,7 @@ class="cmr-12">through PSBLAS.

This guide provides a brief description of the functionalities and the user interface of MLD2P4. +class="cmr-12">of AMG4PSBLAS. diff --git a/docs/html/userhtmlli2.html b/docs/html/userhtmlli2.html index 2f15012d..51ce9e89 100644 --- a/docs/html/userhtmlli2.html +++ b/docs/html/userhtmlli2.html @@ -45,7 +45,7 @@ class="cmr-12">Code Distribution
3 Configuring and Building MLD2P4 +class="cmr-12">Configuring and Building AMG4PSBLAS
 3.1 _wrk
7 Adding new smoother and solver objects to MLD2P4 +class="cmr-12">Adding new smoother and solver objects to AMG4PSBLAS
8 ]

Contributors

-

Contributors to version 2:

-

Contributors to version 1: -

+class="cmr-12">Salvatore Filippone, University of Rome Tor-Vergata and IAC-CNR, IT; diff --git a/docs/html/userhtmlli4.html b/docs/html/userhtmlli4.html index f68717f4..ef848d13 100644 --- a/docs/html/userhtmlli4.html +++ b/docs/html/userhtmlli4.html @@ -11,549 +11,645 @@

[[prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

+class="cmbx-12">up]

References

+class="cmbx-12">References

[1]   [1]   P. R. Amestoy, C. Ashcraft, O. Boiteau, A. Buttari, J. L’Excellent, - C. Weisbecker, Improving multifrontal methods by means of block low-rank - representations, SIAM Journal on Scientific Computing, volume 37 (3), 2015, - A1452–A1474. See also P. R. Amestoy, C. Ashcraft, O. Boiteau, A. Buttari, + J. L’Excellent, C. Weisbecker, Improving multifrontal methods + by means of block low-rank representations, SIAM Journal on + Scientific Computing, volume 37 (3), 2015, A1452–A1474. See also + http://mumps.enseeiht.fr. +class="cmbx-12">.

[2]   [2]   M. Brezina, P. Vaněk, A Black-Box Iterative Solver Based on a - Two-Level Schwarz Method, Computing, 63, 1999, 233–263. +class="cmbx-12">M. Brezina, P. Vaněk, A Black-Box Iterative Solver Based + on a Two-Level Schwarz Method, Computing, 63, 1999, 233–263.

[3]   [3]   W. L. Briggs, V. E. Henson, S. F. McCormick, A Multigrid Tutorial, - Second Edition, SIAM, 2000. +class="cmbx-12">W. L. Briggs, V. E. Henson, S. F. McCormick, A Multigrid + Tutorial, Second Edition, SIAM, 2000.

[4]   [4]   A. Buttari, P. D’Ambra, D. di Serafino, S. Filippone, Extending +class="cmbx-12">A. Buttari, PSBLAS to Build Parallel Schwarz Preconditioners, in J. Dongarra, +class="cmbx-12">P. D’Ambra, D. di Serafino, S. Filippone, Extending PSBLAS K. Madsen, J. Wasniewski, editors, Proceedings of PARA 04 Workshop on +class="cmbxti-10x-x-120">to Build Parallel Schwarz Preconditioners, in J. Dongarra, State of the Art in Scientific Computing, Lecture Notes in Computer Science, +class="cmbx-12">K. Madsen, J. Wasniewski, editors, Proceedings of PARA 04 Springer, 2005, 593–602. +class="cmbx-12">Workshop on State of the Art in Scientific Computing, Lecture + Notes in Computer Science, Springer, 2005, 593–602.

[5]   [5]   A. Buttari, P. D’Ambra, D. di Serafino, S. Filippone, 2LEV-D2P4: a - package of high-performance preconditioners for scientific and engineering +class="cmbx-12">A. Buttari, P. D’Ambra, D. di Serafino, S. Filippone, applications, Applicable Algebra in Engineering, Communications and +class="cmbxti-10x-x-120">2LEV-D2P4: a package of high-performance preconditioners Computing, 18 (3) 2007, 223–239. +class="cmbxti-10x-x-120">for scientific and engineering applications, Applicable Algebra + in Engineering, Communications and Computing, 18 (3) 2007, + 223–239.

[6]   [6]   X. C. Cai, M. Sarkis, A Restricted Additive Schwarz Preconditioner for +class="cmbx-12">X. C. Cai, M. Sarkis, A Restricted Additive Schwarz General Sparse Linear Systems, SIAM Journal on Scientific Computing, 21 +class="cmbxti-10x-x-120">Preconditioner for General Sparse Linear Systems, SIAM (2), 1999, 792–797. +class="cmbx-12">Journal on Scientific Computing, 21 (2), 1999, 792–797.

[7]   [7]    + P. D’Ambra, S. Filippone, +class="cmbx-12">P. D’Ambra, S. Filippone, D. di Serafino, On the Development D. di Serafino, On the Development of PSBLAS-based Parallel Two-level +class="cmbxti-10x-x-120">of PSBLAS-based Parallel Two-level Schwarz Preconditioners, Schwarz Preconditioners, Applied Numerical Mathematics, Elsevier Science, +class="cmbx-12">Applied Numerical Mathematics, Elsevier Science, 57 (11-12), 57 (11-12), 2007, 1181-1196. +class="cmbx-12">2007, 1181-1196.

[8]   [8]   P. D’Ambra, D. di Serafino, S. Filippone, MLD2P4: a Package of +class="cmbx-12">P. D’Ambra, D. di Serafino, S. Filippone, MLD2P4: a + Package of Parallel Multilevel Algebraic Domain Decomposition Parallel Multilevel Algebraic Domain Decomposition Preconditioners in +class="cmbxti-10x-x-120">Preconditioners in Fortran 95, ACM Trans. Math. Softw., 37(3), Fortran 95, ACM Trans. Math. Softw., 37(3), 2010, art. 30. +class="cmbx-12">2010, art. 30.

[9]   [9]   A. Buttari, P. D’Ambra, D. di Serafino, S. Filippone, + 2LEV-D2P4: a Package of High-Performance Preconditioners + for Scientific and Engineering Applications, Appl. Algebra + Engrg. Comm. Comput., 18(3), 2007, 223–239. +

+

+ [10]   P. D’Ambra, F Durastante, S. Filippone, AMG + preconditioners for Linear Solvers towards Extreme Scale, 2020, + arXiv:2006.16147v2. +

+

+ [11]   T. A. Davis, Algorithm 832: UMFPACK +class="cmbx-12">T. A. Davis, Algorithm + 832: UMFPACK - an Unsymmetric-pattern Multifrontal Method - an Unsymmetric-pattern Multifrontal Method with a Column Pre-ordering +class="cmbxti-10x-x-120">with a Column Pre-ordering Strategy, ACM Transactions Strategy, ACM Transactions on Mathematical Software, 30, 2004, 196–199. +class="cmbx-12">on Mathematical Software, 30, 2004, 196–199. (See also (See also http://www.cise.ufl.edu/~davis/) +class="cmbx-12">) + + +

[10]   [12]   J. W. Demmel, S. C. Eisenstat, J. R. Gilbert, - X. S. Li, J. W. H. Liu, A supernodal approach to sparse partial pivoting, - SIAM Journal on Matrix Analysis and Applications, 20 (3), 1999, 720–755. +class="cmbx-12">J. W. Demmel, S. C. Eisenstat, J. R. Gilbert, X. S. Li, + J. W. H. Liu, A supernodal approach to sparse partial pivoting, + SIAM Journal on Matrix Analysis and Applications, 20 (3), 1999, + 720–755.

[11]   [13]   J. J. Dongarra, J. Du Croz, I. S. Duff, S. Hammarling, A set of Level - 3 Basic Linear Algebra Subprograms, ACM Transactions on Mathematical - Software, 16 (1) 1990, 1–17. +class="cmbx-12">J. J. Dongarra, J. Du Croz, I. S. Duff, S. Hammarling, + A set of Level 3 Basic Linear Algebra Subprograms, ACM + Transactions on Mathematical Software, 16 (1) 1990, 1–17.

[12]   [14]    + J. J. Dongarra, J. Du Croz, S. Hammarling, R. J. Hanson, An - extended set of FORTRAN Basic Linear Algebra Subprograms, ACM - Transactions on Mathematical Software, 14 (1) 1988, 1–17. - - - +class="cmbx-12">J. J. Dongarra, J. Du Croz, S. Hammarling, R. J. Hanson, An + extended set of FORTRAN Basic Linear Algebra Subprograms, + ACM Transactions on Mathematical Software, 14 (1) 1988, 1–17.

[13]   [15]   S. Filippone, A. Buttari, PSBLAS 3.5.0 User’s Guide. A Reference +class="cmbx-12">S. Filippone, A. Buttari, PSBLAS 3.5.0 User’s Guide. A Guide for the Parallel Sparse BLAS Library, 2012, available from +class="cmbxti-10x-x-120">Reference + Guide for the Parallel Sparse BLAS Library, 2012, available from https://github.com/sfilippone/psblas3/tree/master/docs. +class="cmbx-12">.

[14]   [16]   S. Filippone, A. Buttari, Object-Oriented Techniques for Sparse Matrix +class="cmbx-12">S. Filippone, A. Buttari, Object-Oriented Techniques for Computations in Fortran 2003. ACM Transactions on on Mathematical +class="cmbxti-10x-x-120">Sparse Matrix Computations in Fortran 2003. ACM Transactions Software, 38 (4), 2012, art. 23. +class="cmbx-12">on on Mathematical Software, 38 (4), 2012, art. 23.

[15]   [17]   S. Filippone, M. Colajanni, PSBLAS: A +class="cmbx-12">S. Filippone, M. Colajanni, PSBLAS: A Library for Parallel Library for Parallel Linear Algebra Computation on Sparse Matrices, ACM +class="cmbxti-10x-x-120">Linear Algebra Computation on Sparse Matrices, ACM Transactions on Mathematical Software, 26 (4), 2000, 527–550. +class="cmbx-12">Transactions on Mathematical Software, 26 (4), 2000, 527–550.

[16]   [18]   S. Gratton, P. Henon, P. Jiranek and X. Vasseur, Reducing complexity of +class="cmbx-12">S. Gratton, P. Henon, P. Jiranek and X. Vasseur, Reducing algebraic multigrid by aggregation, Numerical Lin. Algebra with Applications, +class="cmbxti-10x-x-120">complexity of algebraic multigrid by aggregation, Numerical Lin. 2016, 23:501-518 +class="cmbx-12">Algebra with Applications, 2016, 23:501-518 + + +

[17]   [19]   W. Gropp, S. Huss-Lederman, A. Lumsdaine, E. Lusk, B. Nitzberg, - W. Saphir, M. Snir, MPI: The Complete Reference. Volume 2 - The MPI-2 - Extensions, MIT Press, 1998. +class="cmbx-12">W. Gropp, S. Huss-Lederman, A. Lumsdaine, + E. Lusk, B. Nitzberg, W. Saphir, M. Snir, MPI: The Complete + Reference. Volume 2 - The MPI-2 Extensions, MIT Press, 1998.

[18]   [20]   C. L. Lawson, R. J. Hanson, D. Kincaid, F. T. Krogh, Basic Linear - Algebra Subprograms for FORTRAN usage, ACM Transactions on - Mathematical Software, 5 (3), 1979, 308–323. +class="cmbx-12">C. L. Lawson, R. J. Hanson, D. Kincaid, F. T. Krogh, + Basic Linear Algebra Subprograms for FORTRAN usage, ACM + Transactions on Mathematical Software, 5 (3), 1979, 308–323.

[19]   [21]   X. S. Li, J. W. Demmel, SuperLU_DIST: A Scalable - Distributed-memory Sparse Direct Solver for Unsymmetric Linear Systems, - ACM Transactions on Mathematical Software, 29 (2), 2003, 110–140. - - - +class="cmbx-12">X. S. Li, J. W. Demmel, + SuperLU_DIST: A Scalable Distributed-memory Sparse Direct + Solver for Unsymmetric Linear Systems, ACM Transactions on + Mathematical Software, 29 (2), 2003, 110–140.

[20]   [22]   Y. Notay, P. S. Vassilevski, Recursive Krylov-based multigrid cycles, - Numerical Linear Algebra with Applications, 15 (5), 2008, 473–487. +class="cmbx-12">Y. Notay, P. S. Vassilevski, Recursive Krylov-based + multigrid cycles, Numerical Linear Algebra with Applications, 15 + (5), 2008, 473–487.

[21]   [23]   Y. Saad, Iterative methods for sparse linear systems, 2nd edition, SIAM, +class="cmbx-12">Y. Saad, Iterative methods for sparse linear systems, 2nd 2003. +class="cmbx-12">edition, SIAM, 2003.

[22]   [24]   B. Smith, P. Bjorstad, W. Gropp, Domain Decomposition: Parallel +class="cmbx-12">B. Smith, P. Bjorstad, W. Gropp, Domain Decomposition: Multilevel Methods for Elliptic Partial Differential Equations, Cambridge +class="cmbxti-10x-x-120">Parallel Multilevel Methods for Elliptic Partial Differential University Press, 1996. +class="cmbxti-10x-x-120">Equations, Cambridge University Press, 1996.

[23]   [25]   M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI: - The Complete Reference. Volume 1 - The MPI Core, second edition, MIT - Press, 1998. +class="cmbx-12">M. Snir, + S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI: The + Complete Reference. Volume 1 - The MPI Core, second edition, + MIT Press, 1998. + + +

[24]   [26]   K. Stüben, An Introduction to Algebraic Multigrid, in A. Schüller, - U. Trottenberg, C. Oosterlee, Multigrid, Academic Press, 2001. +class="cmbx-12">K. Stüben, An Introduction to Algebraic Multigrid, in + A. Schüller, U. Trottenberg, C. Oosterlee, Multigrid, Academic + Press, 2001.

[25]   [27]   R. S. Tuminaro, C. Tong, Parallel Smoothed Aggregation Multigrid: +class="cmbx-12">R. S. Tuminaro, Aggregation Strategies on Massively Parallel Machines, in J. Donnelley, +class="cmbx-12">C. Tong, Parallel Smoothed Aggregation Multigrid: Aggregation editor, Proceedings of SuperComputing 2000, Dallas, 2000. +class="cmbxti-10x-x-120">Strategies on Massively Parallel Machines, in J. Donnelley, + editor, Proceedings of SuperComputing 2000, Dallas, 2000.

[26]   [28]   P. Vaněk, J. Mandel, M. Brezina, Algebraic Multigrid by Smoothed - Aggregation for Second and Fourth Order Elliptic Problems, Computing, 56 - (3) 1996, 179–196. -

-
+class="cmbx-12">P. Vaněk, J. Mandel, M. Brezina, Algebraic Multigrid by + Smoothed Aggregation for Second and Fourth Order Elliptic + Problems, Computing, 56 (3) 1996, 179–196. +

+

+ [29]   P. D’Ambra and P. S. Vassilevski, Adaptive AMG with + coarsening based on compatible weighted matching, Computing + and Visualization in Science, 16, (2013) 59–76. +

+

+ [30]   P. D’Ambra, S. Filippone and P. S. Vassilevski, BootCMatch: + a software package for bootstrap AMG based on graph weighted + matching, ACM Transactions on Mathematical Software, 44, + (2018) 39:1–39:25.

@@ -561,19 +657,19 @@ class="cmr-12">(3) 1996, 179–196.

[[prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

+class="cmbx-12">up]

diff --git a/docs/html/userhtmlse1.html b/docs/html/userhtmlse1.html index 55f5d6ba..2cfc937a 100644 --- a/docs/html/userhtmlse1.html +++ b/docs/html/userhtmlse1.html @@ -33,39 +33,22 @@ class="cmr-12">1 General Overview

The MuAltiLevgel Dombrain Decomposic Multion PaiGrallel Pid Preconers -Ps Packsed on PSBLAS (MLD2P4) provides parallel Algebraic MultiGrid +class="small-caps">n PSBLAS (AMG) and Domain Decomposition preconditioners (see, e.g., (AMG4PSBLAS) provides parallel Algebraic MultiGrid (AMG) preconditioners (see, +e.g., [3, 24, 2226]), to be used -in the iterative solution of linear systems, +class="cmr-12">), to be used in the iterative solution of linear systems,
@@ -121,25 +98,19 @@ src="userhtml0x.png" alt="Ax = b, " class="math-display" >
(1)
-

+

where A is a square, real or complex, sparse matrix. The name of the package comes -from its original implementation, containing multilevel additive and hybrid Schwarz +class="cmr-12">is a square, real or complex, sparse symmetric positive definite (s.p.d) preconditioners, as well as one-level additive Schwarz preconditioners. The current +class="cmr-12">matrix. +

The preconditioners implemented in AMG4PSBLAS are obtained by combining 3 version extends the original plan by including multilevel cycles and smoothers widely +class="cmr-12">different types of AMG cycles with smoothers and coarsest-level solvers. The V-, W-, used in multigrid methods. -

The multilevel preconditioners implemented in MLD2P4 are obtained by -combining AMG cycles with smoothers and coarsest-level solvers. The V-, W-, and -K-cyclesand a version of a Krylov-type cycle (K-cycle) [3, 2022] are available, which allow to define almost all the preconditioners in +class="cmr-12">are available, which can be the package, including the multilevel hybrid Schwarz ones; a specific cycle is +class="cmr-12">combined with weighted versions of Jacobi, hybrid forward/backward Gauss-Seidel, implemented to obtain multilevel additive Schwarz preconditioners. The Jacobi, +class="cmr-12">block-Jacobi, and additive Schwarz smoothers. An algebraic approach is used to hybrid forward/backward Gauss-Seidel, block-Jacobi, and additive Schwarz +class="cmr-12">generate a hierarchy of coarse-level matrices and operators, without explicitly using methods are available as smoothers. An algebraic approach is used to generate a +class="cmr-12">any information on the geometry of the original problem, e.g., the discretization of a hierarchy of coarse-level matrices and operators, without explicitly using any +class="cmr-12">PDE. To this end, two different coarsening strategies, based on aggregation, are information on the geometry of the original problem, e.g., the discretization of a -PDE. To this end, the smoothed aggregation techniqueavailable: +

+

Either exact or approximate solvers can be used on the coarsest-level system. +Specifically, different sparse LU factorizations from external packages, native block-Jacobi solvers are available. All smoothers can be also exploited as one-level +class="cmr-12">incomplete LU factorizations, weighted Jacobi, hybrid Gauss-Seidel, and block-Jacobi +solvers are available. All the smoothers can be also exploited as one-level preconditioners. -

MLD2P4 is written in Fortran

AMG4PSBLAS is written in Fortran 2003, following an object-oriented design through the exploitation of features such as abstract data type creation, type extension, functional overloading, and dynamic memory management. The +class="cmr-12">extension, functional overloading, and dynamic memory management. The parallel parallel implementation is based on a Single Program Multiple Data (SPMD) +class="cmr-12">implementation is based on a Single Program Multiple Data (SPMD) paradigm. paradigm. Single and double precision implementations of MLD2P4 are available +class="cmr-12">Single and double precision implementations of AMG4PSBLAS are available for both the real and the complex case, which can be used through a single interface. -

MLD2P4 has been designed to implement scalable and easy-to-use multilevel +

AMG4PSBLAS has been designed to implement scalable and easy-to-use multilevel preconditioners in the context of the PSBLAS (Parallel Sparse BLAS) computational framework [1517, 1416]. PSBLAS provides basic linear algebra operators and data management facilities for distributed sparse matrices, as well as parallel Krylov solvers which can be used with the MLD2P4 preconditioners. The choice of PSBLAS has been +class="cmr-12">which can be used with the AMG4PSBLAS preconditioners. The choice of PSBLAS +has been mainly motivated by the need of having a portable and efficient +software infrastructure implementing “de facto” standard parallel sparse linear mainly motivated by the need of having a portable and efficient software infrastructure +class="cmr-12">algebra kernels, to pursue goals such as performance, portability, modularity implementing “de facto” standard parallel sparse linear algebra kernels, to pursue goals +class="cmr-12">ed extensibility in the development of the preconditioner package. On the such as performance, portability, modularity ed extensibility in the development of the +class="cmr-12">other hand, the implementation of AMG4PSBLAS, which was driven by the preconditioner package. On the other hand, the implementation of MLD2P4 has led to +class="cmr-12">need to face the exascale challenge, has led to some important revisions and some revisions and extentions of the original PSBLAS kernels. The inter-process +class="cmr-12">extentions of the PSBLAS infrastructure. The inter-process comunication comunication required by MLD2P4 is encapsulated in the PSBLAS routines; therefore, +class="cmr-12">required by AMG4PSBLAS is encapsulated in the PSBLAS routines; therefore, MLD2P4 can be run on any parallel machine where PSBLAS implementations are +class="cmr-12">AMG4PSBLAS can be run on any parallel machine where PSBLAS implementations available. -

MLD2P4 has a layered and modular software architecture where three main layers +class="cmr-12">are available. +

AMG4PSBLAS has a layered and modular software architecture where three main can be identified. The lower layer consists of the PSBLAS kernels, the middle one +class="cmr-12">layers can be identified. The lower layer consists of the PSBLAS kernels, the middle implements the construction and application phases of the preconditioners, and the +class="cmr-12">one implements the construction and application phases of the preconditioners, and the upper one provides a uniform interface to all the preconditioners. This architecture allows for different levels of use of the package: few black-box layer allow all users to easily build and apply any preconditioner available in MLD2P4; facilities are also available allowing expert users to extend the set of +class="cmr-12">AMG4PSBLAS; facilities are also available allowing expert users to extend the set of smoothers and solvers for building new versions of the preconditioners (see  7). -

We note that the user interface of MLD2P4 2.1 has been extended with respect to -the previous versions in order to separate the construction of the multilevel -hierarchy from the construction of the smoothers and solvers, and to allow for -more flexibility at each level. The software architecture described in [8] has -significantly evolved too, in order to fully exploit the Fortran 2003 features -implemented in PSBLAS 3. However, compatibility with previous versions has been -preserved. -

This guide is organized as follows. General information on the distribution of the source code is reported in Sectionof the package are given in Section 3. A short description of the preconditioners -implemented in MLD2P4 is provided in Section 4, to help the users in choosing among - - - +class="cmr-12">. The basics for building and applying the them. The basics for building and applying the preconditioners with the Krylov solvers +class="cmr-12">preconditioners with the Krylov solvers implemented in PSBLAS are reported implemented in PSBLAS are reported inin Section 5, where the Fortran codes of a few -sample programs are also shown. A reference guide for the user interface routines is +class="cmr-12">, where the Fortran codes of a few sample programs are also shown. + + + provided in SectionA reference guide for the user interface routines is provided in Section 6. Information on the extension of the package through the +class="cmr-12">. +Information on the extension of the package through the addition of new addition of new smoothers and solvers is reported in Sectionsmoothers and solvers is reported in Section 7. The error handling +class="cmr-12">. The error handling mechanism mechanism used by the package is briefly described in Sectionused by the package is briefly described in Section 8. The copyright +class="cmr-12">. The copyright terms terms concerning the distribution and modification of MLD2P4 are reported in +class="cmr-12">concerning the distribution and modification of AMG4PSBLAS are reported in Appendix 2 Code Distribution

MLD2P4 is available from the web site +class="cmr-12">AMG4PSBLAS is available from the web site

https://github.com/sfilippone/mld2p4-2

+class="cmtt-12">https://github.com/psctoolkit/amg4psblas

where contact points for further information can be also found.

into account when treating derived works. class="cmr-12">The library defines a version string with the constant

mld_version_string_ +src=

whose current value is 2.1.01.0.

diff --git a/docs/html/userhtmlse3.html b/docs/html/userhtmlse3.html index 963e7225..cab86ca8 100644 --- a/docs/html/userhtmlse3.html +++ b/docs/html/userhtmlse3.html @@ -1,7 +1,7 @@ -Configuring and Building MLD2P4 +Configuring and Building AMG4PSBLAS @@ -30,9 +30,9 @@ class="cmr-12">]

3 Configuring and Building MLD2P4

+class="cmr-12">Configuring and Building AMG4PSBLAS

In order to build MLD2P4 it is necessary to set up a Makefile with appropriate +class="cmr-12">In order to build AMG4PSBLAS it is necessary to set up a Makefile with appropriate system-dependent variables; this is done by means of the configure distribution also includes the autoconf and automake sources empl script, but usually this is not needed to build the software.

MLD2P4 is implemented almost entirely in Fortran 2003, with some interfaces to +class="cmr-12">AMG4PSBLAS is implemented almost entirely in Fortran 2003, with some external libraries in C; the Fortran compiler must support the Fortran 2003 standard +class="cmr-12">interfaces to external libraries in C; the Fortran compiler must support the plus the extension Fortran 2003 standard plus the extension MOLD= feature, which enhances the usability of ALLOCATE. Many +class="cmr-12">feature, which enhances the usability compilers do this; in particular, this is supported by the GNU Fortran compiler, for +class="cmr-12">of ALLOCATE. Many compilers do this; in particular, this is supported by the GNU which we recommend to use at least version 4.8. The software defines data +class="cmr-12">Fortran compiler, for which we recommend to use at least version 4.8. The software types and interfaces for real and complex data, in both single and double +class="cmr-12">defines data types and interfaces for real and complex data, in both single and double precision.

Building MLD2P4 requires some base libraries (see SectionBuilding AMG4PSBLAS requires some base libraries (see Section 3.1); interfaces to optional third-party libraries, which extend the functionalities of MLD2P4 (see +class="cmr-12">optional third-party libraries, which extend the functionalities of AMG4PSBLAS Section(see Section 3.2), are also available. Many Linux distributions (e.g., Ubuntu, Fedora, +class="cmr-12">), are also available. Many Linux distributions (e.g., Ubuntu, CentOS) provide precompiled packages for the prerequisite and optional software. In +class="cmr-12">Fedora, CentOS) provide precompiled packages for the prerequisite and optional many cases these packages are split between a runtime part and a “developer” part; in +class="cmr-12">software. In many cases these packages are split between a runtime part and a order to build MLD2P4 you need both. A description of the base and optional software +class="cmr-12">“developer” part; in order to build AMG4PSBLAS you need both. A description of used by MLD2P4 is given in the next sections. +class="cmr-12">the base and optional software used by AMG4PSBLAS is given in the next +sections.

Example and test programs

[[next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

+class="cmbx-12">up]

diff --git a/docs/html/userhtmlse4.html b/docs/html/userhtmlse4.html index 05f04566..65eb9195 100644 --- a/docs/html/userhtmlse4.html +++ b/docs/html/userhtmlse4.html @@ -11,188 +11,199 @@

[[next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

+class="cmbx-12">up]

4 4 Multigrid Background

+class="cmbx-12">Multigrid Background

Multigrid preconditioners, coupled with Krylov iterative solvers, are widely used in the +class="cmbx-12">Multigrid preconditioners, coupled with Krylov iterative solvers, are widely parallel solution of large and sparse linear systems, because of their optimality in the +class="cmbx-12">used in the parallel solution of large and sparse linear systems, because of solution of linear systems arising from the discretization of scalar elliptic Partial +class="cmbx-12">their optimality in the solution of linear systems arising from the Differential Equations (PDEs) on regular grids. Optimality, also known as algorithmic +class="cmbx-12">discretization of scalar elliptic Partial Differential Equations (PDEs) on scalability, is the property of having a computational cost per iteration that depends +class="cmbx-12">regular grids. Optimality, also known as algorithmic scalability, is the linearly on the problem size, and a convergence rate that is independent of the problem +class="cmbx-12">property of having a computational cost per iteration that depends linearly size. +class="cmbx-12">on the problem size, and a convergence rate that is independent of the +problem size.

Multigrid preconditioners are based on a recursive application of a two-grid process +class="cmbx-12">Multigrid preconditioners are based on a recursive application of a +two-grid process consisting of smoother iterations and a coarse-space (or +coarse-level) correction. The smoothers may be either basic iterative consisting of smoother iterations and a coarse-space (or coarse-level) correction. The +class="cmbx-12">methods, such as the Jacobi and Gauss-Seidel ones, or more complex smoothers may be either basic iterative methods, such as the Jacobi and Gauss-Seidel +class="cmbx-12">subspace-correction methods, such as the Schwarz ones. The coarse-space ones, or more complex subspace-correction methods, such as the Schwarz ones. The +class="cmbx-12">correction consists of solving, in an appropriately chosen coarse space, the coarse-space correction consists of solving, in an appropriately chosen coarse space, the +class="cmbx-12">residual equation associated with the approximate solution computed by residual equation associated with the approximate solution computed by the +class="cmbx-12">the smoother, and of using the solution of this equation to correct the smoother, and of using the solution of this equation to correct the previous +class="cmbx-12">previous approximation. The transfer of information between the original approximation. The transfer of information between the original (fine) space and +class="cmbx-12">(fine) space and the coarse one is performed by using suitable restriction the coarse one is performed by using suitable restriction and prolongation +class="cmbx-12">and prolongation operators. The construction of the coarse space and the operators. The construction of the coarse space and the corresponding transfer +class="cmbx-12">corresponding transfer operators is carried out by applying a so-called operators is carried out by applying a so-called coarsening algorithm to the +class="cmbx-12">coarsening algorithm to the system matrix. Two main approaches system matrix. Two main approaches can be used to perform coarsening: +class="cmbx-12">can be used to perform coarsening: the geometric approach, which the geometric approach, which exploits the knowledge of some physical grid +class="cmbx-12">exploits the knowledge of some physical grid associated with the associated with the matrix and requires the user to define transfer operators +class="cmbx-12">matrix and requires the user to define transfer operators from the from the fine to the coarse level and vice versa, and the algebraic approach, +class="cmbx-12">fine to the coarse level and vice versa, and the algebraic approach, which builds the coarse-space correction and the associate transfer operators +class="cmbx-12">which builds the coarse-space correction and the associate transfer using only matrix information. The first approach may be difficult when the +class="cmbx-12">operators using only matrix information. The first approach may be system comes from discretizations on complex geometries; furthermore, ad hoc +class="cmbx-12">difficult when the system comes from discretizations on complex one-level smoothers may be required to get an efficient interplay between +class="cmbx-12">geometries; furthermore, ad hoc one-level smoothers may be required to fine and coarse levels, e.g., when matrices with highly varying coefficients are +class="cmbx-12">get an efficient interplay between fine and coarse levels, e.g., when considered. The second approach performs a fully automatic coarsening and +class="cmbx-12">matrices with highly varying coefficients are considered. The second enforces the interplay between fine and coarse level by suitably choosing the +class="cmbx-12">approach performs a fully automatic coarsening and enforces the coarse space and the coarse-to-fine interpolation (see, e.g., [interplay between fine and coarse level by suitably choosing the coarse +space and the coarse-to-fine interpolation (see, e.g., [3, 3, 24, 26, 22] for +class="cmbx-12">24] for + + + details.) +class="cmbx-12">details.)

MLD2P4 uses a pure algebraic approach, based on the smoothed aggregation +class="cmbx-12">MLD2P4 uses a pure algebraic approach, based on the smoothed algorithm [aggregation algorithm [2, 2, 26], for building the sequence of coarse matrices and transfer +class="cmbx-12">28], for building the sequence of coarse matrices operators, starting from the original one. A decoupled version of this algorithm - - - +class="cmbx-12">and transfer operators, starting from the original one. A decoupled version is implemented, where the smoothed aggregation is applied locally to each +class="cmbx-12">of this algorithm is implemented, where the smoothed aggregation is submatrix [applied locally to each submatrix [25]. A brief description of the AMG preconditioners implemented in +class="cmbx-12">27]. A brief description of the AMG MLD2P4 is given in Sections preconditioners implemented in MLD2P4 is given in Sections 4.1-4.1-4.3. For further details the reader is referred to -[4.3. For +further details the reader is referred to [4, 4, 5, 5, 7, 7, 8]. +class="cmbx-12">8].

We note that optimal multigrid preconditioners do not necessarily correspond to +class="cmbx-12">We note that optimal multigrid preconditioners do not necessarily +correspond to minimum execution times in a parallel setting. Indeed, to minimum execution times in a parallel setting. Indeed, to obtain effective parallel +class="cmbx-12">obtain effective parallel multigrid preconditioners, a tradeoff between the multigrid preconditioners, a tradeoff between the optimality and the cost of +class="cmbx-12">optimality and the cost of building and applying the smoothers and building and applying the smoothers and the coarse-space corrections must be +class="cmbx-12">the coarse-space corrections must be achieved. Effective parallel achieved. Effective parallel preconditioners require algorithmic scalability to +class="cmbx-12">preconditioners require algorithmic scalability to be coupled with be coupled with implementation scalability, i.e., a computational cost per +class="cmbx-12">implementation scalability, i.e., a computational cost per iteration iteration which remains (almost) constant as the number of parallel processors +class="cmbx-12">which remains (almost) constant as the number of parallel processors increases. +class="cmbx-12">increases.

 4.1  4.1 AMG preconditioners +class="cmbx-12">AMG preconditioners
 4.2  4.2 Smoothed Aggregation +class="cmbx-12">Smoothed Aggregation
 4.3  4.3 Smoothers and coarsest-level solvers +class="cmbx-12">Smoothers and coarsest-level solvers
@@ -200,22 +211,22 @@ class="cmr-12">Smoothers and coarsest-level solvers

[[next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

+class="cmbx-12">up]

diff --git a/docs/html/userhtmlse5.html b/docs/html/userhtmlse5.html index c2bedd5d..4f6e83fd 100644 --- a/docs/html/userhtmlse5.html +++ b/docs/html/userhtmlse5.html @@ -11,215 +11,227 @@

[[next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

+class="cmbx-12">up]

5 5 Getting Started

+class="cmbx-12">Getting Started

We describe the basics for building and applying MLD2P4 one-level and multilevel +class="cmbx-12">We describe the basics for building and applying AMG4PSBLAS one-level (i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS [13]. The +class="cmbx-12">and multilevel (i.e., AMG) preconditioners with the Krylov solvers included following steps are required: +class="cmbx-12">in PSBLAS [15]. The following steps are required:

  1. Declare the preconditioner data structure. It is a derived data type, - mld_xDeclare the preconditioner data structure. It is a derived data + type, amg_xprec_ type, where x may be , where x may be s, , d, , c or or z, according to the basic +class="cmbx-12">, according to the data type of the sparse matrix (basic data type of the sparse matrix (s = real single precision; = real single precision; d = real double +class="cmbx-12">= precision; real double precision; c = complex single precision; = complex single precision; z = complex double precision). This +class="cmbx-12">= complex data structure is accessed by the user only through the MLD2P4 routines, +class="cmbx-12">double precision). This data structure is accessed by the user only following an object-oriented approach. +class="cmbx-12">through the AMG4PSBLAS routines, following an object-oriented + approach.
  2. Allocate and initialize the preconditioner data structure, according to a +class="cmbxti-10x-x-120">Allocate and initialize the preconditioner data structure, + according to a preconditioner type chosen by the user. This is preconditioner type chosen by the user. This is performed by the routine - performed by the routine init, which also sets defaults for each preconditioner type selected by +class="cmbx-12">, which also sets defaults for each the user. The preconditioner types and the defaults associated with them +class="cmbx-12">preconditioner type selected by the user. The preconditioner types are given in Table and the defaults associated with them are given in Table 1, where the strings used by 1, where + the strings used by init to identify the +class="cmbx-12">to identify the preconditioner types are preconditioner types are also given. Note that these strings are valid also if +class="cmbx-12">also given. Note that these strings are valid also if uppercase letters uppercase letters are substituted by corresponding lowercase ones. +class="cmbx-12">are substituted by corresponding lowercase ones.
  3. Modify the selected preconditioner type, by properly setting preconditioner +class="cmbxti-10x-x-120">Modify the selected preconditioner type, by properly setting parameters. This is performed by the routine preconditioner parameters. This is performed by the routine set. This routine must be +class="cmbx-12">. called only if the user wants to modify the default values of the parameters +class="cmbx-12">This routine must be called only if the user wants to modify associated with the selected preconditioner type, to obtain a variant of that +class="cmbx-12">the default values of the parameters associated with the selected preconditioner. Examples of use of preconditioner type, to obtain a variant of that preconditioner. + Examples of use of set are given in Section are given in Section 5.1; a complete +class="cmbx-12">5.1; a complete list list of all the preconditioner parameters and their allowed and default values +class="cmbx-12">of all the preconditioner parameters and their allowed and default is provided in Section values is provided in Section 6, Tables 6, Tables 2-2-8. +class="cmbx-12">8.
  4. Build the preconditioner for a given matrix. If the selected preconditioner is +class="cmbxti-10x-x-120">Build the preconditioner for a given matrix. If the selected + preconditioner is multilevel, then two steps must be performed, as multilevel, then two steps must be performed, as specified next. +class="cmbx-12">specified next. + + +
    1. Build the aggregation hierarchy for a given matrix. This is performed +class="cmbxti-10x-x-120">Build the aggregation hierarchy for a given matrix. This is by the routine performed by the routine hierarchy_build. - - - +class="cmbx-12">.
    2. Build the preconditioner for a given matrix. This is performed by the +class="cmbxti-10x-x-120">Build the preconditioner for a given matrix. This is routine performed by the routine smoothers_build.
    -

    If the selected preconditioner is one-level, it is built in a single step, performed by +class="cmbx-12">.

+

If the selected preconditioner is one-level, it is built in a single step, the routine performed by the routine bld. +class="cmbx-12">.

  • Apply the preconditioner at each iteration of a Krylov solver. This is performed by +class="cmbxti-10x-x-120">Apply the preconditioner at each iteration of a Krylov solver. This is the method performed by the method apply. When using the PSBLAS Krylov solvers, this step is +class="cmbx-12">. When using the PSBLAS Krylov completely transparent to the user, since solvers, this step is completely transparent to the user, since apply is called by the PSBLAS routine +class="cmbx-12">is + called by the PSBLAS routine implementing the Krylov solver implementing the Krylov solver ((psb_krylov). +class="cmbx-12">).
  • Free the preconditioner data structure. This is performed by the routine free. +class="cmbxti-10x-x-120">Free the preconditioner data structure. This is performed by the This step is complementary to step 1 and should be performed when the +class="cmbx-12">routine free. This step is complementary to step 1 and should be preconditioner is no more used.
    • -

    All the previous routines are available as methods of the preconditioner object. A +class="cmbx-12">performed when the preconditioner is no more used. +

    All the previous routines are available as methods of the preconditioner detailed description of them is given in Section object. A detailed description of them is given in Section 6. Examples showing the basic use of +class="cmbx-12">6. Examples MLD2P4 are reported in Section showing the basic use of AMG4PSBLAS are reported in Section 5.1. +class="cmbx-12">5.1.

    -

    @@ -227,7 +239,7 @@ class="cmr-12">.
    -

    +

    type @@ -296,41 +308,41 @@ to 1. class="hline"> +class="td11">

    Block-Jacobi with ILU(0) on the local blocks.

    smoother

    +class="cmtt-12">class(amg_x_base_smoother_type) +class="cmbx-12">preconditioner. +class="cmtt-12">class(amg_x_base_solver_type)

    string

    der

    No preconditioner

    ’NONE’

    Considered to use the PSBLAS Krylov solvers +class="td11">

    Considered to use the PSBLAS Krylov solvers with no preconditioner.

    Diagonal

    ’DIAG’ or ’JACOBI’

    Diagonal preconditioner. For any zero diagonal +class="td11">

    Diagonal preconditioner. For any zero diagonal entry of the matrix to be preconditioned, the corresponding entry of the preconditioner is set to 1.

    Gauss-Seidel

    ’GS’

    Hybrid Gauss-Seidel (forward), that is, global +class="td11">

    Hybrid Gauss-Seidel (forward), that is, global block Jacobi with Gauss-Seidel as local solver.

    Symmetrized Gauss-Seidel

    ’FBGS’

    Symmetrized +class="td11">

    Symmetrized hybrid Gauss-Seidel,that is, forward Gauss-Seidel followed by backward Gauss-Seidel.

    Block Jacobi

    ’BJAC’

    Block-Jacobi with ILU(0) on the local blocks.

    Additive Schwarz

    ’AS’

    Additive Schwarz (AS), with overlap 1 and +class="td11">

    Additive Schwarz (AS), with overlap 1 and ILU(0) on the local blocks.

    Multilevel

    ’ML’

    V-cycle with one hybrid forward Gauss-Seidel +class="td11">

    V-cycle with one hybrid forward Gauss-Seidel (GS) sweep as pre-smoother and one hybrid backward GS sweep as post-smoother, basic smoothed aggregation as coarsening algorithm, @@ -352,68 +364,73 @@ class="content">Preconditioner types, corresponding strings and default choices.

    -

    Note that the module mld_prec_mod, containing the definition of the preconditioner +

    Note that the module amg_prec_mod, containing the definition of +the preconditioner data type and the interfaces to the routines of data type and the interfaces to the routines of MLD2P4, must be used in any program +class="cmbx-12">AMG4PSBLAS, must be used in any program calling such routines. The calling such routines. The modules modules psb_base_mod, for the sparse matrix and +class="cmbx-12">, for the sparse matrix and communication descriptor communication descriptor data types, and data types, and psb_krylov_mod, for interfacing with the +class="cmbx-12">, for interfacing with the Krylov solvers, Krylov solvers, must be also used (see Section must be also used (see Section 5.1).
    5.1    ).
    -

    Remark 1. Coarsest-level solvers based on the LU factorization, such as those +

    Remark 1. Coarsest-level solvers based on the LU factorization, such as +those implemented in UMFPACK, MUMPS, SuperLU, and SuperLU_Dist, implemented in UMFPACK, MUMPS, SuperLU, and SuperLU_Dist, usually lead to +class="cmbx-12">usually lead to smaller numbers of preconditioned Krylov iterations smaller numbers of preconditioned Krylov iterations than inexact solvers, when the +class="cmbx-12">than inexact solvers, when the linear system comes from a standard linear system comes from a standard discretization of basic scalar elliptic PDE +class="cmbx-12">discretization of basic scalar elliptic PDE problems. However, this does not problems. However, this does not necessarily correspond to the smallest execution time +class="cmbx-12">necessarily correspond to the smallest execution time on parallel on parallel computers. +class="cmbx-12">computers. +

    DA MODIFICARE PER INSERIRE TIPO DI AGGREGAZIONE

     5.1  5.1 Examples +class="cmbx-12">Examples

    [[next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    +class="cmbx-12">up]

    diff --git a/docs/html/userhtmlse6.html b/docs/html/userhtmlse6.html index b9c69afd..6c84e382 100644 --- a/docs/html/userhtmlse6.html +++ b/docs/html/userhtmlse6.html @@ -11,234 +11,239 @@

    [[next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    6 6 User Interface

    +class="cmbx-12">User Interface

    The basic user interface of MLD2P4 consists of eight methods. The six methods The basic user interface of AMG4PBLAS consists of eight methods. The six +methods init, -, set, , build, , hierarchy_build, , smoothers_build and apply encapsulate all the +class="cmbx-12">and apply +encapsulate all the functionalities for the setup and the application of any functionalities for the setup and the application of any multilevel and one-level +class="cmbx-12">multilevel and one-level preconditioner implemented in the package. The preconditioner implemented in the package. The method method free deallocates the +class="cmbx-12">deallocates the preconditioner data structure, while descr preconditioner data structure, while descr prints a description of the preconditioner +class="cmbx-12">prints a description of the preconditioner setup by the user. For setup by the user. For backward compatibility, methods are also accessible as +class="cmbx-12">backward compatibility, methods are also accessible as stand-alone stand-alone subroutines. +class="cmbx-12">subroutines.

    For each method, the same user interface is overloaded with respect to the real/ +class="cmbx-12">For each method, the same user interface is overloaded with respect to complex case and the single/double precision; arguments with appropriate data types +class="cmbx-12">the real/ complex case and the single/double precision; arguments with must be passed to the method, i.e., +class="cmbx-12">appropriate data types must be passed to the method, i.e.,

    • the sparse matrix data structure, containing the matrix to be preconditioned, +class="cmbx-12">the sparse matrix data structure, containing the matrix to be must be of type preconditioned, must be of type psb_xxspmat_type with x = with x = s for real single precision, x +class="cmbx-12">for = real single precision, x = d for real double precision, x = for real double precision, x = c for complex single precision, x = z for +class="cmbx-12">for complex double precision; +class="cmbx-12">complex single precision, x = z for complex double precision;
    • the preconditioner data structure must be of type mld_xthe preconditioner data structure must be of type amg_xprec_type, with x +class="cmbx-12">, = with x = s, , d, , c, , z, according to the sparse matrix data structure; +class="cmbx-12">, according to the sparse matrix data structure;
    • the arrays containing the vectors v and w involved in the preconditioner +class="cmbx-12">the arrays containing the vectors v and w involved in application w = the preconditioner application w = B-1v must be of type v must be of type + psb_xxvect_type with x = with x = s, , d, , c, - , z, in a manner completely analogous to the sparse matrix type; +class="cmbx-12">, in a manner completely + analogous to the sparse matrix type;
    • real parameters defining the preconditioner must be declared according to +class="cmbx-12">real parameters defining the preconditioner must be declared the precision of the sparse matrix and preconditioner data structures (see +class="cmbx-12">according to the precision of the sparse matrix and preconditioner Section data structures (see Section 6.2).
    +class="cmbx-12">6.2).

    A description of each method is given in the remainder of this section. +class="cmbx-12">A description of each method is given in the remainder of this section.

     6.1  6.1 Method init +class="cmbx-12">Method init
     6.2  6.2 Method set +class="cmbx-12">Method set
     6.3  6.3 Method hierarchy_build +class="cmbx-12">Method hierarchy_build
     6.4  6.4 Method smoothers_build +class="cmbx-12">Method smoothers_build
     6.5  6.5 Method build +class="cmbx-12">Method build
     6.6  6.6 Method apply +class="cmbx-12">Method apply
     6.7  6.7 Method free +class="cmbx-12">Method free
     6.8  6.8 Method descr +class="cmbx-12">Method descr
     6.9  6.9 Auxiliary Methods +class="cmbx-12">Auxiliary Methods
      6.9.1   6.9.1 Method: dump +class="cmbx-12">Method: dump
      6.9.2   6.9.2 Method: clone +class="cmbx-12">Method: clone
      6.9.3   6.9.3 Method: sizeof +class="cmbx-12">Method: sizeof
      6.9.4   6.9.4 Method: allocate_wrk +class="cmbx-12">Method: allocate_wrk
      6.9.5   6.9.5 Method: free_wrk +class="cmbx-12">Method: free_wrk
    @@ -252,22 +257,22 @@ class="cmr-12">_wrk

    [[next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    +class="cmbx-12">up]

    diff --git a/docs/html/userhtmlse7.html b/docs/html/userhtmlse7.html index bb62c447..0a78097d 100644 --- a/docs/html/userhtmlse7.html +++ b/docs/html/userhtmlse7.html @@ -1,7 +1,7 @@ -Adding new smoother and solver objects to MLD2P4 +Adding new smoother and solver objects to AMG4PSBLAS @@ -11,65 +11,71 @@

    [[next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    7 7 Adding new smoother and solver objects to MLD2P4

    +class="cmbx-12">Adding new smoother and solver objects to AMG4PSBLAS

    Developers can add completely new smoother and/or solver classes derived from the +class="cmbx-12">Developers can add completely new smoother and/or solver classes derived base objects in the library (see Remark 2 in Section from the base objects in the library (see Remark 2 in Section 6.2), without recompiling the +class="cmbx-12">6.2), without library itself. +class="cmbx-12">recompiling the library itself.

    To do so, it is necessary first to select the base type to be extended. In our +class="cmbx-12">To do so, it is necessary first to select the base type to be extended. In experience, it is quite likely that the new application needs only the definition of a +class="cmbx-12">our experience, it is quite likely that the new application needs only the “solver” object, which is almost always acting only on the local part of the distributed +class="cmbx-12">definition of a “solver” object, which is almost always acting only on the matrix. The parallel actions required to connect the various solver objects are most +class="cmbx-12">local part of the distributed matrix. The parallel actions required to often already provided by the block-Jacobi or the additive Schwarz smoothers. To +class="cmbx-12">connect the various solver objects are most often already provided by the define a new solver, the developer will then have to define its components and +class="cmbx-12">block-Jacobi or the additive Schwarz smoothers. To define a new solver, the methods, perhaps taking one of the predefined solvers as a starting point, if +class="cmbx-12">developer will then have to define its components and methods, possible. +class="cmbx-12">perhaps taking one of the predefined solvers as a starting point, if +possible.

    Once the new smoother/solver class has been developed, to use it in the context of +class="cmbx-12">Once the new smoother/solver class has been developed, to use +it in the context of the multilevel preconditioners it is necessary the multilevel preconditioners it is necessary to: +class="cmbx-12">to:

    • declare in the application program a variable of the new type; +class="cmbx-12">declare in the application program a variable of the new type;
    • pass that variable as the argument to the pass that variable as the argument to the set routine as in the following: +class="cmbx-12">routine as in the + following:

      @@ -83,55 +89,60 @@ class="cmtt-12"> p%set(solver,info [,ilev,ilmax,pos])

    • link the code implementing the various methods into the application +class="cmbx-12">link the code implementing the various methods into the application executable.
    +class="cmbx-12">executable.

    The new solver object is then dynamically included in the preconditioner structure, and +class="cmbx-12">The new solver object is then dynamically included in the preconditioner acts as a mold to which the preconditioner will conform, even though the MLD2P4 +class="cmbx-12">structure, and acts as a mold to which the preconditioner will conform, library has not been modified to account for this new development. -

    It is possible to define new values for the keyword WHAT in the set routine; if the -library code does not recognize a keyword, it passes it down the composition hierarchy +class="cmbx-12">even though the AMG4PSBLAS library has not been modified to account (levels containing smoothers containing in turn solvers), so that it can be eventually +class="cmbx-12">for this new development. +

    It is possible to define new values for the keyword WHAT in the set caught by the new solver. By the same token, any keyword/value pair that does not +class="cmbx-12">routine; if the library code does not recognize a keyword, it passes it down pertain to a given smoother should be passed down to the contained solver, and +class="cmbx-12">the composition hierarchy (levels containing smoothers containing in turn any keyword/value pair that does not pertain to a given solver is by default +class="cmbx-12">solvers), so that it can be eventually caught by the new solver. By the ignored. +class="cmbx-12">same token, any keyword/value pair that does not pertain to a given +smoother should be passed down to the contained solver, and any +keyword/value pair that does not pertain to a given solver is by default +ignored.

    An example is provided in the source code distribution under the folder +class="cmbx-12">An example is provided in the source code distribution under the folder tests/newslv. In this example we are implementing a new incomplete factorization +class="cmbx-12">. In this example we are implementing a new incomplete variant (which is simply the ILU(0) factorization under a new name). Because of the +class="cmbx-12">factorization variant (which is simply the ILU(0) factorization under a new specifics of this case, it is possible to reuse the basic structure of the ILU solver, with +class="cmbx-12">name). Because of the specifics of this case, it is possible to reuse the basic its L/D/U components and the methods needed to apply the solver; only a few +class="cmbx-12">structure of the ILU solver, with its L/D/U components and the methods, such as the description and most importantly the build, need to be +class="cmbx-12">methods needed to apply the solver; only a few methods, such as the ovverridden (rewritten). +class="cmbx-12">description and most importantly the build, need to be ovverridden +(rewritten).

    The interfaces for the calls shown above are defined using +class="cmbx-12">The interfaces for the calls shown above are defined using

    @@ -144,46 +155,49 @@ id="TBL-21-2">

    class(mld_x_base_smoother_type)

    The user-defined new smoother to be employed in the +class="cmbx-12">The user-defined new smoother to be employed in the preconditioner.

    solver

    class(mld_x_base_solver_type)

    The user-defined new solver to be employed in the preconditioner.

    +class="cmbx-12">The user-defined new solver to be employed in the +preconditioner. +

    The other arguments are defined in the way described in Sec. The other arguments are defined in the way described in Sec. 6.2. As an example, in the -tests/newslv code we define a new object of type mld_d_tlu_solver_type, and we +class="cmbx-12">6.2. As an pass it as follows: +class="cmbx-12">example, in the tests/newslv code we define a new object of type +amg_d_tlu_solver_type, and we pass it as follows:

     
      ! sparse matrix and preconditioner  
      type(psb_dspmat_type) :: a - 
      type(mld_dprec_type)  :: prec - 
      type(mld_d_tlu_solver_type) :: tlusv + 
      type(amg_dprec_type)  :: prec + 
      type(amg_d_tlu_solver_type) :: tlusv  
     
    ......  
      ! @@ -208,22 +222,22 @@ class="cmr-12">pass it as follows:

    [[next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    +class="cmbx-12">up]

    diff --git a/docs/html/userhtmlse8.html b/docs/html/userhtmlse8.html index 7f8b5937..87c0ebd9 100644 --- a/docs/html/userhtmlse8.html +++ b/docs/html/userhtmlse8.html @@ -11,50 +11,52 @@

    [[next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    8 8 Error Handling

    +class="cmbx-12">Error Handling

    The error handling in MLD2P4 is based on the PSBLAS error handling. Error +class="cmbx-12">The error handling in AMG4PSBLAS is based on the PSBLAS error conditions are signaled via an integer argument handling. Error conditions are signaled via an integer argument info; whenever an error condition is +class="cmbx-12">; detected, an error trace stack is built by the library up to the top-level, user-callable +class="cmbx-12">whenever an error condition is detected, an error trace stack is built by the routine. This routine will then decide, according to the user preferences, whether +class="cmbx-12">library up to the top-level, user-callable routine. This routine will then the error should be handled by terminating the program or by returning the +class="cmbx-12">decide, according to the user preferences, whether the error should be error condition to the user code, which will then take action, and whether +class="cmbx-12">handled by terminating the program or by returning the error condition to an error message should be printed. These options may be set by using the +class="cmbx-12">the user code, which will then take action, and whether an error message PSBLAS error handling routines; for further details see the PSBLAS User’s Guide +class="cmbx-12">should be printed. These options may be set by using the PSBLAS error +handling routines; for further details see the PSBLAS User’s Guide [[13]. +class="cmbx-12">15]. @@ -68,22 +70,22 @@ class="cmr-12">.

    [[next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    +class="cmbx-12">up]

    diff --git a/docs/html/userhtmlse9.html b/docs/html/userhtmlse9.html index 5d6436a1..bd832bf7 100644 --- a/docs/html/userhtmlse9.html +++ b/docs/html/userhtmlse9.html @@ -11,41 +11,47 @@

    [[next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    A A License

    +class="cmbx-12">License

    The MLD2P4 is freely distributable under the following copyright terms: +class="cmbx-12">DA CONTROLLARE E MODIFICARE INCLUDENDO I CREDITS A +MLD2P4 +

    The AMG4PSBLAS is freely distributable under the following copyright +terms:

    - 
                               MLD2P4  version 2.1 - 
      MultiLevel Domain Decomposition Parallel Preconditioners Package + 
                               AMG4PSBLAS  version 1.0 + 
                  Algebraic MultiGrid Preconditioners Package  
                 based on PSBLAS (Parallel Sparse BLAS version 3.5)  
     
      (C) Copyright 2008, 2010, 2012, 2015, 2017  
    - 
      Salvatore Filippone    Cranfield University, Cranfield, UK - 
      Pasqua D’Ambra         IAC-CNR, Naples, IT - 
      Daniela di Serafino    University of Campania L. Vanvitelli, Caserta, IT + 
      Pasqua D’Ambra         IAC-CNR, IT + 
      Fabio Durastante       University of Pisa and IAC-CNR, IT + 
      Salvatore Filippone    University of Rome Tor-Vergata and IAC-CNR, IT  
     
      Redistribution and use in source and binary forms, with or without  
      modification, are permitted provided that the following conditions @@ -72,7 +78,7 @@ class="cmr-12">The MLD2P4 is freely distributable under the following copyright  
      POSSIBILITY OF SUCH DAMAGE.  
    -

    +

    @@ -90,22 +96,22 @@ class="cmr-12">The MLD2P4 is freely distributable under the following copyright

    [[next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    +class="cmbx-12">up]

    diff --git a/docs/html/userhtmlsu1.html b/docs/html/userhtmlsu1.html index 55b36829..aed4944e 100644 --- a/docs/html/userhtmlsu1.html +++ b/docs/html/userhtmlsu1.html @@ -36,15 +36,15 @@ class="cmbx-12">BLAS

    [1113, 1214, 1820] Many vendors provide optimized versions of BLAS; if no www.netlib.org/blas) are meant to define the standard behaviour of the BLAS interface, so they are not optimized for any +class="cmr-12">behaviour of the BLAS interface, so they are not optimized for any particular particular plaftorm, and should only be used as a last resort. Note that +class="cmr-12">platform, and should only be used as a last resort. Note that BLAS BLAS computations form a relatively small part of the MLD2P4/PSBLAS +class="cmr-12">computations form a relatively small part of the AMG4PSBLAS/PSBLAS computations; they are however critical when using preconditioners based MPI
    [1719, 2325] A version of MPI is available on most high-performance computing PSBLAS
    [1315, 1517] Parallel Sparse BLAS (PSBLAS) is available from github.com/sfilippone/psblas3; version 3.5.0 (or later) is required. +class="cmtt-12">github.com/sfilippone/psblas3 ?? Mettere tutto sotto psctoolkit; + version 3.5.0 (or later) is required. Indeed, all the prerequisites listed so far Indeed, all the prerequisites listed so far are also prerequisites of PSBLAS.
    +class="cmr-12">are also prerequisites of PSBLAS.

    Please note that the four previous libraries must have Fortran interfaces compatible with MLD2P4; usually this means that they should all be built with the same compiler as +class="cmr-12">AMG4PSBLAS; usually this means that they should all be built with the same MLD2P4. +class="cmr-12">compiler as AMG4PSBLAS. diff --git a/docs/html/userhtmlsu10.html b/docs/html/userhtmlsu10.html index 5fa35dfd..7596f920 100644 --- a/docs/html/userhtmlsu10.html +++ b/docs/html/userhtmlsu10.html @@ -11,20 +11,20 @@

    [[next] [next] [tail] [tail] [up]

    +class="cmbx-12">up]

    6.1 6.1 Method init

    +class="cmbx-12">Method init

    @@ -32,11 +32,11 @@ class="cmr-12">Method init class="cmtt-12">call p%init(icontx,ptype,info)

    This method allocates and initializes the preconditioner This method allocates and initializes the preconditioner p, according to the +class="cmbx-12">, according to the preconditioner type chosen by the user. +class="cmbx-12">preconditioner type chosen by the user.

    Arguments

    +class="cmbx-12">.

    +class="cmbx-12">. +class="cmbx-12">1. +class="td11">

    +class="cmbx-12">. +class="cmbx-12">8for +details.

    icontxt

    integer, intent(in).

    The communication context.

    The communication context.

    ptype

    character(len=*), intent(in).

    The type of preconditioner. Its values are specified in Table 

    The type of preconditioner. Its values are specified in +Table 1.

    Note that the strings are case insensitive.

    Note that the strings are case insensitive.

    info

    integer, intent(out).

    Error code. If no error, 0 is returned. See Section 

    Error code. If no error, 0 is returned. See Section 8 for details.

    -

    For compatibility with the previous versions of MLD2P4, this method can be also +

    For compatibility with the previous versions of MLD2P4, this method invoked as follows: +class="cmbx-12">can be also invoked as follows:

    -

    -

    +

    call mld_precinit(p,ptype,info)

    +class="cmtt-12"> amg_precinit(p,ptype,info) -

    [

    [next] [next] [front] [front] [up]

    -

    up]

    +

    diff --git a/docs/html/userhtmlsu11.html b/docs/html/userhtmlsu11.html index 22267e04..2f2eb041 100644 --- a/docs/html/userhtmlsu11.html +++ b/docs/html/userhtmlsu11.html @@ -10,48 +10,49 @@ -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    6.2 6.2 Method set

    +class="cmbx-12">Method set
    -

    -

    +

    call p%set(what,val,info [,ilev, ilmax, pos, idx])

    -

    This method sets the parameters defining the preconditioner

    This method sets the parameters defining the preconditioner p. More precisely, the +class="cmbx-12">. More parameter identified by precisely, the parameter identified by what is assigned the value contained in is assigned the value contained in +val. -

    . +

    Arguments @@ -62,415 +63,431 @@ cellspacing="0" cellpadding="0" id="TBL-3-1">

    what

    character(len=*). +class="cmbx-12">.

    The parameter to be set. It can be specified through its name; the +class="td11">

    The parameter to be set. It can be specified through its string is case-insensitive. See Tables name; the string is case-insensitive. See Tables 2-2-8. +class="cmbx-12">8.

    val 

    integer or character(len=*) or real(psb_spk_) or +class="td11">

    integer or character(len=*) or real(psb_spk_) or real(psb_dpk_), , intent(in). +class="cmbx-12">.

    The value of the parameter to be set. The list of allowed values and +class="td11">

    The value of the parameter to be set. The list of allowed the corresponding data types is given in Tables values and the corresponding data types is given in +Tables 2-2-8. When the value -is of type 8. When the value is of type character(len=*), it is also treated as case insensitive. +class="cmbx-12">, it +is also treated as case insensitive.

    info

    integer, intent(out). +class="cmbx-12">.

    Error code. If no error, 0 is returned. See Section 

    Error code. If no error, 0 is returned. See Section 8 for details. +class="cmbx-12">8 for +details.

    ilev

    integer, optional, intent(in). +class="cmbx-12">.

    For the multilevel preconditioner, the level at which the +class="td11">

    For the multilevel preconditioner, the level at which the preconditioner parameter has to be set. The levels are numbered +class="cmbx-12">preconditioner parameter has to be set. The levels are in increasing order starting from the finest one, i.e., level 1 is the +class="cmbx-12">numbered in increasing order starting from the finest one, finest level. If i.e., level 1 is the finest level. If ilev is not present, the parameter identified by what +class="cmbx-12">is not present, the is set at all the appropriate levels (see Tables parameter identified by what is set at all the appropriate +levels (see Tables 2-2-8). +class="cmbx-12">8).

    ilmax

    integer, optional, intent(in). +class="cmbx-12">.

    For the multilevel preconditioner, when both

    For the multilevel preconditioner, when both ilev and and +ilmax are -present, the settings are applied at all levels ilev:ilmax. When +class="cmbx-12">are present, the settings are applied at all levels ilev:ilmax. When ilev is present but is present but ilmax is not, then the default is is not, then the +default is ilmax=ilev. +class="cmbx-12">. The levels are numbered in increasing The levels are numbered in increasing order starting from the finest +class="cmbx-12">order starting from the finest one, i.e., level 1 is the finest one, i.e., level 1 is the finest level. +class="cmbx-12">level.

    pos

    charater(len=*), optional, intent(in). +class="cmbx-12">.

    Whether the other arguments apply only to the pre-smoother +class="td11">

    Whether the other arguments apply only to the (pre-smoother (’PRE’) or to the post-smoother () or to the post-smoother (’POST’). If ). +If pos is not present, +class="cmbx-12">is not present, the other arguments are applied the other arguments are applied to both smoothers. If the +class="cmbx-12">to both smoothers. If the preconditioner is one-level or preconditioner is one-level or the parameter identified by the parameter identified by what does +class="cmbx-12">does not concern the not concern the smoothers, smoothers, pos is ignored. +class="cmbx-12">is ignored.

    idx

    integer, optional, intent(in). +class="cmbx-12">.

    An auxiliary input argument that can be passed to the underlying +class="td11">

    An auxiliary input argument that can be passed to the objects. +class="cmbx-12">underlying objects. -

    For compatibility with the previous versions of MLD2P4, this method can be also +

    For compatibility with the previous versions of MLD2P4, this method invoked as follows: +class="cmbx-12">can be also invoked as follows:

    -

    -

    +

    call mld_precset(p,what,val,info)

    -

    However, in this case the optional arguments  amg_precset(p,what,val,info) +

    However, in this case the optional arguments ilev, , ilmax, , pos and idx cannot be -used.
    -

    A variety of preconditioners can be obtained by a suitable setting of the -preconditioner parameters. These parameters can be logically divided into four groups, +class="cmbx-12">and idx i.e., parameters defining +class="cmbx-12">cannot be used.
    +

    A variety of preconditioners can be obtained by a suitable setting of the +preconditioner parameters. These parameters can be logically divided into +four groups, i.e., parameters defining

    1. the type of multilevel cycle and how many cycles must be applied; +class="cmbx-12">the type of multilevel cycle and how many cycles must be applied;
    2. the aggregation algorithm; +class="cmbx-12">the aggregation algorithm;
    3. the coarse-space correction at the coarsest level (for multilevel +class="cmbx-12">the coarse-space correction at the coarsest level (for multilevel preconditioners only); +class="cmbx-12">preconditioners only);
    4. the smoother of the multilevel preconditioners, or the one-level +class="cmbx-12">the smoother of the multilevel preconditioners, or the one-level preconditioner. +class="cmbx-12">preconditioner.
    -

    A list of the parameters that can be set, along with their allowed and default values, is +

    A list of the parameters that can be set, along with their allowed and default given in Tables values, is given in Tables 2-2-8. For a description of the meaning of the parameters, please refer +class="cmbx-12">8. For a description of the meaning of the also to Section parameters, please refer also to Section 4.
    4.
    -

    Remark 2. A smoother is usually obtained by combining two objects: +

    Remark 2. A smoother is usually obtained by combining two objects: a a smoother (smoother (SMOOTHER_TYPE) and a local solver () and a local solver (SUB_SOLVE), as specified +class="cmbx-12">), as specified in in Tables Tables 7-7-8. For example, the block-Jacobi smoother using ILU(0) on the +class="cmbx-12">8. For example, the block-Jacobi smoother using ILU(0) on the blocks is obtained by combining the block-Jacobi smoother object with the +class="cmbx-12">blocks is obtained by combining the block-Jacobi smoother object with the ILU(0) solver object. Similarly, the hybrid Gauss-Seidel smoother (see Note in +class="cmbx-12">ILU(0) solver object. Similarly, the hybrid Gauss-Seidel smoother (see Note Table in Table 7) is obtained by combining the block-Jacobi smoother object with a +class="cmbx-12">7) is obtained by combining the block-Jacobi smoother object with single sweep of the Gauss-Seidel solver object, while the point-Jacobi smoother +class="cmbx-12">a single sweep of the Gauss-Seidel solver object, while the point-Jacobi is the result of combining the block-Jacobi smoother object with a single +class="cmbx-12">smoother is the result of combining the block-Jacobi smoother object sweep of the pointwise-Jacobi solver object. However, for simplicity, shortcuts +class="cmbx-12">with a single sweep of the pointwise-Jacobi solver object. However, are provided to set point-Jacobi, hybrid (forward) Gauss-Seidel, and hybrid +class="cmbx-12">for simplicity, shortcuts are provided to set point-Jacobi, hybrid backward Gauss-Seidel, i.e., the previous smoothers can be defined by setting only -(forward) Gauss-Seidel, and hybrid backward Gauss-Seidel, i.e., the +previous smoothers can be defined by setting only SMOOTHER_TYPE to appropriate values (see Tables to +appropriate values (see Tables 7), i.e., without setting 7), i.e., without setting SUB_SOLVE too. -

    The smoother and solver objects are arranged in a hierarchical manner. When +class="cmbx-12">too. +

    The smoother and solver objects are arranged in a hierarchical manner. +When specifying a smoother object, its parameters, including the specifying a smoother object, its parameters, including the local solver, are set to +class="cmbx-12">local solver, are set to their default values, and when a solver object their default values, and when a solver object is specified, its defaults are also +class="cmbx-12">is specified, its defaults are also set, overriding in both cases any +previous settings even if explicitly specified. Therefore if the user sets + + + set, overriding in both cases any previous settings even if explicitly specified. +class="cmbx-12">a smoother, and wishes to use a solver different from the default Therefore if the user sets a smoother, and wishes to use a solver different from +class="cmbx-12">one, the call to set the solver must come after the call to set the the default one, the call to set the solver must come after the call to set the +class="cmbx-12">smoother. +

    Similar considerations apply to the point-Jacobi, Gauss-Seidel and smoother. -

    Similar considerations apply to the point-Jacobi, Gauss-Seidel and block-Jacobi +class="cmbx-12">block-Jacobi coarsest-level solvers, and shortcuts are available in this case coarsest-level solvers, and shortcuts are available in this case too (see Table too (see Table 5). -
    5).
    - - - -

    Remark 3. In general, a coarsest-level solver cannot be used with both the +

    Remark 3. In general, a coarsest-level solver cannot be used with both replicated and distributed coarsest-matrix layout; therefore, setting the solver after the +class="cmbx-12">the replicated and distributed coarsest-matrix layout; therefore, setting the layout may change the layout. Similarly, setting the layout after the solver may change +class="cmbx-12">solver after the layout may change the layout. Similarly, setting the layout the solver. -

    More precisely, UMFPACK and SuperLU require the coarsest-level matrix to be +class="cmbx-12">after the solver may change the solver. +

    More precisely, UMFPACK and SuperLU require the coarsest-level replicated, while SuperLU_Dist requires it to be distributed. In these cases, setting the +class="cmbx-12">matrix to be replicated, while SuperLU_Dist requires it to be distributed. coarsest-level solver implies that the layout is redefined according to the solver, +class="cmbx-12">In these cases, setting the coarsest-level solver implies that the layout is ovverriding any previous settings. MUMPS, point-Jacobi, hybrid Gauss-Seidel and +class="cmbx-12">redefined according to the solver, ovverriding any previous settings. block-Jacobi can be applied to replicated and distributed matrices, thus their choice +class="cmbx-12">MUMPS, point-Jacobi, hybrid Gauss-Seidel and block-Jacobi can be does not modify any previously specified layout. It is worth noting that, when the +class="cmbx-12">applied to replicated and distributed matrices, thus their choice does not matrix is replicated, the point-Jacobi, hybrid Gauss-Seidel and block-Jacobi +class="cmbx-12">modify any previously specified layout. It is worth noting that, when the solvers reduce to the corresponding local solver objects (see Remark 2). For the +class="cmbx-12">matrix is replicated, the point-Jacobi, hybrid Gauss-Seidel and block-Jacobi point-Jacobi and Gauss-Seidel solvers, these objects correspond to a single +class="cmbx-12">solvers reduce to the corresponding local solver objects (see Remark 2). point-Jacobi sweep and a single Gauss-Seidel sweep, respectively, which are very poor +class="cmbx-12">For the point-Jacobi and Gauss-Seidel solvers, these objects correspond to a solvers. -

    On the other hand, the distributed layout can be used with any solver but +class="cmbxti-10x-x-120">single point-Jacobi sweep and a single Gauss-Seidel sweep, respectively, UMFPACK and SuperLU; therefore, if any of these two solvers has already been +class="cmbx-12">which are very poor solvers. +

    On the other hand, the distributed layout can be used with any solver selected, the coarsest-level solver is changed to block-Jacobi, with the previously +class="cmbx-12">but UMFPACK and SuperLU; therefore, if any of these two solvers chosen solver applied to the local blocks. Likewise, the replicated layout can be +class="cmbx-12">has already been selected, the coarsest-level solver is changed to used with any solver but SuperLu_Dist; therefore, if SuperLu_Dist has been +class="cmbx-12">block-Jacobi, with the previously chosen solver applied to the local previously set, the coarsest-level solver is changed to the default sequential +class="cmbx-12">blocks. Likewise, the replicated layout can be used with any solver solver. -

    Remark 4. The argument but SuperLu_Dist; therefore, if SuperLu_Dist has been previously +set, the coarsest-level solver is changed to the default sequential +solver. +

    Remark 4. The argument idx can be used to allow finer control for those solvers; +class="cmbx-12">can be used to allow finer control for those for instance, by specifying the keyword solvers; for instance, by specifying the keyword MUMPS_IPAR_ENTRY and an appropriate value +class="cmbx-12">and an for appropriate value for idx, it is possible to set any entry in the MUMPS integer control array. See also +class="cmbx-12">, it is possible to set any entry in the MUMPS Sec. integer control array. See also Sec. 7. +class="cmbx-12">7.

    -

    @@ -478,7 +495,7 @@ class="cmr-12">.
    -

    +

    +class="td11">

    1

    what

    		type

    val

    deault

    cots

    ’ML_CYCLE’

    		character(len=*)

    ’VCYCLE’ -

    ’WCYCLE’ -

    ’KCYCLE’ -

    ’MULT’ -

    ’ADD’

    ’VCYCLE’

    Multilevel cycle: V-cycle, W-cycle, K-cycle, +class="td11">

    Multilevel cycle: V-cycle, W-cycle, K-cycle, hybrid Multiplicative Schwarz, and Additive Schwarz. -

    Note that hybrid Multiplicative Schwarz +

    Note that hybrid Multiplicative Schwarz is equivalent to V-cycle and is included for compatibility with previous versions of MLD2P4.

    ’OUTER_SWEEPS’

    		integer

    Any integer -

    number

    Any integer +

    number ≥ 1

    1

    Number of multilevel cycles.

    Number of multilevel cycles.

    -

    @@ -584,7 +601,7 @@ applied.
    -

    +

    +than or equal to this threshold (see Note). +

    +href="userhtmlli4.html#XGrHeJi:16">18]. Parameters defining the aggregation algorithm.

    @@ -774,7 +792,7 @@ class="content">Parameters defining the aggregation algorithm.

    +

    what

    		type

    val

    deault

    cos

    ’MIN_COARSE_SIZE’

    		integer

    Any number -

    Any number +

    > 0

    ⌊40√ -- 3 nn is the dimension of the matrix at the finest level

    Coarse size threshold. The aggregation +class="td11">

    Coarse size threshold. The aggregation stops if the global number of variables of the computed coarsest matrix is lower -than or equal to this threshold (see Note).

    ’MIN_CR_RATIO’

    		real

    Any number -

    Any number +

    > 1

    1.5

    Minimum +class="td11">

    1.5

    Minimum coarsening ratio. The aggregation stops if the ratio between the matrix dimensions at two consecutive levels is lower than or @@ -670,32 +688,32 @@ equal to this threshold (see Note).

    ’MAX_LEVS’

    		integer

    Any integer -

    number

    Any integer +

    number > 1

    20

    Maximum number of levels. The +class="td11">

    20

    Maximum number of levels. The aggregation stops if the number of levels reaches this value (see Note).

    ’PAR_AGGR_ALG’

    		character(len=*)

    ’DEC’, ’SYMDEC’

    ’DEC’

    Parallel aggregation algorithm. -

    Currently, only the decoupled +class="td11">

    Parallel aggregation algorithm. +

    Currently, only the decoupled aggregation (DEC) is available; the SYMDEC @@ -707,36 +725,36 @@ class="cmmi-8">T .

    ’AGGR_TYPE’

    		character(len=*)

    ’SOC1’

    ’SOC1’, ’SOC2’

    Type of aggregation algorithm: currently, +class="td11">

    Type of aggregation algorithm: currently, we implement to measures of strength of connection, the one by Vaněk, Mandel and Brezina [26], and the one by Gratton +href="userhtmlli4.html#XVANEK_MANDEL_BREZINA">28], and the one by Gratton et al [16].

    ’AGGR_PROL’

    		character(len=*)

    ’SMOOTHED’, ’UNSMOOTHED’

    ’SMOOTHED’

    Prolongator used by the aggregation +class="td11">

    Prolongator used by the aggregation algorithm: smoothed or unsmoothed (i.e., tentative prolongator).

    < style="vertical-align:baseline;" id="TBL-6-5-">
    Note. Different thresholds at different levels, such as those used in [26, Section 5.1], can be easily set by invoking the rou-
    +href="userhtmlli4.html#XVANEK_MANDEL_BREZINA">28, Section 5.1], can be easily set by invoking the rou-
    tine Parameters defining the aggregation algorithm (continued).

    @@ -910,7 +928,7 @@ class="content">Parameters defining the aggregation algorithm (continued). -

    +

    what

    		type

    val

    deault

    cots

    ’AGGR_ORD’

    		character(len=*)

    ’NATURAL’ -

    ’DEGREE’

    ’NATURAL’

    Initial ordering of indices for the +class="td11">

    Initial ordering of indices for the aggregation algorithm: either natural ordering or sorted by descending degrees of the nodes in the matrix @@ -838,20 +856,20 @@ graph.

    ’AGGR_THRESH’

    		real(kind_parameter)

    Any real -

    number 

    Any real +

    number ∈ [0,1]

    0.01

    The threshold

    0.01

    The threshold θ in the aggregation algorithm, see (3) in Section 

    ’AGGR_FILTER’

    		character(len=*)

    ’FILTER’ -

    ’NOFILTER’

    ’NOFILTER’

    Matrix used in computing the smoothed +class="td11">

    Matrix used in computing the smoothed prolongator: filtered or unfiltered (see (5) in Section 

    what

    		type

    val

    deault

    cots

    ’COARSE_MAT’

    		character(len=*)

    ’DIST’ -

    ’REPL’

    ’REPL’

    Coarsest matrix layout: distributed among the +class="td11">

    Coarsest matrix layout: distributed among the processes or replicated on each of them.

    ’COARSE_SOLVE’

    		character(len=*)

    ’MUMPS’ -

    ’UMF’ -

    ’SLU’ -

    ’SLUDIST’ -

    ’JACOBI’ -

    ’GS’ -

    ’BJAC’

    See Note.

    Solver used at the coarsest level: sequential LU +class="td11">

    See Note.

    Solver used at the coarsest level: sequential LU from MUMPS, UMFPACK, or SuperLU (plus triangular solve); distributed LU from MUMPS or SuperLU_Dist (plus triangular solve); point-Jacobi, hybrid Gauss-Seidel or block-Jacobi. -

    Note that

    Note that UMF and SLU require the coarsest matrix to be replicated,

    ’COARSE_SUBSOLVE’

    		character(len=*)

    ’ILU’ -

    ’ILUT’ -

    ’MILU’ -

    ’MUMPS’ -

    ’SLU’ -

    ’UMF’

    See Note.

    Solver for the diagonal blocks of the coarse matrix, +class="td11">

    See Note.

    Solver for the diagonal blocks of the coarse matrix, in case the block Jacobi solver is chosen as coarsest-level solver: ILU(p), ILU(Parameters defining the coarse-space correction at the coarsest -

    @@ -1087,7 +1105,7 @@ class="content">Parameters defining the coarse-space correction at the coarsest
    -

    +

    @@ -1194,7 +1212,7 @@ class="content">Parameters defining the coarse-space correction at the co -

    @@ -1202,7 +1220,7 @@ class="content">Parameters defining the coarse-space correction at the co
    -

    +

    what

    		type

    val

    deault

    cots

    ’COARSE_SWEEPS’

    		integer

    Any integer -

    number

    Any integer +

    number > 0

    10

    Number of sweeps when

    10

    Number of sweeps when JACOBI, GS or BJAC @@ -1149,31 +1167,31 @@ is chosen as coarsest-level solver.

    ’COARSE_FILLIN’

    		integer

    Any integer -

    number

    Any integer +

    number ≥ 0

    0

    Fill-in level

    0

    Fill-in level p of the ILU factorizations.

    ’COARSE_ILUTHRS’

    		real(kind_parameter)

    Any real -

    number

    Any real +

    number ≥ 0

    0

    Drop tolerance

    0

    Drop tolerance t in the ILU(p,t) factorization.

    @@ -1416,7 +1434,7 @@ preconditioner. -

    @@ -1424,7 +1442,7 @@ preconditioner.
    -

    +

    what

    		type

    val

    deault

    cots

    ’SMOOTHER_TYPE’

    		character(len=*)

    ’JACOBI’ -

    ’GS’ -

    ’BGS’ -

    ’BJAC’ -

    ’AS’

    ’FBGS’

    Type of smoother used in the multilevel preconditioner: point-Jacobi, hybrid @@ -1274,34 +1292,34 @@ class="cmr-10">(forward) Gauss-Seidel, hybrid backward class="cmr-10">Gauss-Seidel, block-Jacobi, and Additive Schwarz. -

    It is ignored by one-level preconditioners.

    ’SUB_SOLVE’

    		character(len=*)

    ’JACOBI’ -

    ’GS’ -

    ’BGS’ -

    ’ILU’ -

    ’ILUT’ -

    ’MILU’ -

    ’MUMPS’ -

    ’SLU’ -

    ’UMF’

    GS and BGS multilevel class="cmr-10">preconditioners, respectively -

    ILU for block-Jacobi and Additive Schwarz class="cmr-10">one-level preconditioners

    The local solver to be used with the smoother or one-level preconditioner (see @@ -1350,20 +1368,20 @@ class="cmr-10">Note for details on hybrid Gauss-Seidel.

    ’SMOOTHER_SWEEPS’

    		integer

    Any integer -

    number ≥ 0

    1

    Number of sweeps of the smoother or one-level preconditioner. In the multilevel @@ -1382,20 +1400,20 @@ class="cmr-10">respectively.

    ’SUB_OVR’

    		integer

    Any integer -

    number ≥ 0

    1

    Number of overlap layers, for Additive Schwarz only.

    what

    		type

    val

    deault

    cots

    ’SUB_RESTR’

    		character(len=*)

    ’HALO’ -

    ’NONE’

    ’HALO’

    Type of restriction operator, for Additive Schwarz only: for taking into account the class="cmr-10">overlap, NONE for neglecting it. -

    Note that HALO must be chosen for the classical @@ -1501,17 +1519,17 @@ class="cmr-10">variant.

    ’SUB_PROL’

    		character(len=*)

    ’SUM’ -

    ’NONE’

    ’NONE’

    Type of prolongation operator, for Additive Schwarz only: for adding the contributions class="cmr-10">from the overlap, NONE for neglecting them. -

    Note that SUM must be chosen for the classical @@ -1534,20 +1552,20 @@ class="cmr-10">RAS variant.

    ’SUB_FILLIN’

    		integer

    Any integer -

    number ≥ 0

    0

    Fill-in level p of the incomplete LU @@ -1556,23 +1574,23 @@ class="cmr-10">factorizations. <

    ’SUB_ILUTHRS’

    		real(kind_parameter)

    Any real number ≥ 0

    0

    Drop tolerance t in the ILU(p,t) factorization.

    ’MUMPS_LOC_GLOB’

    		character(len=*)

    LOCAL_SOLVER’ -

    GLOBAL_SOLVER’

    GLOBAL_SOLVER’

    Whether MUMPS should be used as a distributed solver, or as a serial solver acting @@ -1603,17 +1621,17 @@ class="cmr-10">only on the part of the matrix local to each class="cmr-10">process.

    ’MUMPS_IPAR_ENTRY’

    		integer

    Any integer number

    0

    Set an entry in the MUMPS integer control array, as chosen via the idx optional argument.

    ’MUMPS_RPAR_ENTRY’

    		real

    Any real number

    0

    Set an entry in the MUMPS real control array, as chosen via the Parameters defining the smoother or the details of the one-level -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    -

    up]

    +

    diff --git a/docs/html/userhtmlsu12.html b/docs/html/userhtmlsu12.html index d703caee..345ac4b2 100644 --- a/docs/html/userhtmlsu12.html +++ b/docs/html/userhtmlsu12.html @@ -10,48 +10,48 @@ -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    6.3 6.3 Method hierarchy_build

    +class="cmbx-12">Method hierarchy_build
    -

    -

    +

    call p%hierarchy_build(a,desc_a,info)

    -

    This method builds the hierarchy of matrices and restriction/prolongation operators for +

    This method builds the hierarchy of matrices and restriction/prolongation the multilevel preconditioner operators for the multilevel preconditioner p, according to the requirements made by the user +class="cmbx-12">, according to the requirements through the methods made by the user through the methods init and and set. -

    . +

    Arguments

    +class="cmbx-12">. +class="cmbx-12">15]. +class="cmbx-12">. +class="cmbx-12">15]. +class="cmbx-12">. +class="cmbx-12">8for +details.

    a

    type(psb_xxspmat_type), intent(in).

    The sparse matrix structure containing the local part of the matrix +class="td11">

    The sparse matrix structure containing the local part to be preconditioned. Note that x must be chosen according to +class="cmbx-12">of the matrix to be preconditioned. Note that x must the real/complex, single/double precision version of MLD2P4 under +class="cmbx-12">be chosen according to the real/complex, single/double use. See the PSBLAS User’s Guide for details [precision version of MLD2P4 under use. See the PSBLAS +User’s Guide for details [13].

    desc_a

    type(psb_desc_type), intent(in).

    The communication descriptor of

    The communication descriptor of a. See the PSBLAS User’s Guide +class="cmbx-12">. See the PSBLAS for details [User’s Guide for details [13].

    info

    integer, intent(out).

    Error code. If no error, 0 is returned. See Section 

    Error code. If no error, 0 is returned. See Section 8 for details.

    @@ -133,23 +137,23 @@ class="td11">
    -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    -

    up]

    +

    diff --git a/docs/html/userhtmlsu13.html b/docs/html/userhtmlsu13.html index 70382613..d23e9e36 100644 --- a/docs/html/userhtmlsu13.html +++ b/docs/html/userhtmlsu13.html @@ -10,54 +10,58 @@ -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    6.4 6.4 Method smoothers_build

    +class="cmbx-12">Method smoothers_build
    -

    -

    +

    call p%smoothers_build(a,desc_a,p,info[,amold,vmold,imold])

    -

    This method builds the smoothers and the coarsest-level solvers for the multilevel +

    This method builds the smoothers and the coarsest-level solvers for the preconditioner multilevel preconditioner p, according to the requirements made by the user through the methods -, according to the requirements made +by the user through the methods init and and set, and based on the aggregation hierarchy produced by a previous call to -, and based on the +aggregation hierarchy produced by a previous call to hierarchy_build (see Section (see +Section 6.3). -

    6.3). +

    Arguments

    +class="cmbx-12">. +class="cmbx-12">15]. +class="cmbx-12">. +class="cmbx-12">15]. +class="cmbx-12">. +class="cmbx-12">8for +details. +class="cmbx-12">. +class="cmbx-12">15]. +class="cmbx-12">. +class="cmbx-12">this allows e.g. running on GPUs. +class="cmbx-12">. +class="cmbx-12">components; this allows e.g. running on GPUs.

    a

    type(psb_xxspmat_type), intent(in).

    The sparse matrix structure containing the local part of the matrix +class="td11">

    The sparse matrix structure containing the local part +of the matrix to be preconditioned. Note that x must to be preconditioned. Note that x must be chosen according to +class="cmbx-12">be chosen according to the real/complex, single/double the real/complex, single/double precision version of MLD2P4 under +class="cmbx-12">precision version of MLD2P4 under use. See the PSBLAS use. See the PSBLAS User’s Guide for details [User’s Guide for details [13].

    desc_a

    type(psb_desc_type), intent(in).

    The communication descriptor of

    The communication descriptor of a. See the PSBLAS User’s Guide +class="cmbx-12">. See the PSBLAS for details [User’s Guide for details [13].

    info

    integer, intent(out).

    Error code. If no error, 0 is returned. See Section 

    Error code. If no error, 0 is returned. See Section 8 for details.

    amold

    class(psb_xx_base_sparse_mat), intent(in), optional.

    The desired dynamic type for internal matrix components; this +class="td11">

    The desired dynamic type for internal matrix components; allows e.g. running on GPUs; it needs not be the same on all +class="cmbx-12">this allows e.g. running on GPUs; it needs not be the same processes. See the PSBLAS User’s Guide for details [on all processes. See the PSBLAS User’s Guide for details +[13].

    vmold

    class(psb_xx_base_vect_type), intent(in), optional.

    The desired dynamic type for internal vector components; this +class="td11">

    The desired dynamic type for internal vector components; allows e.g. running on GPUs.

    imold

    class(psb_i_base_vect_type), intent(in), optional.

    The desired dynamic type for internal integer vector components; +class="td11">

    The desired dynamic type for internal integer vector this allows e.g. running on GPUs.

    @@ -198,23 +207,26 @@ class="td11">
    -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    -

    up]

    +

    diff --git a/docs/html/userhtmlsu14.html b/docs/html/userhtmlsu14.html index 6e534a23..88966c45 100644 --- a/docs/html/userhtmlsu14.html +++ b/docs/html/userhtmlsu14.html @@ -10,236 +10,243 @@ -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    6.5 6.5 Method build

    +class="cmbx-12">Method build
    -

    -

    +

    call p%build(a,desc_a,info[,amold,vmold,imold])

    -

    This method builds the preconditioner

    This method builds the preconditioner p according to the requirements made by the +class="cmbx-12">according to the requirements user through the methods made by the user through the methods init and and set (see Sections (see Sections 6.3 and 6.3 +and 6.4 for multilevel +class="cmbx-12">6.4 for multilevel preconditioners). It is mostly provided for backward preconditioners). It is mostly provided for backward compatibility; indeed, it is +class="cmbx-12">compatibility; indeed, it is internally implemented by invoking the internally implemented by invoking the two previous methods two previous methods hierarchy_build and -and smoothers_build, whose nomenclature would however be somewhat unnatural when +class="cmbx-12">, whose +nomenclature would however be somewhat unnatural when dealing with dealing with simple one-level preconditioners. -

    simple one-level preconditioners. +

    Arguments + + +

    +class="cmbx-12">. +class="cmbx-12">15]. +class="cmbx-12">. +class="cmbx-12">15]. +class="cmbx-12">. +class="cmbx-12">8for +details. +class="cmbx-12">. +class="cmbx-12">15]. +class="cmbx-12">. +class="cmbx-12">this allows e.g. running on GPUs. +class="cmbx-12">. +class="cmbx-12">components; this allows e.g. running on GPUs.

    a

    type(psb_xxspmat_type), intent(in).

    The sparse matrix structure containing the local part of the matrix +class="td11">

    The sparse matrix structure containing the local part to be preconditioned. Note that x must be chosen according to +class="cmbx-12">of the matrix to be preconditioned. Note that x must the real/complex, single/double precision version of MLD2P4 under +class="cmbx-12">be chosen according to the real/complex, single/double use. See the PSBLAS User’s Guide for details [precision version of MLD2P4 under use. See the PSBLAS +User’s Guide for details [13].

    desc_a

    type(psb_desc_type), intent(in).

    The communication descriptor of

    The communication descriptor of a. See the PSBLAS User’s Guide +class="cmbx-12">. See the PSBLAS for details [User’s Guide for details [13].

    info

    integer, intent(out).

    Error code. If no error, 0 is returned. See Section 

    Error code. If no error, 0 is returned. See Section 8 for details.

    amold

    class(psb_xx_base_sparse_mat), intent(in), optional.

    The desired dynamic type for internal matrix components; this +class="td11">

    The desired dynamic type for internal matrix components; allows e.g. running on GPUs; it needs not be the same on all +class="cmbx-12">this allows e.g. running on GPUs; it needs not be the same processes. See the PSBLAS User’s Guide for details [on all processes. See the PSBLAS User’s Guide for details +[13].

    vmold

    class(psb_xx_base_vect_type), intent(in), optional.

    The desired dynamic type for internal vector components; this +class="td11">

    The desired dynamic type for internal vector components; allows e.g. running on GPUs.

    imold

    class(psb_i_base_vect_type), intent(in), optional.

    The desired dynamic type for internal integer vector components; +class="td11">

    The desired dynamic type for internal integer vector this allows e.g. running on GPUs.

    - - - -

    For compatibility with the previous versions of MLD2P4, this method can be also +

    For compatibility with the previous versions of MLD2P4, this method invoked as follows: +class="cmbx-12">can be also invoked as follows:

    -

    -

    +

    call mld_precbld(p,what,val,info[,amold,vmold,imold])

    -

    The method can be used to build multilevel preconditioners too. +class="cmtt-12"> amg_precbld(p,what,val,info[,amold,vmold,imold])

    +

    The method can be used to build multilevel preconditioners too. -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    -

    up]

    +

    diff --git a/docs/html/userhtmlsu15.html b/docs/html/userhtmlsu15.html index 4630b72a..71fdaa57 100644 --- a/docs/html/userhtmlsu15.html +++ b/docs/html/userhtmlsu15.html @@ -10,37 +10,37 @@ -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    6.6 6.6 Method apply

    +class="cmbx-12">Method apply
    -

    -

    +

    call p%apply(x,y,desc_a,info [,trans,work])

    -

    This method computes

    This method computes y = op-1) x, where , where B is a previously built preconditioner, +class="cmbx-12">is a previously built stored into preconditioner, stored into p, and , and op denotes the preconditioner itself or its transpose, according to the +class="cmbx-12">denotes the preconditioner itself or its value of transpose, according to the value of trans. Note that, when MLD2P4 is used with a Krylov solver from PSBLAS, -. Note that, when MLD2P4 is +used with a Krylov solver from PSBLAS, p%apply is called within the PSBLAS method is called within the +PSBLAS method psb_krylov and hence it is completely +class="cmbx-12">and hence it is completely transparent to the transparent to the user. -

    user. +

    Arguments + + +

    +class="cmbx-12">. +class="cmbx-12">under use. +class="cmbx-12">. +class="cmbx-12">under use. +class="cmbx-12">. +class="cmbx-12">be preconditioned. +class="cmbx-12">. +class="cmbx-12">8for +details. +class="cmr-12">). +class="cmbx-12">. +class="cmbx-12">precision version of MLD2P4 under use.

    x

    type

    type(kind_parameterkind_parameter), dimension(:), intent(in).

    The local part of the vector

    The local part of the vector x. Note that type and kind_parameter +class="cmbx-12">. Note that type +and kind_parameter must be chosen according to the must be chosen according to the real/complex, single/double +class="cmbx-12">real/complex, single/double precision version of MLD2P4 precision version of MLD2P4 under use.

    y

    type

    type(kind_parameterkind_parameter), dimension(:), intent(out).

    The local part of the vector

    The local part of the vector y. Note that type and kind_parameter +class="cmbx-12">. Note that type +and kind_parameter must be chosen according to the must be chosen according to the real/complex, single/double +class="cmbx-12">real/complex, single/double precision version of MLD2P4 precision version of MLD2P4 under use.

    desc_a

    type(psb_desc_type), intent(in).

    The communication descriptor associated to the matrix to be +class="td11">

    The communication descriptor associated to the matrix to preconditioned.

    info

    integer, intent(out).

    Error code. If no error, 0 is returned. See Section 

    Error code. If no error, 0 is returned. See Section 8 for details.

    trans

    character(len=1), optional, intent(in).

    If

    If trans = = ’N’,’n’ then then op(B-1) = ) = B-1; if ; if trans = = ’T’,’t’ then then op(B) = B-T (transpose of (transpose of B-1); if ); if trans = ’C’,’c’ then +class="cmbx-12">= ’C’,’c’ then op(B) = B-C (conjugate transpose of (conjugate transpose of B-1).

    work

    type

    type(kind_parameterkind_parameter), dimension(:), optional, target.

    Workspace. Its size should be at least

    Workspace. Its size should be at +least 4 * psb_cd_get_local_ - psb_cd_get_local_ cols(desc_a) (see the PSBLAS User’s Guide). Note that type +class="cmbx-12">(see the PSBLAS +User’s Guide). Note that type and kind_parameter must and kind_parameter must be chosen according to the real/complex, +class="cmbx-12">be chosen according to the real/complex, single/double single/double precision version of MLD2P4 under use.

    - - - -

    For compatibility with the previous versions of MLD2P4, this method can be also +

    For compatibility with the previous versions of MLD2P4, this method invoked as follows: +class="cmbx-12">can be also invoked as follows:

    -

    -

    +

    call mld_precaply(p,what,val,info)

    +class="cmtt-12"> amg_precaply(p,what,val,info) -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    -

    up]

    +

    diff --git a/docs/html/userhtmlsu16.html b/docs/html/userhtmlsu16.html index e412079b..fb748b57 100644 --- a/docs/html/userhtmlsu16.html +++ b/docs/html/userhtmlsu16.html @@ -10,39 +10,39 @@ -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    6.7 6.7 Method free

    +class="cmbx-12">Method free
    -

    -

    +

    call p%free(p,info)

    -

    This method deallocates the preconditioner data structure

    This method deallocates the preconditioner data structure p. -

    . +

    Arguments

    +class="cmbx-12">. +class="cmbx-12">for details.

    info

    integer, intent(out).

    Error code. If no error, 0 is returned. See Section 

    Error code. If no error, 0 is returned. See Section 8 for +class="cmbx-12">8 details.

    -

    For compatibility with the previous versions of MLD2P4, this method can be also +

    For compatibility with the previous versions of MLD2P4, this method invoked as follows: +class="cmbx-12">can be also invoked as follows:

    -

    -

    +

    call mld_precfree(p,info)

    +class="cmtt-12"> amg_precfree(p,info) -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    -

    up]

    +

    diff --git a/docs/html/userhtmlsu17.html b/docs/html/userhtmlsu17.html index 06df7c92..d3f1bbda 100644 --- a/docs/html/userhtmlsu17.html +++ b/docs/html/userhtmlsu17.html @@ -10,50 +10,50 @@ -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    6.8 6.8 Method descr

    +class="cmbx-12">Method descr
    -

    -

    +

    call p%descr(info, [iout])

    -

    This method prints a description of the preconditioner

    This method prints a description of the preconditioner p to the standard output or to a +class="cmbx-12">to the standard file. It must be called after output or to a file. It must be called after hierachy_build and and smoothers_build, or build, have +class="cmbx-12">, been called. -

    or build, have been called. +

    Arguments

    +class="cmbx-12">. +class="cmbx-12">8for +details. +class="cmbx-12">. +class="cmbx-12">be printed; the default is the standard output.

    info

    integer, intent(out).

    Error code. If no error, 0 is returned. See Section 

    Error code. If no error, 0 is returned. See Section 8 for details.

    iout

    integer, intent(in), optional.

    The id of the file where the preconditioner description will be +class="td11">

    The id of the file where the preconditioner description will printed; the default is the standard output.

    -

    For compatibility with the previous versions of MLD2P4, this method can be also +

    For compatibility with the previous versions of MLD2P4, this method invoked as follows: +class="cmbx-12">can be also invoked as follows:

    -

    -

    +

    call mld_precdescr(p,info amg_precdescr(p,info [,iout])

    -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    -

    up]

    +

    diff --git a/docs/html/userhtmlsu18.html b/docs/html/userhtmlsu18.html index fe5a234e..92a43874 100644 --- a/docs/html/userhtmlsu18.html +++ b/docs/html/userhtmlsu18.html @@ -10,43 +10,43 @@ -

    [

    [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    6.9 6.9 Auxiliary Methods

    -

    Various functionalities are implemented as additional methods of the preconditioner +class="cmbx-12">Auxiliary Methods +

    Various functionalities are implemented as additional methods of the object. -

    +class="cmbx-12">preconditioner object. +

    6.9.1 6.9.1 Method: dump
    +class="cmbx-12">Method: dump
    -

    -

    +

    call p%dump(info[,istart,iend,prefix,head,ac,rp,smoother,solver,global_num])

    -

    Dump on file. -

    Dump on file. +

    Arguments

    +class="cmbx-12">. +class="cmbx-12">8for +details. +class="cmbx-12">. +class="cmbx-12">15].

    info

    integer, intent(out).

    Error code. If no error, 0 is returned. See Section 

    Error code. If no error, 0 is returned. See Section 8 for details.

    amold

    class(psb_xx_base_sparse_mat), intent(in), optional.

    The desired dynamic type for internal matrix components; this +class="td11">

    The desired dynamic type for internal matrix components; allows e.g. running on GPUs; it needs not be the same on all +class="cmbx-12">this allows e.g. running on GPUs; it needs not be the same processes. See the PSBLAS User’s Guide for details [on all processes. See the PSBLAS User’s Guide for details +[13].

    -

    +

    6.9.2 6.9.2 Method: clone
    +class="cmbx-12">Method: clone
    -

    -

    +

    call p%clone(pout,info)

    -

    Create a (deep) copy of the preconditioner object. -

    Create a (deep) copy of the preconditioner object. +

    Arguments

    +class="cmbx-12">. +class="cmbx-12">single/double precision version of MLD2P4 under use. +class="cmbx-12">. +class="cmbx-12">8for +details.

    pout

    type(mld_x

    type(amg_xprec_type), intent(out).

    The copy of the preconditioner data structure. Note that x must +class="td11">

    The copy of the preconditioner data structure. Note be chosen according to the real/complex, single/double precision +class="cmbx-12">that x must be chosen according to the real/complex, version of MLD2P4 under use.

    info

    integer, intent(out).

    Error code. If no error, 0 is returned. See Section 

    Error code. If no error, 0 is returned. See Section 8 for details.

    -

    +

    6.9.3 6.9.3 Method: sizeof
    +class="cmbx-12">Method: sizeof
    -

    -

    +

    sz =  p%sizeof()

    -

    Return memory footprint in bytes. -

    +

    Return memory footprint in bytes. +

    6.9.4 6.9.4 Method: allocate_wrk
    +class="cmbx-12">Method: allocate_wrk
    -

    -

    +

    call p%allocate_wrk(info[, vmold])

    -

    Allocate internal work vectors. Each application of the preconditioner uses a number of +

    Allocate internal work vectors. Each application of the preconditioner work vectors which are allocated internally as necessary; therefore allocation and +class="cmbx-12">uses a number of work vectors which are allocated internally as deallocation of memory occurs multiple times during the execution of a Krylov method. +class="cmbx-12">necessary; therefore allocation and deallocation of memory occurs In most cases this strategy is perfectly acceptable, but on some platforms, most +class="cmbx-12">multiple times during the execution of a Krylov method. In most cases notably GPUs, memory allocation is a slow operation, and the default behaviour would +class="cmbx-12">this strategy is perfectly acceptable, but on some platforms, most lead to a slowdown. This method allows to trade space for time by preallocating +class="cmbx-12">notably GPUs, memory allocation is a slow operation, and the default the internal workspace outside of the invocation of a Krylov method. When +class="cmbx-12">behaviour would lead to a slowdown. This method allows to trade using GPUs or other specialized devices, the vmold argument is also necessary -to ensure the internal work vectors are of the appropriate dynamic type to +class="cmbx-12">space for time by preallocating the internal workspace outside of the exploit the accelerator hardware; when allocation occurs internally this is +class="cmbx-12">invocation of a Krylov method. When using GPUs or other specialized +devices, the vmold argument is also necessary to ensure the internal +work vectors are of the appropriate dynamic type to exploit the +accelerator hardware; when allocation occurs internally this is taken taken care of based on the dynamic type of the care of based on the dynamic type of the x argument to the argument to the apply method. -

    method. +

    Arguments

    +class="cmbx-12">. +class="cmbx-12">8for +details. +class="cmbx-12">. +class="cmbx-12">this allows e.g. running on GPUs.

    info

    integer, intent(out).

    Error code. If no error, 0 is returned. See Section 

    Error code. If no error, 0 is returned. See Section 8 for details.

    vmold

    class(psb_xx_base_vect_type), intent(in), optional.

    The desired dynamic type for internal vector components; this +class="td11">

    The desired dynamic type for internal vector components; allows e.g. running on GPUs.

    -

    +

    6.9.5 6.9.5 Method: free_wrk
    +class="cmbx-12">Method: free_wrk
    -

    -

    +

    call p%free_wrk(info)

    -

    Deallocate internal work vectors. -

    Deallocate internal work vectors. +

    Arguments

    +class="cmbx-12">. +class="cmbx-12">8for +details.

    info

    integer, intent(out).

    Error code. If no error, 0 is returned. See Section 

    Error code. If no error, 0 is returned. See Section 8 for details.

    @@ -318,19 +331,19 @@ class="td11">

    [[prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    +class="cmbx-12">up]

    diff --git a/docs/html/userhtmlsu2.html b/docs/html/userhtmlsu2.html index edfab22b..67c015dc 100644 --- a/docs/html/userhtmlsu2.html +++ b/docs/html/userhtmlsu2.html @@ -44,7 +44,7 @@ class="cmbx-12">UMFPACK

    [911] A sparse LU factorization package included in the SuiteSparse SuperLU
    [1012] A sparse LU factorization package available from _Dist
    [1921] A sparse LU factorization package available from the same 3.3 Configuration options

    In order to build MLD2P4, the first step is to use the In order to build AMG4PSBLAS, the first step is to use the configure script in the main +class="cmr-12">script in the directory to generate the necessary makefile. -

    As a minimal example consider the following: +class="cmr-12">main directory to generate the necessary makefile. +

    DA RISCRIVERE +

    As a minimal example consider the following:

    ./configure --with-psblas=PSB-INSTALL-DIR
    -

    which assumes that the various MPI compilers and support libraries are available in +

    which assumes that the various MPI compilers and support libraries are the standard directories on the system, and specifies only the PSBLAS install directory +class="cmbx-12">available in the standard directories on the system, and specifies only (note that the latter directory must be specified with an absolute path). The full set of +class="cmbx-12">the PSBLAS install directory (note that the latter directory must options may be looked at by issuing the command be specified with an absolute path). The full set of options may +be looked at by issuing the command ./configure --help, which +class="cmbx-12">, which produces: +class="cmbx-12">produces: @@ -237,18 +241,17 @@ class="cmr-12">produces:  
     
    Report bugs to <https://github.com/sfilippone/mld2p4-2/issues>.

    -

    -

    For instance, if a user has built and installed PSBLAS 3.5 under the /opt directory +

    +

    For instance, if a user has built and installed PSBLAS 3.5 under the +/opt directory and is using the SuiteSparse package (which includes and is using the SuiteSparse package (which includes UMFPACK), then MLD2P4 -might be configured with: +class="cmbx-12">UMFPACK), then MLD2P4 might be configured with: @@ -256,72 +259,74 @@ class="cmr-12">might be configured with:  ./configure --with-psblas=/opt/psblas-3.5/ \  
     --with-umfpackincdir=/usr/include/suitesparse/

    -

    Once the configure script has completed execution, it will have generated the file -

    Once the configure script has completed execution, it will have generated +the file Make.inc which will then be used by all Makefiles in the directory tree; this file will be +class="cmbx-12">which will then be used by all Makefiles in the directory copied in the install directory under the name tree; this file will be copied in the install directory under the name +Make.inc.MLD2P4. -

    To use the MUMPS solver package, the user has to add the appropriate options to +class="cmbx-12">. +

    To use the MUMPS solver package, the user has to add the appropriate the configure script; by default we are looking for the libraries -ldmumps -lsmumps +class="cmbx-12">options to the configure script; by default we are looking for the libraries -ldmumps -lsmumps  -lzmumps -lcmumps -mumps_common -lpord. MUMPS often uses additional +class="cmbx-12">. MUMPS often packages such as ScaLAPACK, ParMETIS, SCOTCH, as well as enabling OpenMP; in +class="cmbx-12">uses additional packages such as ScaLAPACK, ParMETIS, SCOTCH, as such cases it is necessary to add linker options with the --with-extra-libs configure +class="cmbx-12">well as enabling OpenMP; in such cases it is necessary to add linker options option. -

    To build the library the user will now enter +class="cmbx-12">with the --with-extra-libs configure option. +

    To build the library the user will now enter

    make
    -

    followed (optionally) by +

    followed (optionally) by

    make install
    -

    +

    -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    -

    up]

    +

    diff --git a/docs/html/userhtmlsu4.html b/docs/html/userhtmlsu4.html index 3fd7df3a..4a2f91ff 100644 --- a/docs/html/userhtmlsu4.html +++ b/docs/html/userhtmlsu4.html @@ -10,60 +10,61 @@ -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    3.4 3.4 Bug reporting

    -

    If you find any bugs in our codes, please report them through our issues page +class="cmbx-12">Bug reporting +

    If you find any bugs in our codes, please report them through our issues on
    page on
    https://github.com/sfilippone/mld2p4-2/issues
    To enable us to track the bug, please provide a log from the failing application, the +href="https://github.com/psctoolkit/amg4psblas/issues" class="url" >https://github.com/psctoolkit/amg4psblas/issues
    +

    To enable us to track the bug, please provide a log from the failing test conditions, and ideally a self-contained test program reproducing the +class="cmbx-12">application, the test conditions, and ideally a self-contained test program issue. +class="cmbx-12">reproducing the issue. -

    [

    [next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    -

    up]

    +

    diff --git a/docs/html/userhtmlsu5.html b/docs/html/userhtmlsu5.html index c56540f1..d7acc695 100644 --- a/docs/html/userhtmlsu5.html +++ b/docs/html/userhtmlsu5.html @@ -10,69 +10,72 @@ -

    [

    [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    3.5 3.5 Example and test programs

    -

    The package contains the Example and test programs +

    The package contains the examples and and tests directories; both of them are +class="cmbx-12">directories; both of them are further divided into further divided into fileread and and pdegen subdirectories. Their purpose is as +class="cmbx-12">subdirectories. Their purpose is as follows: +class="cmbx-12">follows:

    examples
    contains a set of simple example programs with a predefined choice of +class="cmbx-12">contains a set of simple example programs with a predefined preconditioners, selectable via integer values. These are intended to get an +class="cmbx-12">choice of preconditioners, selectable via integer values. These acquaintance with the multilevel preconditioners available in MLD2P4. +class="cmbx-12">are intended to get an acquaintance with the multilevel + preconditioners available in AMG4PSBLAS.
    tests
    contains a set of more sophisticated examples that will allow the user, via +class="cmbx-12">contains a set of more sophisticated examples that will allow the the input files in the user, via the input files in the runs subdirectories, to experiment with the full range +class="cmbx-12">subdirectories, to experiment of preconditioners implemented in the package.
    -

    The with the full range of preconditioners implemented in the package. +

    The fileread directories contain sample programs that read sparse matrices from files, +class="cmbx-12">directories contain sample programs that read sparse matrices according to the Matrix Market or the Harwell-Boeing storage format; the pdegen +class="cmbx-12">from files, according to the Matrix Market or the Harwell-Boeing storage programs generate matrices in full parallel mode from the discretization of a sample +class="cmbx-12">format; the pdegen programs generate matrices in full parallel mode from partial differential equation. +class="cmbx-12">the discretization of a sample partial differential equation. @@ -80,19 +83,19 @@ class="cmr-12">partial differential equation.

    [[prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    +class="cmbx-12">up]

    diff --git a/docs/html/userhtmlsu6.html b/docs/html/userhtmlsu6.html index 019b2fe6..79197f21 100644 --- a/docs/html/userhtmlsu6.html +++ b/docs/html/userhtmlsu6.html @@ -11,35 +11,38 @@

    [[next] [next] [tail] [tail] [up]

    +class="cmbx-12">up]

    4.1 4.1 AMG preconditioners

    +class="cmbx-12">AMG preconditioners

    In order to describe the AMG preconditioners available in MLD2P4, we consider a +class="cmbx-12">In order to describe the AMG preconditioners available in MLD2P4, we linear system +class="cmbx-12">consider a linear system
    Ax = b, + + +
    		(2)

    where where A = (aℝn×n is a nonsingular sparse matrix; for ease of presentation we +class="cmbx-12">is a nonsingular sparse matrix; for ease of assume presentation we assume A has a symmetric sparsity pattern. - - - +class="cmbx-12">has a symmetric sparsity pattern.

    Let us consider as finest index space the set of row (column) indices of Let us consider as finest index space the set of row (column) indices of A, +class="cmbx-12">, i.e., Ω = i.e., Ω = {1, ,…,n}. Any algebraic multilevel preconditioners implemented in +class="cmbx-12">. Any algebraic multilevel preconditioners implemented in MLD2P4 generates a hierarchy of index spaces and a corresponding hierarchy of +class="cmbx-12">MLD2P4 generates a hierarchy of index spaces and a corresponding matrices, +class="cmbx-12">hierarchy of matrices,

    1 2 nlev 1 2 nlev -Ω ≡ Ω ⊃ Ω ⊃ ...⊃ Ω , A ≡ A, A ,...,A , +src=

    by using the information contained in by using the information contained in A, without assuming any knowledge of +class="cmbx-12">, without assuming any knowledge the geometry of the problem from which of the geometry of the problem from which A originates. A vector space originates. A vector space ℝnk is +class="cmmi-6">k associated with Ωis associated with Ωk, where , where n k is the size of Ωis the size of Ωk. For all . For all k < nlev, a restriction +class="cmbx-12">, a operator and a prolongation one are built, which connect two levels k and +class="cmbx-12">restriction operator and a prolongation one are built, which connect two levels k + 1: +class="cmbx-12">and k + 1:

    P k ∈ ℝnk×nk+1, Rk ∈ ℝnk+1×nk ; +src=

    the matrix the matrix Ak+1 is computed by using the previous operators according to the +class="cmr-8">+1 is computed by using the previous operators according to Galerkin approach, i.e., +class="cmbx-12">the Galerkin approach, i.e.,

    k+1 k k k -A = R A P . +src=

    In the current implementation of MLD2P4 we have In the current implementation of MLD2P4 we have Rk = (Pk)T A smoother with +class="cmbx-12">A smoother iteration matrix with iteration matrix Mk is set up at each level is set up at each level k < nlev, and a solver is set up at the +class="cmbx-12">, and a solver is set coarsest level, so that they are ready for application (for example, setting up a solver +class="cmbx-12">up at the coarsest level, so that they are ready for application (for example, based on the setting up a solver based on the LU factorization means computing and storing the factorization means computing and +storing the L and and U factors). The +class="cmbx-12">factors). The construction of the hierarchy of AMG construction of the hierarchy of AMG components described so far corresponds to the +class="cmbx-12">components described so far corresponds to the so-called build phase of the so-called build phase of the preconditioner. +class="cmbx-12">preconditioner.

    @@ -178,9 +183,9 @@ class="cmr-12">so-called build phase of the preconditioner. cellpadding="0" border="0" cellspacing="0" class="tabbing">

    Application phase of a V-cycle preconditioner.

    The components produced in the build phase may be combined in several ways to +class="cmbx-12">The components produced in the build phase may be combined in obtain different multilevel preconditioners; this is done in the application phase, i.e., in +class="cmbx-12">several ways to obtain different multilevel preconditioners; this is done in the computation of a vector of type the application phase, i.e., in the computation of a vector of type w = B-1v, where , +where B denotes the preconditioner, +class="cmbx-12">denotes the preconditioner, usually within an iteration of a Krylov usually within an iteration of a Krylov solver [solver [21]. An example of such a combination, +class="cmbx-12">23]. An example of such a combination, known as V-cycle, is given in known as V-cycle, is given in Figure Figure 1. In this case, a single iteration of the same +class="cmbx-12">1. In this case, a single iteration of the same smoother is used before smoother is used before and after the the recursive call to the V-cycle (i.e., in the +class="cmbx-12">and after the the recursive call to the V-cycle (i.e., in the pre-smoothing pre-smoothing and post-smoothing phases); however, different choices can be +class="cmbx-12">and post-smoothing phases); however, different choices can be performed. performed. Other cycles can be defined; in MLD2P4, we implemented the +class="cmbx-12">Other cycles can be defined; in MLD2P4, we implemented the standard standard V-cycle and W-cycle [V-cycle and W-cycle [3], and a version of the K-cycle described +class="cmbx-12">3], and a version of the K-cycle described in [in [20]. +class="cmbx-12">22].

    [[next] [next] [front] [front] [up]

    +class="cmbx-12">up]

    diff --git a/docs/html/userhtmlsu7.html b/docs/html/userhtmlsu7.html index 3574e286..8b6d8567 100644 --- a/docs/html/userhtmlsu7.html +++ b/docs/html/userhtmlsu7.html @@ -11,89 +11,96 @@

    [[next] [next] [prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    4.2 4.2 Smoothed Aggregation

    +class="cmbx-12">Smoothed Aggregation

    In order to define the prolongator In order to define the prolongator Pk, used to compute the coarse-level matrix , used to compute the coarse-level +matrix Ak+1, +class="cmbx-12">, MLD2P4 uses the smoothed aggregation algorithm described MLD2P4 uses the smoothed aggregation algorithm described in [in [2, 2, 26]. The basic idea +class="cmbx-12">28]. The basic idea of this algorithm is to build a coarse set of indices of this algorithm is to build a coarse set of indices ΩΩk+1 by suitably grouping the -indices of Ω+1 by suitably grouping the indices of Ωk into disjoint subsets (aggregates), and to define the coarse-to-fine space +class="cmbx-12">into disjoint subsets transfer operator (aggregates), and to define the coarse-to-fine space transfer operator Pk by applying a suitable smoother to a simple piecewise constant +class="cmbx-12">by prolongation operator, with the aim of improving the quality of the coarse-space +class="cmbx-12">applying a suitable smoother to a simple piecewise constant prolongation correction. +class="cmbx-12">operator, with the aim of improving the quality of the coarse-space +correction.

    Three main steps can be identified in the smoothed aggregation procedure: +class="cmbx-12">Three main steps can be identified in the smoothed aggregation +procedure:

    1. aggregation of the indices of Ωaggregation of the indices of Ωk to obtain Ωto obtain Ωk+1; +class="cmbx-12">;
    2. construction of the prolongator construction of the prolongator Pk; +class="cmbx-12">;
    3. application of application of Pk and and Rk = (Pk)T to build to build Ak+1.
    +class="cmbx-12">.

    In order to perform the coarsening step, the smoothed aggregation algorithm +class="cmbx-12">In order to perform the coarsening step, the smoothed aggregation described in [algorithm described in [26] is used. In this algorithm, each index 28] is used. In this algorithm, each index j ∈ Ωk+1 corresponds +class="cmr-8">+1 to an aggregate Ωcorresponds to an aggregate Ωjk of Ωof Ωk, consisting of a suitably chosen index , consisting of a suitably chosen index +i ∈ Ωk and +class="cmbx-12">and indices that are (usually) contained in a strongly-coupled indices that are (usually) contained in a strongly-coupled neighborood of neighborood of i, -i.e., +class="cmbx-12">, i.e.,

    { ∘ -------} -Ωkj ⊂ N ki (θ) = r ∈ Ωk : |akir| > θ |akiiakrr| ∪ {i} , +src=
    		(3)
    @@ -154,53 +161,57 @@ class="cmr-12">(3)

    for a given threshold for a given threshold θ ∈ [0, 1] (see [1] (see [26] for the details). Since this algorithm has a +class="cmbx-12">28] for the details). Since this algorithm +has a sequential nature, a decoupled version of it is applied, where each sequential nature, a decoupled version of it is applied, where each processor +class="cmbx-12">processor independently executes the algorithm on the set of indices independently executes the algorithm on the set of indices assigned to it in the initial +class="cmbx-12">assigned to it in the initial data distribution. This version is embarrassingly data distribution. This version is embarrassingly parallel, since it does not require any +class="cmbx-12">parallel, since it does not require any data communication. On the other data communication. On the other hand, it may produce some nonuniform aggregates +class="cmbx-12">hand, it may produce some nonuniform aggregates and is strongly and is strongly dependent on the number of processors and on the initial +class="cmbx-12">dependent on the number of processors and on the initial partitioning of partitioning of the matrix the matrix A. Nevertheless, this parallel algorithm has been chosen +class="cmbx-12">. Nevertheless, this parallel algorithm has been chosen for for MLD2P4, since it has been shown to produce good results in practice +class="cmbx-12">MLD2P4, since it has been shown to produce good results in practice [[5, 5, 7, 7, 25]. +class="cmbx-12">27].

    The prolongator The prolongator Pk is built starting from a tentative prolongator is built starting from a tentative prolongator +Pk ∈ ×nk+1, -defined as +class="cmbx-12">, defined as
    { k -PŻk = (Żpkij), pŻkij = 1 if i ∈ Ω j, - 0 otherwise, +src=
    		(4)

    where Ωwhere Ωjk is the aggregate of Ωis the aggregate of Ωk corresponding to the index corresponding to the index j ∈ Ωk+1. . Pk is obtained +class="cmbx-12">is by applying to obtained by applying to Pk a smoother a smoother Sk ∈ k×nk: +class="cmbx-12">:

    Pk = Sk ŻPk,
    in +src="userhtml15x.png" alt="Pk = Sk ŻP k, " class="math-display" > +in order to remove nonsmooth components from the range of the order to remove nonsmooth components from the range of the prolongator, and hence +class="cmbx-12">prolongator, and hence to improve the convergence properties of the to improve the convergence properties of the multilevel method [multilevel method [2, 2, 24]. A simple -choice for 26]. A simple choice for Sk is the damped Jacobi smoother: +class="cmbx-12">is the damped Jacobi +smoother: + + +
    k k k -1 k -S = I - ω (D ) A F, +src=

    where where Dk is the diagonal matrix with the same diagonal entries as is the diagonal matrix with the same diagonal entries as Ak, A +class="cmbx-12">, AF k = (a ijk) is -the filtered matrix defined as +class="cmr-12">) is the filtered matrix defined as
    { k k ∑ -aŻkij = aij if j ∈ N i (θ), (j ⁄= i), Żakii = akii - (akij - Żakij), - 0 otherwise, j⁄=i +src=
    		(5)

    and and ωk is an approximation of 4is an approximation of 4∕(3ρk), where ), where ρk is the spectral radius of (is the spectral radius of +(Dk)1A F k -[k [2]. In MLD2P4 this approximation is obtained by using 2]. In MLD2P4 this approximation is obtained by using ∥AA +F k∥ ∞ as an estimate of ∞ +as an estimate of ρk. +class="cmbx-12">. Note that for systems coming from uniformly Note that for systems coming from uniformly elliptic problems, filtering the matrix elliptic problems, filtering the matrix Ak +class="cmmi-8">k has little or no effect, and has little or no effect, and Ak can be used instead of can be used instead of A F k. The latter choice is the +class="cmbx-12">. The latter choice is the default in default in MLD2P4. +class="cmbx-12">MLD2P4.

    [[next] [next] [prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    +class="cmbx-12">up]

    diff --git a/docs/html/userhtmlsu8.html b/docs/html/userhtmlsu8.html index 861caf18..78898188 100644 --- a/docs/html/userhtmlsu8.html +++ b/docs/html/userhtmlsu8.html @@ -11,69 +11,73 @@

    [[prev] [prev] [prev-tail] [prev-tail] [tail] [tail] [up]

    +class="cmbx-12">up]

    4.3 4.3 Smoothers and coarsest-level solvers

    +class="cmbx-12">Smoothers and coarsest-level solvers

    The smoothers implemented in MLD2P4 include the Jacobi and block-Jacobi methods, +class="cmbx-12">The smoothers implemented in MLD2P4 include the Jacobi and a hybrid version of the forward and backward Gauss-Seidel methods, and the additive +class="cmbx-12">block-Jacobi methods, a hybrid version of the forward and backward Schwarz (AS) ones (see, e.g., [Gauss-Seidel methods, and the additive Schwarz (AS) ones (see, e.g., +[21, 23, 22]). +class="cmbx-12">24]).

    The hybrid Gauss-Seidel version is considered because the original Gauss-Seidel +class="cmbx-12">The hybrid Gauss-Seidel version is considered because the original method is inherently sequential. At each iteration of the hybrid version, each parallel +class="cmbx-12">Gauss-Seidel method is inherently sequential. At each iteration of the process uses the most recent values of its own local variables and the values +class="cmbx-12">hybrid version, each parallel process uses the most recent values of its own of the non-local variables computed at the previous iteration, obtained by +class="cmbx-12">local variables and the values of the non-local variables computed at the exchanging data with other processes before the beginning of the current +class="cmbx-12">previous iteration, obtained by exchanging data with other processes before iteration. +class="cmbx-12">the beginning of the current iteration.

    In the AS methods, the index space ΩIn the AS methods, the index space Ωk is divided into is divided into m k subsets Ωsubsets Ωik of +class="cmbx-12">of size size nk,i, possibly overlapping. For each , possibly overlapping. For each i we consider the restriction operator +class="cmbx-12">we consider the restriction operator Rik k,i×nk that maps a vector that maps a vector xk to the vector to the vector x ik made of the components of +class="cmbx-12">made of the components of xk with indices in Ω +class="cmbx-12">with indices in Ω ik, and the prolongation operator P +class="cmbx-12">, and the prolongation operator Pik = (ik)T . These +class="cmbx-12">. These operators are then used to build A operators are then used to build Aik = P ik, which is the restriction of +class="cmbx-12">, which is the restriction of Ak to the index space Ω +class="cmbx-12">to the index space Ω ik. The classical AS preconditioner M +class="cmbx-12">. The classical AS preconditioner MASk is defined -as +class="cmbx-12">is defined as

    m∑k -(M AkS )-1 = Pki (Aki)-1Rki, - i=1 +src=

    where where Aik is supposed to be nonsingular. We observe that an approximate inverse of +class="cmbx-12">is supposed to be nonsingular. We observe that an approximate inverse of Aik is usually considered instead of (is usually considered instead of (A ik)-1. The setup of . The setup of M ASk during the multilevel +class="cmmi-8">k build phase involves +class="cmbx-12">during the multilevel build phase involves

    +class="cmbx-12">some form of incomplete factorization).

    The computation of The computation of zk = ASkwk, with , with wk ∈ ℝnk, during the multilevel application +class="cmbx-12">, during the multilevel phase, requires +class="cmbx-12">application phase, requires

    +class="cmbx-12">.

    Variants of the classical AS method, which use modifications of the restriction and +class="cmbx-12">Variants of the classical AS method, which use modifications of the restriction prolongation operators, are also implemented in MLD2P4. Among them, the Restricted +class="cmbx-12">and prolongation operators, are also implemented in MLD2P4. Among AS (RAS) preconditioner usually outperforms the classical AS preconditioner in terms +class="cmbx-12">them, the Restricted AS (RAS) preconditioner usually outperforms of convergence rate and of computation and communication time on parallel +class="cmbx-12">the classical AS preconditioner in terms of convergence rate and of distributed-memory computers, and is therefore the most widely used among the AS +class="cmbx-12">computation and communication time on parallel distributed-memory preconditioners [computers, and is therefore the most widely used among the AS +preconditioners [6]. +class="cmbx-12">6].

    Direct solvers based on sparse LU factorizations, implemented in the third-party +class="cmbx-12">Direct solvers based on sparse LU factorizations, implemented in libraries reported in Section the third-party libraries reported in Section 3.2, can be applied as coarsest-level solvers by +class="cmbx-12">3.2, can be applied as +coarsest-level solvers by MLD2P4. Native inexact solvers based on MLD2P4. Native inexact solvers based on incomplete LU factorizations, as well as +class="cmbx-12">incomplete LU factorizations, as well as Jacobi, hybrid (forward) Jacobi, hybrid (forward) Gauss-Seidel, and block Jacobi preconditioners are +class="cmbx-12">Gauss-Seidel, and block Jacobi preconditioners are also available. Direct also available. Direct solvers usually lead to more effective preconditioners in +class="cmbx-12">solvers usually lead to more effective preconditioners in terms of terms of algorithmic scalability; however, this does not guarantee parallel +class="cmbx-12">algorithmic scalability; however, this does not guarantee parallel efficiency. +class="cmbx-12">efficiency. @@ -337,19 +349,19 @@ class="cmr-12">efficiency.

    [[prev] [prev] [prev-tail] [prev-tail] [front] [front] [up]

    +class="cmbx-12">up]

    diff --git a/docs/html/userhtmlsu9.html b/docs/html/userhtmlsu9.html index 0f3ef716..2a2f9ce2 100644 --- a/docs/html/userhtmlsu9.html +++ b/docs/html/userhtmlsu9.html @@ -10,102 +10,107 @@ -

    [

    [tail] [tail] [up]

    +class="cmbx-12">up]

    5.1 5.1 Examples

    -

    The code reported in Figure Examples +

    The code reported in Figure 2 shows how to set and apply the default multilevel +class="cmbx-12">2 shows how to set and apply the default preconditioner available in the real double precision version of MLD2P4 (see Table multilevel preconditioner available in the real double precision version of +AMG4PSBLAS (see Table 1). +class="cmbx-12">1). This preconditioner is chosen by simply This preconditioner is chosen by simply specifying specifying ’ML’ as the second argument of -as the second argument of P%init (a call to (a call to P%set is not needed) and is applied with the CG solver provided by +class="cmbx-12">is not PSBLAS (the matrix of the system to be solved is assumed to be positive definite). As +class="cmbx-12">needed) and is applied with the CG solver provided by PSBLAS (the previously observed, the modules psb_base_mod, mld_prec_mod and psb_krylov_mod +class="cmbx-12">matrix of the system to be solved is assumed to be positive definite). As must be used by the example program. -

    The part of the code concerning the reading and assembling of the sparse matrix +class="cmbx-12">previously observed, the modules psb_base_mod, amg_prec_mod and +psb_krylov_mod must be used by the example program. +

    The part of the code concerning the reading and assembling of the and the right-hand side vector, performed through the PSBLAS routines for sparse +class="cmbx-12">sparse matrix and the right-hand side vector, performed through the matrix and vector management, is not reported here for brevity; the statements +class="cmbx-12">PSBLAS routines for sparse matrix and vector management, is not concerning the deallocation of the PSBLAS data structure are neglected too. The +class="cmbx-12">reported here for brevity; the statements concerning the deallocation of the complete code can be found in the example program file mld_dexample_ml.f90, +class="cmbx-12">PSBLAS data structure are neglected too. The complete code can be found in the directory in the example program file amg_dexample_ml.f90, in the directory +examples/fileread of the MLD2P4 implementation (see -Section of the AMG4PSBLAS implementation (see Section 3.5). A sample test problem along with the relevant input data is available in +class="cmbx-12">3.5). +A sample test problem along with the relevant input data is available in + + + examples/fileread/runs. For details on the use of the PSBLAS routines, see the +class="cmbx-12">. For details on the use of the PSBLAS routines, see PSBLAS User’s Guide [the PSBLAS User’s Guide [13]. -

    The setup and application of the default multilevel preconditioner for the real single +class="cmbx-12">15]. +

    The setup and application of the default multilevel preconditioner for precision and the complex, single and double precision, versions are obtained +class="cmbx-12">the real single precision and the complex, single and double precision, with straightforward modifications of the previous example (see Section versions are obtained with straightforward modifications of the previous +example (see Section 6 for - - - +class="cmbx-12">6 for details). If these versions are installed, the details). If these versions are installed, the corresponding codes are available in -corresponding codes are available in examples/fileread/. -

    . +

    @@ -117,13 +122,13 @@ class="cmr-12">.
    -

    +

      use psb_base_mod - 
      use mld_prec_mod + 
      use amg_prec_mod  
      use psb_krylov_mod  
    ... ...  
    ! @@ -132,7 +137,7 @@ class="cmr-12">.  
    ! sparse matrix descriptor  
      type(psb_desc_type)   :: desc_A  
    ! preconditioner - 
      type(mld_dprec_type)  :: P + 
      type(amg_dprec_type)  :: P  
    ! right-hand side and solution vectors  
      type(psb_d_vect_type) :: b, x  
    ... ... @@ -174,7 +179,7 @@ class="cmr-12">.  
      call psb_exit(ictxt)  
      stop
    -

    +

    @@ -185,80 +190,86 @@ class="content">setup and application of the default multilevel preconditioner ( -

    -

    Different versions of the multilevel preconditioner can be obtained by changing the +

    +

    Different versions of the multilevel preconditioner can be obtained by +changing the default values of the preconditioner parameters. The code default values of the preconditioner parameters. The code reported in Figure reported in Figure 3 shows +class="cmbx-12">3 shows how to set a V-cycle preconditioner which how to set a V-cycle preconditioner which applies 1 block-Jacobi sweep as pre- and +class="cmbx-12">applies 1 block-Jacobi sweep as pre- and post-smoother, and solves the post-smoother, and solves the coarsest-level system with 8 block-Jacobi sweeps. Note +class="cmbx-12">coarsest-level system with 8 block-Jacobi sweeps. Note that the ILU(0) that the ILU(0) factorization (plus triangular solve) is used as local solver for the +class="cmbx-12">factorization (plus triangular solve) is used as local solver for the block-Jacobi sweeps, since this is the default associated with block-Jacobi and set +class="cmbx-12">block-Jacobi sweeps, since this is the default associated with block-Jacobi by and set by P%init. Furthermore, specifying block-Jacobi as coarsest-level solver implies that +class="cmbx-12">. Furthermore, specifying block-Jacobi as coarsest-level the coarsest-level matrix is distributed among the processes. Figure solver implies that the coarsest-level matrix is distributed among the +processes. Figure 4 shows how to set +class="cmbx-12">4 shows how to set a W-cycle preconditioner which a W-cycle preconditioner which applies 2 hybrid Gauss-Seidel sweeps as pre- and +class="cmbx-12">applies 2 hybrid Gauss-Seidel sweeps as pre- and post-smoother, and solves post-smoother, and solves the coarsest-level system with the multifrontal LU +class="cmbx-12">the coarsest-level system with the multifrontal LU factorization factorization implemented in MUMPS. It is specified that the coarsest-level matrix is +class="cmbx-12">implemented in MUMPS. It is specified that the coarsest-level matrix is distributed, since MUMPS can be used on both replicated and distributed matrices, +class="cmbx-12">distributed, since MUMPS can be used on both replicated and distributed and by default it is used on replicated ones. The code fragments shown in +class="cmbx-12">matrices, and by default it is used on replicated ones. The code fragments Figures shown in Figures 3 and 3 and 4 are included in the example program file mld_dexample_ml.f90 -too. -

    Finally, Figure 4 are included in the example program file +amg_dexample_ml.f90 too. +

    Finally, Figure 5 shows the setup of a one-level additive Schwarz preconditioner, +class="cmbx-12">5 shows the setup of a one-level additive Schwarz i.e., RAS with overlap 2. Note also that a Krylov method different from CG +class="cmbx-12">preconditioner, i.e., RAS with overlap 2. Note also that a Krylov method must be used to solve the preconditioned system, since the preconditione in +class="cmbx-12">different from CG must be used to solve the preconditioned system, since nonsymmetric. The corresponding example program is available in the file -mld_dexample_1lev.f90. -

    For all the previous preconditioners, example programs where the sparse matrix and +class="cmbx-12">the preconditione in nonsymmetric. The corresponding example program is the right-hand side are generated by discretizing a PDE with Dirichlet boundary +class="cmbx-12">available in the file amg_dexample_1lev.f90. +

    For all the previous preconditioners, example programs where the sparse conditions are also available in the directory matrix and the right-hand side are generated by discretizing a PDE with +Dirichlet boundary conditions are also available in the directory +examples/pdegen. -

    . +

    @@ -270,7 +281,7 @@ class="cmr-12">.
    -

    +

    ... ...  
    ! build a V-cycle preconditioner with 1 block-Jacobi sweep (with @@ -284,7 +295,7 @@ class="cmr-12">.  
      call P%smoothers_build(A,desc_A,info)  
    ... ...
    -

    +


    Figure 3: setup of a multilevel preconditioner
    @@ -292,8 +303,8 @@ class="content">setup of a multilevel preconditioner

    -

    +

    @@ -305,7 +316,7 @@ class="content">setup of a multilevel preconditioner

    +

    ... ...  
    ! build a W-cycle preconditioner with 2 hybrid Gauss-Seidel sweeps @@ -321,7 +332,7 @@ class="content">setup of a multilevel preconditioner

    +


    Figure 4: setup of a multilevel preconditioner
    @@ -329,8 +340,8 @@ class="content">setup of a multilevel preconditioner

    -

    +

    @@ -342,7 +353,7 @@ class="content">setup of a multilevel preconditioner

    +

    ... ...  
    ! set RAS with overlap 2 and ILU(0) on the local blocks @@ -353,7 +364,7 @@ class="content">setup of a multilevel preconditioner

    +


    Figure 5: setup of a one-level Schwarz preconditioner.
    @@ -361,7 +372,7 @@ class="content">setup of a one-level Schwarz preconditioner.

    +

    @@ -369,13 +380,13 @@ class="content">setup of a one-level Schwarz preconditioner.

    [[front] [front] [up]

    +class="cmbx-12">up]

    diff --git a/docs/mld2p4-2.2-guide.pdf b/docs/mld2p4-2.2-guide.pdf deleted file mode 100644 index dada05df..00000000 --- a/docs/mld2p4-2.2-guide.pdf +++ /dev/null @@ -1,10752 +0,0 @@ -%PDF-1.5 -%ÔĊĜ -145 0 obj -<< -/Length 1210 ->> -stream -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -BT -/F17 24.7871 Tf 394.538 617.737 Td [(MLD2P4)]TJ -229.059 -27.023 Td [(User's)-375(and)-375(Reference)-375(Guide)]TJ -ET -q -1 0 0 1 93.6 572.468 cm -0 0 412.451 4.981 re f -Q -BT -/F19 14.3462 Tf 197.154 547.49 Td [(A)-350(guide)-350(for)-350(the)-350(MultiL)50(evel)-350(Domain)-350(De)50(c)50(omp)50(osition)]TJ -10.534 -17.256 Td [(Par)50(al)-50(lel)-350(Pr)50(e)50(c)50(onditioners)-350(Package)-350(b)50(ase)50(d)-350(on)-350(PSBLAS)]TJ -0 g 0 G -0 g 0 G -/F17 11.9552 Tf 218.644 -80.484 Td [(P)31(asqua)-375(D'Am)31(bra)]TJ/F37 11.9552 Tf -22.655 -13.948 Td [(IA)27(C-CNR,)-326(Naples,)-326(Italy)]TJ/F17 11.9552 Tf 11.494 -29.39 Td [(Daniela)-375(di)-375(Sera\014no)]TJ/F37 11.9552 Tf -181.63 -13.948 Td [(Univ)27(ersit)27(y)-326(of)-326(Campania)-326(\134Luigi)-327(V)82(an)27(vitelli",)-326(Caserta,)-326(Italy)]TJ/F17 11.9552 Tf 179.561 -29.389 Td [(Salv)62(atore)-375(Filipp)-31(one)]TJ/F37 11.9552 Tf -134.787 -13.948 Td [(Cran\014eld)-326(Univ)27(ersit)27(y)82(,)-326(Cran\014eld,)-327(United)-326(Kingdom)]TJ -0 g 0 G -0 g 0 G - 141.76 -80.02 Td [(Soft)27(w)28(are)-327(v)27(ersion)1(:)-436(2.2)]TJ 38.924 -13.948 Td [(July)-326(31,)-327(2018)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -154 0 obj -<< -/Length 143 ->> -stream -0 g 0 G -0 g 0 G -BT -/F19 11.9552 Tf 207.996 662.241 Td [(This)-350(p)50(age)-350(intentional)-50(ly)-350(left)-350(blank)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -158 0 obj -<< -/Length 3888 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 503.021 740.002 Td [(i)]TJ -0 g 0 G -/F17 14.3462 Tf -409.421 -35.866 Td [(Abstract)]TJ/F42 10.9091 Tf 0 -24.352 Td [(MLD2P4)-590(\050Mul)67(tiLevel)-591(D)1(omain)-591(Deco)1(mposition)-590(P)87(arallel)-590(Preconditioners)]TJ 0 -13.549 Td [(P)88(a)22(cka)22(ge)-480(based)-480(on)-480(PSBLAS)]TJ/F15 10.9091 Tf 152.9 0 Td [(\051)-431(is)-430(a)-431(pac)28(k)56(age)-431(of)-431(parallel)-430(algebraic)-431(m)28(ultilev)28(el)-431(precon-)]TJ -152.9 -13.549 Td [(ditioners.)-564(Th)1(e)-374(\014rst)-373(release)-373(of)-373(MLD2P4)-373(made)-373(a)28(v)56(ailable)-373(m)27(ultilev)28(el)-373(additiv)28(e)-373(and)-373(h)28(ybrid)]TJ 0 -13.549 Td [(Sc)28(h)28(w)27(arz)-443(preconditioners,)-471(as)-444(w)28(ell)-444(as)-444(one-lev)28(el)-444(additiv)28(e)-444(Sc)28(h)28(w)28(arz)-444(preconditioners.)-775(The)]TJ 0 -13.55 Td [(pac)28(k)55(age)-396(has)-397(b)-27(een)-397(extended)-396(to)-397(includ)1(e)-397(further)-396(m)28(ultilev)27(el)-396(cycles)-397(and)-396(smo)-28(others)-396(widely)]TJ 0 -13.549 Td [(used)-384(in)-384(m)28(ultigrid)-384(metho)-28(ds.)-597(In)-384(the)-384(m)28(ultilev)27(el)-384(case,)-397(a)-384(purely)-384(algebraic)-384(approac)28(h)-384(is)-384(ap-)]TJ 0 -13.549 Td [(plied)-402(to)-401(generate)-402(coarse-lev)28(el)-402(corrections,)-419(so)-402(that)-401(no)-402(geometric)-402(bac)28(kground)-402(i)1(s)-402(needed)]TJ 0 -13.549 Td [(concerning)-342(the)-342(matrix)-342(to)-341(b)-28(e)-342(preconditioned.)-470(The)-342(matrix)-342(is)-342(assumed)-341(to)-342(b)-28(e)-342(square,)-344(real)]TJ 0 -13.549 Td [(or)-333(complex.)]TJ 16.937 -13.55 Td [(MLD2P4)-362(has)-361(b)-28(een)-362(designed)-361(to)-362(pro)28(vide)-362(scalable)-361(and)-362(easy-to-use)-362(preconditioners)-361(in)]TJ -16.937 -13.549 Td [(the)-346(con)28(text)-346(of)-345(the)-346(PSBLAS)-345(\050P)27(arallel)-345(Sparse)-346(Basic)-346(Linear)-345(Algebra)-346(Subprograms\051)-345(com)-1(-)]TJ 0 -13.549 Td [(putational)-265(framew)28(ork)-265(and)-265(can)-266(b)-27(e)-265(used)-266(in)-265(conjuction)-265(with)-265(the)-265(Krylo)28(v)-265(solv)28(ers)-266(a)28(v)56(ailable)-265(in)]TJ 0 -13.549 Td [(this)-350(framew)28(ork.)-494(MLD2P4)-349(e)-1(n)1(ables)-350(the)-350(user)-350(to)-350(easily)-349(s)-1(p)-27(ecify)-350(di\013eren)28(t)-350(features)-350(of)-350(an)-349(al-)]TJ 0 -13.549 Td [(gebraic)-316(m)28(ultilev)28(el)-316(preconditioner,)-319(th)28(us)-316(allo)28(wing)-316(to)-315(searc)27(h)-315(for)-316(the)-316(\134b)-28(est")-315(preconditioner)]TJ 0 -13.55 Td [(for)-333(the)-334(prob)1(le)-1(m)-333(at)-333(hand.)]TJ 16.937 -13.549 Td [(The)-307(pac)28(k)55(age)-307(emplo)28(ys)-307(ob)-55(ject-orien)27(ted)-307(design)-306(te)-1(c)28(hniques)-307(in)-307(F)84(ortran)-307(2003,)-312(with)-307(in)28(ter-)]TJ -16.937 -13.549 Td [(faces)-391(to)-391(additional)-391(th)1(ird)-391(part)28(y)-391(libraries)-391(suc)28(h)-391(as)-391(MUMPS,)-391(UMFP)84(A)27(CK,)-390(Sup)-28(erLU,)-391(and)]TJ 0 -13.549 Td [(Sup)-28(erLU)]TJ -ET -q -1 0 0 1 136.861 449.647 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 140.134 449.448 Td [(Dist,)-322(whic)28(h)-319(can)-319(b)-28(e)-319(exploited)-319(in)-319(building)-319(m)28(ultilev)27(el)-319(preconditioners.)-439(The)-319(par-)]TJ -46.534 -13.549 Td [(allel)-382(implemen)27(tation)-382(is)-382(based)-382(on)-383(a)-382(Single)-382(Program)-382(Multiple)-383(D)1(ata)-383(\050SPMD\051)-382(paradigm;)]TJ 0 -13.55 Td [(the)-331(in)28(ter-pro)-27(ce)-1(ss)-330(comm)28(unication)-331(is)-330(based)-331(on)-330(MPI)-331(and)-330(is)-331(managed)-330(mainly)-331(through)-330(PS-)]TJ 0 -13.549 Td [(BLAS.)]TJ 16.937 -13.549 Td [(This)-353(guide)-354(pro)28(vides)-353(a)-354(brief)-353(description)-354(of)-353(the)-354(fu)1(nctionalities)-354(and)-353(the)-354(user)-353(in)28(terface)]TJ -16.937 -13.549 Td [(of)-333(MLD2P4.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -164 0 obj -<< -/Length 143 ->> -stream -0 g 0 G -0 g 0 G -BT -/F19 11.9552 Tf 207.996 662.241 Td [(This)-350(p)50(age)-350(intentional)-50(ly)-350(left)-350(blank)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -202 0 obj -<< -/Length 9442 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 496.96 740.002 Td [(iii)]TJ -0 g 0 G -/F17 14.3462 Tf -403.36 -35.866 Td [(Con)31(ten)31(ts)]TJ -0 0 1 rg 0 0 1 RG -/F44 10.9091 Tf 0 -24.458 Td [(Abstract)]TJ -0 g 0 G - 408.966 0 Td [(i)]TJ -0 0 1 rg 0 0 1 RG - -408.966 -24.458 Td [(1)-925(General)-383(Ov)32(erview)]TJ -0 g 0 G - [-26677(1)]TJ -0 0 1 rg 0 0 1 RG - 0 -24.459 Td [(2)-925(Co)-32(de)-383(Distribution)]TJ -0 g 0 G - [-26593(3)]TJ -0 0 1 rg 0 0 1 RG - 0 -24.458 Td [(3)-925(Con\014guring)-383(and)-384(Building)-383(MLD2P4)]TJ -0 g 0 G - [-17973(4)]TJ -0 0 1 rg 0 0 1 RG -/F15 10.9091 Tf 16.364 -13.549 Td [(3.1)-1022(Prerequisites)]TJ -0 g 0 G - [-947(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1781(4)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(3.2)-1022(Optional)-333(third)-334(par)1(t)27(y)-333(libraries)]TJ -0 g 0 G - [-711(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1781(5)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(3.3)-1022(Con\014guration)-333(options)]TJ -0 g 0 G - [-942(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1781(5)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.55 Td [(3.4)-1022(Bug)-334(r)1(e)-1(p)-27(orting)]TJ -0 g 0 G - [-431(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1280(10)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(3.5)-1022(Example)-333(and)-334(test)-333(programs)]TJ -0 g 0 G - [-669(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1280(10)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG -/F44 10.9091 Tf -16.364 -24.458 Td [(4)-925(Multigrid)-383(Bac)32(k)-1(grou)1(nd)]TJ -0 g 0 G - [-23948(11)]TJ -0 0 1 rg 0 0 1 RG -/F15 10.9091 Tf 16.364 -13.549 Td [(4.1)-1022(AMG)-334(p)1(rec)-1(on)1(ditioners)]TJ -0 g 0 G - [-988(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1281(12)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.55 Td [(4.2)-1022(Smo)-28(othed)-333(Aggregation)]TJ -0 g 0 G - [-447(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1281(12)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(4.3)-1022(Smo)-28(others)-333(and)-334(coarsest-lev)28(el)-333(solv)27(ers)]TJ -0 g 0 G - [-830(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1281(14)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG -/F44 10.9091 Tf -16.364 -24.458 Td [(5)-925(Getting)-383(Started)]TJ -0 g 0 G - [-27184(16)]TJ -0 0 1 rg 0 0 1 RG -/F15 10.9091 Tf 16.364 -13.549 Td [(5.1)-1022(Examples)]TJ -0 g 0 G - [-792(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1280(18)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG -/F44 10.9091 Tf -16.364 -24.459 Td [(6)-925(User)-383(In)32(terface)]TJ -0 g 0 G - [-27997(21)]TJ -0 0 1 rg 0 0 1 RG -/F15 10.9091 Tf 16.364 -13.549 Td [(6.1)-1022(Metho)-28(d)-333(init)]TJ -0 g 0 G - [-561(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1281(22)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(6.2)-1022(Metho)-28(d)-333(set)]TJ -0 g 0 G - [-833(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -0 g 0 G - [-1281(23)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(6.3)-1022(Metho)-28(d)-333(hierarc)28(h)27(y)]TJ -ET -q -1 0 0 1 220.316 370.537 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 223.588 370.338 Td [(build)]TJ -0 g 0 G - [-890(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1280(33)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - -113.624 -13.549 Td [(6.4)-1022(Metho)-28(d)-333(smo)-28(others)]TJ -ET -q -1 0 0 1 224.649 356.988 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 227.922 356.789 Td [(build)]TJ -0 g 0 G - [-492(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1280(34)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - -117.958 -13.55 Td [(6.5)-1022(Metho)-28(d)-333(build)]TJ -0 g 0 G - [-617(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1280(35)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(6.6)-1022(Metho)-28(d)-333(apply)]TJ -0 g 0 G - [-422(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1281(36)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(6.7)-1022(Metho)-28(d)-333(free)]TJ -0 g 0 G - [-475(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1281(37)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(6.8)-1022(Metho)-28(d)-333(descr)]TJ -0 g 0 G - [-608(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -0 g 0 G - [-1281(38)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(6.9)-1022(Auxiliary)-333(Metho)-28(ds)]TJ -0 g 0 G - [-692(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1280(38)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 25.091 -13.55 Td [(6.9.1)-1144(Metho)-28(d:)-445(d)1(ump)]TJ -0 g 0 G - [-639(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1281(38)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(6.9.2)-1144(Metho)-28(d:)-445(clon)1(e)]TJ -0 g 0 G - [-917(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1281(38)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(6.9.3)-1144(Metho)-28(d:)-445(sizeof)]TJ -0 g 0 G - [-772(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1280(39)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - 0 -13.549 Td [(6.9.4)-1144(Metho)-28(d:)-445(al)1(lo)-28(cate)]TJ -ET -q -1 0 0 1 252.134 235.045 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 255.407 234.846 Td [(wrk)]TJ -0 g 0 G - [-887(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1281(39)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - -120.352 -13.549 Td [(6.9.5)-1144(Metho)-28(d:)-445(f)1(ree)]TJ -ET -q -1 0 0 1 232.77 221.496 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 236.043 221.297 Td [(wrk)]TJ -0 g 0 G - [-329(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1280(39)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG -/F44 10.9091 Tf -142.443 -24.459 Td [(7)-925(Adding)-383(new)-384(smo)-32(other)-383(and)-383(solv)32(er)-384(ob)-64(jects)-383(to)-383(MLD2P4)]TJ -0 g 0 G - [-8165(41)]TJ -0 0 1 rg 0 0 1 RG - 0 -24.458 Td [(8)-925(Error)-383(Handling)]TJ -0 g 0 G - [-27434(43)]TJ -0 0 1 rg 0 0 1 RG - 0 -24.458 Td [(A)-631(License)]TJ -0 g 0 G - [-31489(44)]TJ -0 0 1 rg 0 0 1 RG - 0 -24.459 Td [(References)]TJ -0 g 0 G - [-31259(45)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -2 0 obj -<< -/Type /ObjStm -/N 100 -/First 814 -/Length 7188 ->> -stream -1 0 5 38 6 84 9 125 10 146 13 187 14 219 17 260 18 293 21 334 -22 381 25 427 26 458 29 504 30 552 33 598 34 637 37 683 38 714 41 760 -42 803 45 844 46 880 49 926 50 963 53 1009 54 1047 57 1093 58 1147 61 1188 -62 1219 65 1265 66 1291 69 1332 70 1362 73 1408 74 1437 77 1483 78 1511 81 1557 -82 1600 85 1646 86 1689 89 1735 90 1765 93 1811 94 1841 97 1887 98 1916 101 1962 -102 1993 105 2040 106 2076 109 2128 110 2161 113 2213 114 2247 117 2299 118 2334 121 2386 -122 2430 125 2482 126 2522 129 2564 130 2629 133 2671 134 2702 137 2745 138 2769 141 2812 -142 2837 143 2882 146 2996 147 3050 3 3104 144 3156 153 3249 155 3363 152 3417 157 3484 -159 3598 7 3652 156 3704 163 3797 165 3911 162 3965 201 4032 166 4430 167 4576 168 4722 -169 4868 170 5014 171 5166 172 5318 173 5470 174 5621 175 5772 176 5918 177 6070 178 6222 -% 1 0 obj -<< /S /GoTo /D (title.0) >> -% 5 0 obj -(MLD2P4 User's and Reference Guide) -% 6 0 obj -<< /S /GoTo /D (section*.1) >> -% 9 0 obj -(Abstract) -% 10 0 obj -<< /S /GoTo /D (section.1) >> -% 13 0 obj -(1 General Overview) -% 14 0 obj -<< /S /GoTo /D (section.2) >> -% 17 0 obj -(2 Code Distribution) -% 18 0 obj -<< /S /GoTo /D (section.3) >> -% 21 0 obj -(3 Configuring and Building MLD2P4) -% 22 0 obj -<< /S /GoTo /D (subsection.3.1) >> -% 25 0 obj -(3.1 Prerequisites) -% 26 0 obj -<< /S /GoTo /D (subsection.3.2) >> -% 29 0 obj -(3.2 Optional third party libraries) -% 30 0 obj -<< /S /GoTo /D (subsection.3.3) >> -% 33 0 obj -(3.3 Configuration options) -% 34 0 obj -<< /S /GoTo /D (subsection.3.4) >> -% 37 0 obj -(3.4 Bug reporting) -% 38 0 obj -<< /S /GoTo /D (subsection.3.5) >> -% 41 0 obj -(3.5 Example and test programs) -% 42 0 obj -<< /S /GoTo /D (section.4) >> -% 45 0 obj -(4 Multigrid Background) -% 46 0 obj -<< /S /GoTo /D (subsection.4.1) >> -% 49 0 obj -(4.1 AMG preconditioners) -% 50 0 obj -<< /S /GoTo /D (subsection.4.2) >> -% 53 0 obj -(4.2 Smoothed Aggregation) -% 54 0 obj -<< /S /GoTo /D (subsection.4.3) >> -% 57 0 obj -(4.3 Smoothers and coarsest-level solvers) -% 58 0 obj -<< /S /GoTo /D (section.5) >> -% 61 0 obj -(5 Getting Started) -% 62 0 obj -<< /S /GoTo /D (subsection.5.1) >> -% 65 0 obj -(5.1 Examples) -% 66 0 obj -<< /S /GoTo /D (section.6) >> -% 69 0 obj -(6 User Interface) -% 70 0 obj -<< /S /GoTo /D (subsection.6.1) >> -% 73 0 obj -(6.1 Method init) -% 74 0 obj -<< /S /GoTo /D (subsection.6.2) >> -% 77 0 obj -(6.2 Method set) -% 78 0 obj -<< /S /GoTo /D (subsection.6.3) >> -% 81 0 obj -(6.3 Method hierarchy\137build) -% 82 0 obj -<< /S /GoTo /D (subsection.6.4) >> -% 85 0 obj -(6.4 Method smoothers\137build) -% 86 0 obj -<< /S /GoTo /D (subsection.6.5) >> -% 89 0 obj -(6.5 Method build) -% 90 0 obj -<< /S /GoTo /D (subsection.6.6) >> -% 93 0 obj -(6.6 Method apply) -% 94 0 obj -<< /S /GoTo /D (subsection.6.7) >> -% 97 0 obj -(6.7 Method free) -% 98 0 obj -<< /S /GoTo /D (subsection.6.8) >> -% 101 0 obj -(6.8 Method descr) -% 102 0 obj -<< /S /GoTo /D (subsection.6.9) >> -% 105 0 obj -(6.9 Auxiliary Methods) -% 106 0 obj -<< /S /GoTo /D (subsubsection.6.9.1) >> -% 109 0 obj -(6.9.1 Method: dump) -% 110 0 obj -<< /S /GoTo /D (subsubsection.6.9.2) >> -% 113 0 obj -(6.9.2 Method: clone) -% 114 0 obj -<< /S /GoTo /D (subsubsection.6.9.3) >> -% 117 0 obj -(6.9.3 Method: sizeof) -% 118 0 obj -<< /S /GoTo /D (subsubsection.6.9.4) >> -% 121 0 obj -(6.9.4 Method: allocate\137wrk) -% 122 0 obj -<< /S /GoTo /D (subsubsection.6.9.5) >> -% 125 0 obj -(6.9.5 Method: free\137wrk) -% 126 0 obj -<< /S /GoTo /D (section.7) >> -% 129 0 obj -(7 Adding new smoother and solver objects to MLD2P4) -% 130 0 obj -<< /S /GoTo /D (section.8) >> -% 133 0 obj -(8 Error Handling) -% 134 0 obj -<< /S /GoTo /D (appendix.A) >> -% 137 0 obj -(A License) -% 138 0 obj -<< /S /GoTo /D (section*.4) >> -% 141 0 obj -(References) -% 142 0 obj -<< /S /GoTo /D [143 0 R /Fit] >> -% 143 0 obj -<< -/Type /Page -/Contents 145 0 R -/Resources 144 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 151 0 R ->> -% 146 0 obj -<< -/D [143 0 R /XYZ 92.6 752.957 null] ->> -% 147 0 obj -<< -/D [143 0 R /XYZ 93.6 715.095 null] ->> -% 3 0 obj -<< -/D [143 0 R /XYZ 93.6 715.095 null] ->> -% 144 0 obj -<< -/Font << /F17 148 0 R /F19 149 0 R /F37 150 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 153 0 obj -<< -/Type /Page -/Contents 154 0 R -/Resources 152 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 151 0 R ->> -% 155 0 obj -<< -/D [153 0 R /XYZ 85.4 752.957 null] ->> -% 152 0 obj -<< -/Font << /F19 149 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 157 0 obj -<< -/Type /Page -/Contents 158 0 R -/Resources 156 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 151 0 R ->> -% 159 0 obj -<< -/D [157 0 R /XYZ 92.6 752.957 null] ->> -% 7 0 obj -<< -/D [157 0 R /XYZ 93.6 722.069 null] ->> -% 156 0 obj -<< -/Font << /F15 160 0 R /F17 148 0 R /F42 161 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 163 0 obj -<< -/Type /Page -/Contents 164 0 R -/Resources 162 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 151 0 R ->> -% 165 0 obj -<< -/D [163 0 R /XYZ 85.4 752.957 null] ->> -% 162 0 obj -<< -/Font << /F19 149 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 201 0 obj -<< -/Type /Page -/Contents 202 0 R -/Resources 200 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 151 0 R -/Annots [ 166 0 R 167 0 R 168 0 R 169 0 R 170 0 R 171 0 R 172 0 R 173 0 R 174 0 R 175 0 R 176 0 R 177 0 R 178 0 R 179 0 R 180 0 R 181 0 R 182 0 R 183 0 R 184 0 R 185 0 R 186 0 R 187 0 R 188 0 R 189 0 R 190 0 R 191 0 R 192 0 R 193 0 R 194 0 R 195 0 R 196 0 R 197 0 R 198 0 R 199 0 R ] ->> -% 166 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 678.682 142.598 688.25] -/A << /S /GoTo /D (section*.1) >> ->> -% 167 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 654.223 209.755 663.792] -/A << /S /GoTo /D (section.1) >> ->> -% 168 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 629.765 210.673 639.333] -/A << /S /GoTo /D (section.2) >> ->> -% 169 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 603.186 304.709 614.875] -/A << /S /GoTo /D (section.3) >> ->> -% 170 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 589.636 197.294 601.205] -/A << /S /GoTo /D (subsection.3.1) >> ->> -% 171 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 576.087 276.233 587.777] -/A << /S /GoTo /D (subsection.3.2) >> ->> -% 172 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 562.538 239.779 574.228] -/A << /S /GoTo /D (subsection.3.3) >> ->> -% 173 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 548.989 202.93 560.557] -/A << /S /GoTo /D (subsection.3.4) >> ->> -% 174 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 535.44 268.203 547.129] -/A << /S /GoTo /D (subsection.3.5) >> ->> -% 175 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 510.981 233.255 522.671] -/A << /S /GoTo /D (section.4) >> ->> -% 176 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 497.432 239.279 509.122] -/A << /S /GoTo /D (subsection.4.1) >> ->> -% 177 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 483.883 245.172 495.572] -/A << /S /GoTo /D (subsection.4.2) >> ->> -% 178 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 472.455 308.869 482.023] -/A << /S /GoTo /D (subsection.4.3) >> ->> - -endstream -endobj -209 0 obj -<< -/Length 143 ->> -stream -0 g 0 G -0 g 0 G -BT -/F19 11.9552 Tf 207.996 662.241 Td [(This)-350(p)50(age)-350(intentional)-50(ly)-350(left)-350(blank)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -223 0 obj -<< -/Length 7908 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(1)]TJ -0 g 0 G - [-378(General)-378(O)30(ver)88(view)]TJ/F15 10.9091 Tf 406.997 0 Td [(1)]TJ -0 g 0 G -/F17 14.3462 Tf -406.997 -35.866 Td [(1)-1125(General)-375(Ov)31(erview)]TJ/F15 10.9091 Tf 0 -26.019 Td [(The)]TJ/F42 10.9091 Tf 21.602 0 Td [(Mul)67(tiLevel)-299(Domain)-299(Decom)1(position)-299(P)88(a)-1(rallel)-298(Preconditioners)-299(P)88(a)22(cka)22(ge)]TJ -21.602 -13.549 Td [(based)-485(on)-485(PSBLAS)-485(\050MLD2P4)]TJ/F15 10.9091 Tf 158.768 0 Td [(\051)-435(pro)27(vid)1(e)-1(s)-435(parallel)-435(Algebraic)-436(MultiGrid)-435(\050AMG\051)-435(and)]TJ -158.768 -13.55 Td [(Domain)-268(Decomp)-28(osition)-268(preconditioners)-269(\050see,)-281(e.g.,)-281([)]TJ -1 0 0 rg 1 0 0 RG - [(3)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-269(24)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-268(22)]TJ -0 g 0 G - [(]\051,)-281(to)-269(b)-27(e)-269(used)-268(in)-268(the)-269(iterativ)28(e)]TJ 0 -13.549 Td [(solution)-333(of)-334(lin)1(e)-1(ar)-333(systems,)]TJ/F22 10.9091 Tf 186.98 -16.123 Td [(Ax)]TJ/F15 10.9091 Tf 17.447 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(b;)]TJ -0 g 0 G -/F15 10.9091 Tf 182.57 0 Td [(\0501\051)]TJ -0 g 0 G - -398.512 -23.029 Td [(where)]TJ/F22 10.9091 Tf 31.935 0 Td [(A)]TJ/F15 10.9091 Tf 12.208 0 Td [(is)-369(a)-369(square,)-378(real)-369(or)-369(complex,)-378(sparse)-369(matrix.)-552(Th)1(e)-370(name)-369(of)-369(the)-369(pac)28(k)56(age)-369(comes)]TJ -44.143 -13.549 Td [(from)-452(its)-452(original)-452(implemen)28(tation,)-481(con)27(tai)1(ning)-452(m)27(ul)1(tilev)27(el)-452(additi)1(v)27(e)-452(and)-451(h)27(ybrid)-451(Sc)27(h)28(w)28(arz)]TJ 0 -13.549 Td [(preconditioners,)-514(as)-478(w)28(ell)-478(as)-478(one-lev)27(el)-478(additiv)28(e)-478(Sc)28(h)28(w)28(arz)-478(preconditioners.)-879(The)-478(curren)28(t)]TJ 0 -13.549 Td [(v)28(ersion)-381(extends)-381(the)-381(ori)1(ginal)-381(plan)-381(b)28(y)-381(including)-380(m)27(ultilev)28(el)-381(cycles)-380(and)-381(smo)-28(others)-381(widely)]TJ 0 -13.55 Td [(used)-333(in)-334(m)28(ultigrid)-333(metho)-28(ds.)]TJ 16.937 -14.407 Td [(The)-285(m)28(ultilev)28(el)-285(p)1(rec)-1(on)1(ditioners)-285(implemen)28(ted)-285(in)-284(MLD2P4)-285(are)-284(obtained)-285(b)28(y)-284(c)-1(om)28(bining)]TJ -16.937 -13.549 Td [(AMG)-263(cycles)-264(with)-263(smo)-28(others)-263(and)-264(coarsest-lev)28(el)-263(solv)27(ers.)-421(The)-263(V-,)-278(W)1(-)-1(,)-277(and)-263(K-cycles)-264([)]TJ -1 0 0 rg 1 0 0 RG - [(3)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-263(20)]TJ -0 g 0 G - [(])]TJ 0 -13.549 Td [(are)-392(a)28(v)56(ailable,)-407(whic)28(h)-392(allo)28(w)-392(to)-391(de\014ne)-392(almost)-392(all)-391(the)-392(preconditioners)-392(in)-392(th)1(e)-392(pac)28(k)55(age,)-406(in-)]TJ 0 -13.549 Td [(cluding)-394(the)-394(m)28(ultilev)28(el)-394(h)28(ybrid)-394(Sc)28(h)27(w)28(arz)-394(ones;)-424(a)-394(sp)-28(eci\014c)-394(cycle)-394(is)-394(implemen)28(ted)-394(to)-394(obtain)]TJ 0 -13.55 Td [(m)28(ultilev)28(el)-498(additiv)28(e)-498(Sc)28(h)28(w)28(arz)-498(preconditioners.)-937(The)-497(Jacobi,)-539(h)28(ybrid)-498(forw)28(ard/bac)28(kw)28(ard)]TJ 0 -13.549 Td [(Gauss-Seidel,)-366(blo)-27(c)27(k-Jacobi,)-365(and)-359(additiv)28(e)-360(Sc)28(h)28(w)28(arz)-359(m)-1(eth)1(o)-28(ds)-359(are)-360(a)28(v)56(ailable)-359(as)-360(smo)-27(others.)]TJ 0 -13.549 Td [(An)-279(algebraic)-279(appr)1(oac)27(h)-279(i)1(s)-279(used)-279(to)-279(generate)-279(a)-279(hierarc)28(h)28(y)-279(of)-279(coarse-lev)28(el)-279(matrices)-279(and)-278(op)-28(er-)]TJ 0 -13.549 Td [(ators,)-283(without)-270(explicitly)-270(using)-270(an)28(y)-271(inf)1(ormation)-271(on)-270(the)-270(geometry)-270(of)-270(the)-271(original)-270(problem,)]TJ 0 -13.549 Td [(e.g.,)-256(the)-237(discretization)-237(of)-237(a)-237(PDE.)-237(T)84(o)-237(this)-237(end,)-256(the)-237(smo)-28(othed)-237(aggregation)-237(tec)28(hnique)-237([)]TJ -1 0 0 rg 1 0 0 RG - [(2)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-236(26)]TJ -0 g 0 G - [(])]TJ 0 -13.55 Td [(is)-377(applied.)-575(Either)-376(exact)-377(or)-377(appro)28(ximate)-377(solv)28(ers)-377(can)-377(b)-28(e)-377(used)-376(on)-377(the)-377(coarsest-lev)28(el)-377(sys-)]TJ 0 -13.549 Td [(tem.)-441(Sp)-27(eci\014cally)83(,)-324(di\013eren)28(t)-322(sparse)-322(LU)-322(factorizations)-321(from)-322(external)-322(pac)28(k)55(ages,)-324(and)-321(nativ)27(e)]TJ 0 -13.549 Td [(incomplete)-285(LU)-285(factorizations)-285(and)-285(Jacobi,)-295(h)28(ybrid)-285(Gauss-Seidel,)-294(and)-285(blo)-28(c)28(k-Jacobi)-285(solv)28(ers)]TJ 0 -13.549 Td [(are)-333(a)27(v)56(ailable.)-444(All)-334(smo)-28(oth)1(e)-1(r)1(s)-334(can)-333(b)-28(e)-333(also)-334(exploited)-333(as)-333(one-lev)27(el)-333(preconditioners.)]TJ 16.937 -14.408 Td [(MLD2P4)-267(is)-267(written)-268(in)-267(F)84(ortran)-267(2003,)-281(follo)28(wing)-267(an)-267(ob)-56(ject-orien)28(ted)-267(design)-268(th)1(rough)-268(the)]TJ -16.937 -13.549 Td [(exploitation)-338(of)-337(features)-338(suc)28(h)-338(as)-337(abstract)-338(data)-338(t)28(yp)-28(e)-337(creation,)-339(t)28(yp)-28(e)-338(extension,)-338(functional)]TJ 0 -13.549 Td [(o)28(v)28(erloading,)-326(and)-325(dynamic)-324(memory)-325(managemen)28(t.)-441(The)-325(parallel)-324(implemen)28(tation)-325(is)-324(based)]TJ 0 -13.549 Td [(on)-424(a)-424(Single)-424(Program)-424(Multiple)-424(Data)-424(\050SPMD\051)-424(paradigm.)-717(Single)-424(and)-424(double)-424(precision)]TJ 0 -13.549 Td [(implemen)28(tations)-486(of)-486(MLD2P4)-486(are)-486(a)28(v)56(ailable)-486(for)-486(b)-27(oth)-486(the)-486(real)-486(and)-486(the)-486(complex)-485(cas)-1(e,)]TJ 0 -13.55 Td [(whic)28(h)-334(can)-333(b)-28(e)-333(used)-333(through)-333(a)-334(single)-333(in)28(terface.)]TJ 16.937 -14.407 Td [(MLD2P4)-229(has)-230(b)-27(e)-1(en)-229(designed)-229(to)-230(implemen)28(t)-230(scalable)-229(and)-229(easy-to-use)-230(m)28(ultilev)28(el)-230(precon-)]TJ -16.937 -13.549 Td [(ditioners)-349(in)-349(the)-350(con)28(text)-349(of)-349(the)-349(PSBLAS)-349(\050P)27(arallel)-349(Sparse)-349(BLAS\051)-349(computational)-349(frame-)]TJ 0 -13.549 Td [(w)28(ork)-360([)]TJ -1 0 0 rg 1 0 0 RG - [(15)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-360(14)]TJ -0 g 0 G - [(].)-524(PSBLAS)-359(pro)28(vides)-360(basic)-360(linear)-360(algebra)-360(op)-27(erators)-360(and)-360(data)-360(managemen)28(t)]TJ 0 -13.549 Td [(facilities)-414(for)-414(distributed)-414(sparse)-414(matrices,)-434(as)-414(w)27(ell)-414(as)-414(parallel)-414(Krylo)28(v)-414(solv)28(ers)-414(whic)28(h)-414(can)]TJ 0 -13.55 Td [(b)-28(e)-401(used)-402(with)-401(the)-401(MLD2P4)-401(prec)-1(on)1(ditioners.)-649(The)-401(c)27(hoice)-401(of)-401(PSBLAS)-401(has)-402(b)-28(een)-401(mainly)]TJ 0 -13.549 Td [(motiv)56(ated)-431(b)27(y)-431(the)-431(need)-431(of)-430(ha)27(ving)-431(a)-431(p)-27(ortable)-431(and)-431(e\016cien)28(t)-431(soft)27(w)28(are)-431(infrastructure)-431(im-)]TJ 0 -13.549 Td [(plemen)28(ting)-386(\134de)-385(facto")-386(standard)-386(parallel)-385(sparse)-386(linear)-385(algebra)-386(k)28(ernels,)-399(to)-386(pursue)-385(goals)]TJ 0 -13.549 Td [(suc)28(h)-315(as)-316(p)-27(e)-1(r)1(formance,)-319(p)-28(ortabilit)28(y)83(,)-319(mo)-27(dularit)28(y)-316(ed)-315(extensibilit)28(y)-315(in)-315(the)-316(dev)28(elopmen)28(t)-315(of)-315(the)]TJ 0 -13.549 Td [(preconditioner)-403(pac)28(k)56(age.)-653(On)-402(the)-403(other)-403(hand,)-420(the)-402(implemen)27(tation)-402(of)-403(MLD2P4)-402(has)-403(led)]TJ 0 -13.55 Td [(to)-431(some)-431(revisions)-431(and)-431(exten)28(tions)-431(of)-431(the)-431(original)-431(PSBLAS)-431(k)28(ernels.)-737(The)-431(in)28(ter-pro)-28(cess)]TJ 0 -13.549 Td [(com)28(unication)-458(required)-458(b)28(y)-458(MLD2P4)-458(is)-458(encapsulated)-458(in)-457(the)-458(PSBLAS)-458(routines;)-520(there-)]TJ 0 -13.549 Td [(fore,)-298(MLD2P4)-290(can)-289(b)-28(e)-290(r)1(un)-290(on)-289(an)27(y)-289(parallel)-290(mac)28(hine)-289(where)-290(PSBLAS)-289(implemen)28(tations)-290(are)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -247 0 obj -<< -/Length 5319 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(2)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [(a)28(v)55(ailable.)]TJ 16.936 -13.549 Td [(MLD2P4)-342(has)-341(a)-342(la)28(y)28(ered)-342(and)-342(mo)-27(dular)-342(soft)28(w)28(are)-342(arc)28(hitecture)-342(where)-342(three)-341(main)-342(la)28(y)28(ers)]TJ -16.936 -13.549 Td [(can)-458(b)-28(e)-458(iden)28(ti\014ed.)-819(The)-458(lo)28(w)28(er)-458(la)27(y)28(er)-458(consists)-458(of)-458(the)-458(PSBLAS)-458(k)28(ernels,)-490(the)-458(middle)-458(one)]TJ 0 -13.549 Td [(implemen)28(ts)-458(the)-457(construction)-457(and)-458(application)-457(phases)-457(of)-458(the)-457(preconditioners,)-489(and)-457(the)]TJ 0 -13.549 Td [(upp)-28(er)-433(one)-433(pro)28(vides)-433(a)-433(uniform)-433(in)28(terface)-433(to)-433(all)-434(th)1(e)-434(preconditi)1(oners)-1(.)-743(This)-433(arc)27(h)1(ite)-1(ctu)1(re)]TJ 0 -13.55 Td [(allo)28(ws)-413(for)-413(di\013eren)28(t)-413(lev)28(els)-413(of)-412(use)-413(of)-413(the)-413(pac)28(k)56(age:)-604(few)-412(blac)27(k-b)-27(o)27(x)-412(routines)-413(at)-413(the)-412(upp)-28(er)]TJ 0 -13.549 Td [(la)28(y)28(er)-305(allo)28(w)-305(all)-305(users)-304(to)-305(easily)-305(build)-304(and)-305(apply)-304(an)28(y)-305(preconditioner)-305(a)28(v)56(ailable)-305(in)-305(M)1(LD2P4;)]TJ 0 -13.549 Td [(facilities)-432(are)-432(also)-433(a)28(v)56(ailable)-433(allo)28(wing)-432(exp)-28(ert)-432(users)-432(to)-432(exte)-1(n)1(d)-433(the)-432(set)-432(of)-432(smo)-28(others)-432(and)]TJ 0 -13.549 Td [(solv)28(ers)-334(for)-333(building)-333(new)-333(v)27(ersion)1(s)-334(of)-333(the)-333(prec)-1(on)1(ditioners)-334(\050see)-333(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(7)]TJ -0 g 0 G - [(\051.)]TJ 16.936 -13.549 Td [(W)83(e)-347(n)1(ote)-347(that)-347(the)-347(user)-347(in)28(terface)-347(of)-347(MLD2P)1(4)-347(2.1)-347(has)-347(b)-28(een)-347(extend)1(e)-1(d)-346(with)-347(resp)-28(ect)-347(to)]TJ -16.936 -13.55 Td [(the)-369(previous)-368(v)27(ersions)-368(in)-369(order)-369(to)-368(separate)-369(the)-369(construction)-368(of)-369(the)-369(m)28(ultilev)28(el)-369(hierarc)28(h)28(y)]TJ 0 -13.549 Td [(from)-320(the)-320(construction)-321(of)-320(the)-320(smo)-28(others)-320(and)-320(solv)28(ers,)-323(and)-320(to)-321(allo)28(w)-320(for)-320(more)-320(\015exibilit)27(y)-320(at)]TJ 0 -13.549 Td [(eac)28(h)-378(lev)28(el.)-579(The)-378(soft)28(w)28(are)-378(arc)28(hitecture)-378(describ)-28(ed)-378(in)-378([)]TJ -1 0 0 rg 1 0 0 RG - [(8)]TJ -0 g 0 G - [(])-378(has)-378(signi\014can)28(tly)-378(ev)28(olv)28(ed)-378(to)-28(o,)-389(in)]TJ 0 -13.549 Td [(order)-366(to)-365(fully)-366(exploit)-365(the)-366(F)83(ortran)-365(2003)-366(features)-365(impleme)-1(n)28(ted)-365(in)-366(PSBLAS)-365(3.)-542(Ho)28(w)28(ev)27(er,)]TJ 0 -13.549 Td [(compatibilit)28(y)-333(with)-334(previous)-333(v)28(ersions)-334(h)1(as)-334(b)-28(een)-333(preserv)28(ed.)]TJ 16.936 -13.55 Td [(This)-380(guide)-380(is)-380(organized)-380(as)-380(follo)28(ws.)-585(General)-380(information)-380(on)-380(the)-380(distribution)-380(of)-380(the)]TJ -16.936 -13.549 Td [(source)-320(co)-28(de)-320(is)-320(rep)-28(orted)-320(in)-320(Section)]TJ -0 0 1 rg 0 0 1 RG - [-320(2)]TJ -0 g 0 G - [(,)-323(while)-320(details)-320(on)-320(the)-320(con\014guration)-320(and)-320(installation)]TJ 0 -13.549 Td [(of)-394(the)-394(pac)28(k)55(age)-394(are)-394(giv)28(en)-394(in)-394(Section)]TJ -0 0 1 rg 0 0 1 RG - [-394(3)]TJ -0 g 0 G - [(.)-627(A)-394(short)-394(description)-394(of)-394(the)-394(preconditioners)-394(im-)]TJ 0 -13.549 Td [(plemen)28(ted)-395(in)-395(MLD2P4)-395(is)-395(pro)28(vided)-395(in)-395(S)1(e)-1(ction)]TJ -0 0 1 rg 0 0 1 RG - [-394(4)]TJ -0 g 0 G - [(,)-411(to)-395(help)-394(the)-395(users)-395(in)-395(c)28(ho)-28(osing)-395(among)]TJ 0 -13.549 Td [(them.)-430(The)-291(basics)-291(for)-290(building)-291(and)-290(applying)-291(the)-290(preconditioners)-291(with)-290(the)-291(Krylo)28(v)-291(solv)28(ers)]TJ 0 -13.55 Td [(implemen)28(ted)-379(in)-379(PSBLAS)-378(are)-379(rep)-28(orted)-378(in)-379(Section)]TJ -0 0 1 rg 0 0 1 RG - [-379(5)]TJ -0 g 0 G - [(,)-390(where)-379(the)-378(F)83(ortran)-379(co)-27(des)-379(of)-379(a)-379(few)]TJ 0 -13.549 Td [(sample)-405(programs)-405(are)-406(also)-405(sho)28(wn.)-660(A)-405(reference)-405(guide)-405(for)-405(the)-406(u)1(s)-1(er)-405(in)28(terface)-405(routines)-405(is)]TJ 0 -13.549 Td [(pro)28(vided)-258(in)-258(Section)]TJ -0 0 1 rg 0 0 1 RG - [-258(6)]TJ -0 g 0 G - [(.)-420(In)1(formation)-258(on)-258(the)-259(extension)-258(of)-258(the)-258(pac)28(k)56(age)-259(th)1(rough)-258(the)-258(addition)]TJ 0 -13.549 Td [(of)-354(new)-354(smo)-28(others)-354(and)-354(solv)28(ers)-354(is)-354(rep)-28(orted)-354(in)-354(Section)]TJ -0 0 1 rg 0 0 1 RG - [-354(7)]TJ -0 g 0 G - [(.)-507(The)-354(error)-354(handling)-354(mec)28(hanism)]TJ 0 -13.549 Td [(used)-357(b)28(y)-357(the)-357(pac)28(k)55(age)-357(is)-357(brie\015y)-357(describ)-28(ed)-357(in)-357(Section)]TJ -0 0 1 rg 0 0 1 RG - [-357(8)]TJ -0 g 0 G - [(.)-515(The)-357(cop)28(yrigh)28(t)-357(terms)-357(c)-1(on)1(c)-1(ern)1(ing)]TJ 0 -13.549 Td [(the)-333(distribution)-333(and)-334(mo)-27(di\014cation)-334(of)-333(MLD2P4)-333(are)-334(rep)-27(orted)-334(in)-333(App)-28(end)1(ix)]TJ -0 0 1 rg 0 0 1 RG - [-334(A)]TJ -0 g 0 G - [(.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -253 0 obj -<< -/Length 3340 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(2)]TJ -0 g 0 G - [-378(Code)-378(D)1(istri)-1(bution)]TJ/F15 10.9091 Tf 406.997 0 Td [(3)]TJ -0 g 0 G -/F17 14.3462 Tf -406.997 -35.866 Td [(2)-1125(Co)-31(de)-375(Distribution)]TJ/F15 10.9091 Tf 0 -24.352 Td [(MLD2P4)-333(is)-334(a)28(v)56(ailable)-334(f)1(rom)-334(the)-333(w)28(eb)-334(site)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 43.637 -22.515 Td [(https://github.com/sfilippone/mld2p4-2)]TJ/F15 10.9091 Tf -43.637 -22.516 Td [(where)-333(con)27(tact)-333(p)-28(oin)28(ts)-333(for)-333(further)-334(information)-333(can)-333(b)-28(e)-333(also)-334(foun)1(d.)]TJ 16.937 -13.549 Td [(The)-299(soft)28(w)28(are)-299(is)-298(a)27(v)56(ailable)-298(under)-299(a)-299(mo)-27(di\014ed)-299(BSD)-298(lice)-1(n)1(s)-1(e,)-305(as)-299(sp)-28(eci\014ed)-298(in)-299(App)-27(endix)]TJ -0 0 1 rg 0 0 1 RG - [-299(A)]TJ -0 g 0 G - [(;)]TJ -16.937 -13.549 Td [(please)-448(note)-448(that)-448(some)-448(of)-448(the)-448(optional)-448(third)-448(part)28(y)-448(libraries)-448(ma)28(y)-448(b)-28(e)-448(licensed)-448(under)-448(a)]TJ 0 -13.55 Td [(di\013eren)28(t)-366(and)-366(more)-366(stringen)28(t)-366(license,)-374(most)-366(notably)-366(the)-366(GPL,)-366(and)-365(this)-366(should)-366(b)-28(e)-366(tak)28(en)]TJ 0 -13.549 Td [(in)28(to)-333(ac)-1(coun)28(t)-333(when)-333(treating)-334(deriv)28(ed)-333(w)28(orks.)]TJ 16.937 -13.549 Td [(The)-333(library)-333(de\014nes)-334(a)-333(v)28(ersion)-334(string)-333(with)-333(the)-334(constan)28(t)]TJ/F45 10.9091 Tf 134.88 -24.508 Td [(mld_version_string_)]TJ/F15 10.9091 Tf -151.817 -24.508 Td [(whose)-333(curren)27(t)-333(v)56(alue)-334(is)]TJ/F45 10.9091 Tf 109.273 0 Td [(2.1.0)]TJ/F15 10.9091 Tf 28.636 0 Td [(.)]TJ/F17 11.9552 Tf -137.909 -29.213 Td [(Con)31(tributors)]TJ/F15 10.9091 Tf 0 -20.595 Td [(Con)28(tributors)-333(to)-334(v)28(ersion)-333(2:)]TJ -0 g 0 G -/F25 10.9091 Tf 16.364 -22.515 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(Salv)56(atore)-334(Filipp)-27(one,)-334(Cran\014eld)-333(Univ)28(ersit)28(y)83(,)-333(UK;)]TJ -0 g 0 G -/F25 10.9091 Tf -10.909 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(P)28(asqua)-333(D'Am)27(bra,)-333(IA)28(C-CNR,)-334(Naples,)-333(IT;)]TJ -0 g 0 G -/F25 10.9091 Tf -10.909 -22.515 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(Daniela)-333(di)-334(Sera\014)1(no,)-334(Univ)28(ersit)28(y)-333(of)-334(Campania)-333(\134L.)-333(V)83(an)28(vitelli",)-333(Case)-1(r)1(ta,)-334(IT;)]TJ -0 g 0 G -/F25 10.9091 Tf -10.909 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(Am)28(bra)-334(Ab)-27(dullahi)-333(Hassan,)-334(Univ)28(ersit)28(y)-333(of)-334(Rome)-333(\134T)83(or)-333(V)83(ergata",)-333(IT.)]TJ -27.273 -22.515 Td [(Con)28(tributors)-333(to)-334(v)28(ersion)-333(1:)]TJ -0 g 0 G -/F25 10.9091 Tf 16.364 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(Salv)56(atore)-334(Filipp)-27(one;)]TJ -0 g 0 G -/F25 10.9091 Tf -10.909 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(P)28(asqua)-333(D'Am)27(bra;)]TJ -0 g 0 G -/F25 10.9091 Tf -10.909 -22.515 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(Daniela)-333(di)-334(Sera\014)1(no;)]TJ -0 g 0 G -/F25 10.9091 Tf -10.909 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(Alfredo)-333(Buttari,)-333(CNR)-1(S)1(-IR)-1(IT,)-333(T)83(ou)1(louse)-1(,)-333(F.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -273 0 obj -<< -/Length 7597 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(4)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F17 14.3462 Tf -203.265 -35.866 Td [(3)-1125(Con\014guring)-375(and)-375(Building)-375(MLD2P4)]TJ/F15 10.9091 Tf 0 -24.956 Td [(In)-292(order)-293(to)-292(build)-292(MLD2P4)-293(it)-292(is)-292(necessary)-293(to)-292(set)-293(up)-292(a)-292(Mak)28(e)-1(\014)1(le)-293(with)-292(appropriate)-292(sys)-1(t)1(e)-1(m-)]TJ 0 -13.549 Td [(dep)-28(enden)28(t)-367(v)56(ariables;)-384(this)-366(is)-367(done)-367(b)28(y)-367(means)-367(of)-367(the)]TJ/F45 10.9091 Tf 242.533 0 Td [(configure)]TJ/F15 10.9091 Tf 55.547 0 Td [(script.)-545(The)-367(distribution)]TJ -298.08 -13.549 Td [(also)-353(includes)-353(the)-354(auto)-27(c)-1(on)1(f)-354(and)-353(automak)28(e)-353(sources)-354(emplo)28(y)28(ed)-353(to)-354(generate)-353(the)-353(script,)-358(but)]TJ 0 -13.549 Td [(usually)-333(this)-334(i)1(s)-334(not)-333(needed)-333(to)-334(build)-333(the)-333(soft)27(w)28(are.)]TJ 16.936 -13.86 Td [(MLD2P4)-390(is)-390(implemen)28(ted)-391(almost)-390(en)28(tirely)-390(in)-390(F)83(ortran)-390(2003,)-404(with)-390(some)-390(in)28(terfaces)-391(to)]TJ -16.936 -13.549 Td [(external)-373(libraries)-374(in)-373(C;)-373(the)-374(F)84(ortran)-373(com)-1(p)1(iler)-374(m)28(ust)-373(supp)-28(ort)-373(the)-374(F)84(ortran)-374(2003)-373(standard)]TJ 0 -13.55 Td [(plus)-480(the)-480(extension)]TJ/F45 10.9091 Tf 94.928 0 Td [(MOLD=)]TJ/F15 10.9091 Tf 33.875 0 Td [(feature,)-517(whic)28(h)-480(enhances)-481(the)-480(usabilit)28(y)-480(of)]TJ/F45 10.9091 Tf 202.591 0 Td [(ALLOCATE)]TJ/F15 10.9091 Tf 45.818 0 Td [(.)-480(Man)28(y)]TJ -377.212 -13.549 Td [(compilers)-414(do)-414(th)1(is;)-454(in)-414(particular,)-434(this)-414(is)-413(supp)-28(orted)-414(b)28(y)-414(the)-414(GNU)-413(F)83(ortran)-414(compiler,)-433(for)]TJ 0 -13.549 Td [(whic)28(h)-361(w)28(e)-360(recommend)-361(to)-360(use)-361(at)-360(least)-360(v)27(ersion)-360(4.8.)-526(The)-360(soft)28(w)28(are)-361(de\014nes)-360(data)-361(t)28(yp)-28(es)-360(and)]TJ 0 -13.549 Td [(in)28(terfaces)-334(for)-333(real)-333(and)-333(complex)-334(data,)-333(in)-333(b)-28(oth)-333(single)-334(and)-333(double)-333(precision.)]TJ 16.936 -13.86 Td [(Building)-395(MLD2P4)-395(requires)-395(some)-395(base)-395(lib)1(raries)-395(\050see)-395(Section)]TJ -0 0 1 rg 0 0 1 RG - [-395(3.1)]TJ -0 g 0 G - [(\051;)-426(in)28(terfaces)-395(to)-395(op-)]TJ -16.936 -13.549 Td [(tional)-541(third-part)28(y)-541(librari)1(e)-1(s,)-592(whic)27(h)-540(extend)-541(the)-541(functionalities)-541(of)-541(MLD2P4)-541(\050see)-541(Sec-)]TJ 0 -13.55 Td [(tion)]TJ -0 0 1 rg 0 0 1 RG - [-331(3.2)]TJ -0 g 0 G - [(\051,)-331(are)-331(also)-331(a)28(v)55(ailable.)-443(Man)27(y)-331(Lin)28(ux)-331(distrib)1(utions)-331(\050e.g.,)-332(Ubun)28(tu,)-331(F)83(edora,)-331(Cen)27(t)1(OS\051)]TJ 0 -13.549 Td [(pro)28(vide)-289(precompiled)-289(pac)28(k)55(ages)-289(for)-288(the)-289(prerequisite)-289(and)-289(optional)-289(soft)28(w)28(are.)-430(In)-289(man)28(y)-289(cases)]TJ 0 -13.549 Td [(these)-419(pac)28(k)55(ages)-419(are)-419(split)-419(b)-28(et)28(w)27(een)-419(a)-419(run)28(time)-419(part)-419(and)-419(a)-419(\134dev)27(elop)-27(er")-419(part;)-462(in)-419(order)-420(to)]TJ 0 -13.549 Td [(build)-301(MLD2P4)-301(y)28(ou)-302(need)-301(b)-28(oth)1(.)-434(A)-301(description)-302(of)-301(the)-301(base)-301(and)-301(optional)-301(soft)27(w)28(are)-301(used)-301(b)27(y)]TJ 0 -13.549 Td [(MLD2P4)-333(is)-334(giv)28(en)-333(in)-333(the)-334(next)-333(sections.)]TJ/F17 11.9552 Tf 0 -30.989 Td [(3.1)-1125(Prerequisites)]TJ/F15 10.9091 Tf 0 -21.199 Td [(The)-333(follo)28(wing)-334(base)-333(libraries)-333(are)-334(needed:)]TJ -0 g 0 G -/F44 10.9091 Tf 0 -23.758 Td [(BLAS)]TJ -0 g 0 G -/F15 10.9091 Tf 38.378 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(11)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-425(12)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-424(18)]TJ -0 g 0 G - [(])-425(Man)28(y)-425(v)28(endors)-424(pro)27(v)1(ide)-425(optimized)-425(v)28(ersions)-425(of)-424(BLAS;)-425(if)-424(no)-425(v)28(endor)]TJ -11.105 -13.55 Td [(v)28(ersion)-523(is)-524(a)28(v)56(ailable)-523(for)-523(a)-524(giv)28(en)-523(platform,)-570(the)-524(A)84(TLAS)-523(soft)28(w)27(are)-523(\050)]TJ -0 1 0 0 k 0 1 0 0 K -/F45 10.9091 Tf 321.68 0 Td [(math-)-46(atlas.)]TJ -321.68 -13.549 Td [(sourceforge.net)]TJ -0 g 0 G -/F15 10.9091 Tf 85.908 0 Td [(\051)-449(ma)28(y)-449(b)-27(e)-449(emplo)28(y)27(ed.)-790(The)-449(reference)-449(BLAS)-448(from)-449(Netlib)-449(\050)]TJ -0 1 0 0 k 0 1 0 0 K -/F45 10.9091 Tf 276.361 0 Td [(www.)]TJ -362.269 -13.549 Td [(netlib.org/blas)]TJ -0 g 0 G -/F15 10.9091 Tf 85.908 0 Td [(\051)-366(are)-367(mean)28(t)-366(to)-367(de\014ne)-366(the)-367(stand)1(ard)-367(b)-28(eha)28(viour)-366(of)-366(the)-367(BLAS)-366(in-)]TJ -85.908 -13.549 Td [(terface,)-302(so)-294(they)-293(are)-294(not)-294(optimized)-294(for)-294(an)28(y)-294(particular)-293(plaftorm,)-302(and)-294(should)-293(only)-294(b)-28(e)]TJ 0 -13.549 Td [(used)-336(as)-336(a)-336(last)-336(resort.)-452(Note)-336(that)-336(BLAS)-335(com)-1(p)1(utations)-336(form)-336(a)-336(relativ)28(ely)-336(small)-336(part)]TJ 0 -13.55 Td [(of)-466(the)-466(MLD2P4/PSBLAS)-466(computations;)-532(they)-466(are)-466(ho)28(w)27(ev)28(er)-466(critical)-466(when)-466(using)]TJ 0 -13.549 Td [(preconditioners)-311(based)-310(on)-311(MUMPS,)-311(UMFP)84(A)27(CK)-310(or)-311(Sup)-28(erLU)-310(third)-311(part)28(y)-311(libraries.)]TJ 0 -13.549 Td [(Note)-262(that)-262(UMFP)83(A)28(CK)-262(requires)-262(a)-262(full)-262(LAP)83(A)28(CK)-262(library;)-286(our)-262(exp)-28(erience)-262(is)-262(that)-262(con-)]TJ 0 -13.549 Td [(\014guring)-294(A)83(TLAS)-295(f)1(or)-295(building)-294(full)-295(LAP)84(A)27(CK)-294(do)-28(es)-295(not)-294(w)28(ork)-295(in)-294(the)-295(correct)-295(w)28(a)28(y)83(.)-431(Our)]TJ 0 -13.549 Td [(advice)-232(is)-232(\014rst)-232(to)-232(do)28(wnload)-232(the)-232(LAP)84(A)28(CK)-232(tar\014le)-232(from)]TJ -0 1 0 0 k 0 1 0 0 K -/F45 10.9091 Tf 244.801 0 Td [(www.netlib.org/lapack)]TJ -0 g 0 G -/F15 10.9091 Tf 122.801 0 Td [(and)]TJ -367.602 -13.55 Td [(install)-401(it)-402(indep)-27(enden)27(tly)-401(of)-401(A)83(TLAS.)-401(In)-402(this)-401(case,)-419(y)28(ou)-401(need)-402(to)-401(mo)-28(dify)-401(the)-402(OPTS)]TJ 0 -13.549 Td [(and)-394(NOOPT)-393(de\014nitions)-394(for)-394(including)-394(-fPIC)-393(c)-1(omp)1(ilation)-394(option)-394(in)-394(the)-394(mak)28(e.inc)]TJ 0 -13.549 Td [(\014le)-333(of)-334(the)-333(LAP)83(A)28(CK)-333(library)83(.)]TJ -0 g 0 G -/F44 10.9091 Tf -27.273 -23.759 Td [(MPI)]TJ -0 g 0 G -/F15 10.9091 Tf 30.697 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(17)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-340(23)]TJ -0 g 0 G - [(])-340(A)-341(v)28(ersion)-340(of)-340(MPI)-340(is)-341(a)28(v)56(ailable)-341(on)-340(most)-340(high-p)-28(erformance)-340(computing)-340(sys-)]TJ -3.424 -13.549 Td [(tems.)]TJ -0 g 0 G -/F44 10.9091 Tf -27.273 -23.759 Td [(PSBLAS)]TJ -0 g 0 G -/F15 10.9091 Tf 53.924 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-480(15)]TJ -0 g 0 G - [(])-480(P)28(arallel)-480(Sparse)-480(BLAS)-480(\050PSBLAS\051)-480(is)-480(a)27(v)56(ailable)-480(from)]TJ -0 1 0 0 k 0 1 0 0 K -/F45 10.9091 Tf 295.528 0 Td [(github.com/)]TJ -322.179 -13.549 Td [(sfilippone/psblas3)]TJ -0 g 0 G -/F15 10.9091 Tf 103.089 0 Td [(;)-342(v)27(ersion)-339(3.5.0)-339(\050or)-340(later\051)-339(is)-340(required.)-462(Indeed,)-341(all)-339(the)-340(prereq-)]TJ -103.089 -13.549 Td [(uisites)-333(listed)-334(so)-333(far)-333(are)-334(also)-333(prerequisites)-333(of)-334(PSBLAS.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -295 0 obj -<< -/Length 6359 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(3)]TJ -0 g 0 G - [-378(Configuring)-378(and)-377(B)-1(uilding)-377(MLD2P4)]TJ/F15 10.9091 Tf 406.997 0 Td [(5)]TJ -0 g 0 G - -406.997 -35.866 Td [(Please)-430(note)-431(that)-430(the)-430(four)-430(previous)-430(libraries)-431(m)28(ust)-430(ha)28(v)27(e)-430(F)84(ortran)-431(in)28(terfaces)-430(compatible)]TJ 0 -13.549 Td [(with)-300(MLD2P4;)-311(usually)-299(this)-300(means)-300(that)-300(they)-299(should)-300(all)-300(b)-27(e)-300(built)-300(with)-300(the)-299(same)-300(compiler)]TJ 0 -13.549 Td [(as)-333(MLD2P4.)]TJ/F17 11.9552 Tf 0 -33.494 Td [(3.2)-1125(Optional)-375(third)-375(part)31(y)-375(libraries)]TJ/F15 10.9091 Tf 0 -22.05 Td [(W)83(e)-426(pro)28(vide)-427(in)28(terfaces)-427(to)-426(the)-427(follo)28(wing)-426(third-part)28(y)-427(soft)28(w)28(are)-427(libraries;)-473(note)-426(that)-427(these)]TJ 0 -13.549 Td [(are)-370(optional,)-379(but)-369(if)-370(y)28(ou)-370(enable)-370(them)-370(some)-370(default)1(s)-370(for)-370(m)28(ultilev)28(e)-1(l)-369(preconditioners)-370(ma)28(y)]TJ 0 -13.55 Td [(c)28(hange)-334(to)-333(re\015ect)-333(their)-334(pr)1(e)-1(sence.)]TJ -0 g 0 G -/F44 10.9091 Tf 0 -29.25 Td [(UMFP)96(A)32(CK)]TJ -0 g 0 G -/F15 10.9091 Tf 70.47 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(9)]TJ -0 g 0 G - [(])-255(A)-256(sparse)-255(LU)-255(factorization)-256(pac)28(k)56(age)-256(included)-255(in)-255(the)-256(SuiteSparse)-255(library)83(,)]TJ -43.197 -13.549 Td [(a)28(v)55(ailable)-231(f)1(rom)]TJ -0 1 0 0 k 0 1 0 0 K -/F45 10.9091 Tf 68.402 0 Td [(faculty.cse.tamu.edu/davis/suitesparse.html)]TJ -0 g 0 G -/F15 10.9091 Tf 246.27 0 Td [(;)-265(it)-231(pro)28(vides)-231(se-)]TJ -314.672 -13.549 Td [(quen)28(tial)-280(factorization)-279(and)-280(triangular)-279(s)-1(y)1(s)-1(tem)-279(solution)-280(for)-279(double)-280(precision)-280(real)-279(and)]TJ 0 -13.549 Td [(complex)-426(data.)-723(W)84(e)-427(tested)-426(v)28(ersion)-426(4.5.4)-426(of)-426(SuiteSparse.)-723(Note)-426(that)-426(for)-426(con\014gur-)]TJ 0 -13.549 Td [(ing)-424(SuiteSparse)-425(y)28(ou)-425(shou)1(ld)-425(pro)28(vide)-425(the)-424(righ)28(t)-425(path)-424(to)-425(the)-424(BLAS)-425(an)1(d)-425(LAP)83(A)28(CK)]TJ 0 -13.55 Td [(libraries)-333(in)-334(th)1(e)]TJ/F45 10.9091 Tf 73.455 0 Td [(SuiteSparse_config/SuiteSparse_config.mk)]TJ/F15 10.9091 Tf 232.724 0 Td [(\014le.)]TJ -0 g 0 G -/F44 10.9091 Tf -333.452 -25.512 Td [(MUMPS)]TJ -0 g 0 G -/F15 10.9091 Tf 54.47 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(1)]TJ -0 g 0 G - [(])-385(A)-385(sparse)-385(LU)-384(factorization)-385(pac)28(k)55(age)-385(a)28(v)56(ailable)-385(from)]TJ -0 1 0 0 k 0 1 0 0 K -/F45 10.9091 Tf 257.588 0 Td [(mumps.enseeiht.fr)]TJ -0 g 0 G -/F15 10.9091 Tf 97.363 0 Td [(;)]TJ -382.148 -13.549 Td [(it)-399(pro)28(vides)-400(sequen)28(tial)-399(and)-400(parall)1(e)-1(l)-399(factorizations)-399(and)-399(triangular)-400(system)-399(solution)]TJ 0 -13.549 Td [(for)-322(s)-1(in)1(gle)-323(and)-323(dou)1(ble)-323(precision,)-325(real)-322(and)-323(complex)-322(data.)-441(W)83(e)-322(teste)-1(d)-322(v)28(ersions)-323(4.10.0)]TJ 0 -13.549 Td [(and)-333(5.0.1.)]TJ -0 g 0 G -/F44 10.9091 Tf -27.273 -25.513 Td [(Sup)-32(erLU)]TJ -0 g 0 G -/F15 10.9091 Tf 54.826 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(10)]TJ -0 g 0 G - [(])-222(A)-222(sparse)-223(LU)-222(factorization)-222(pac)28(k)56(age)-223(a)28(v)56(ailable)-223(f)1(rom)]TJ -0 1 0 0 k 0 1 0 0 K -/F45 10.9091 Tf 248.846 0 Td [(crd.lbl.gov/)]TJ 68.727 -2.113 Td [(~)]TJ 5.727 2.113 Td [(xiaoye/)]TJ -350.853 -13.549 Td [(SuperLU/)]TJ -0 g 0 G -/F15 10.9091 Tf 45.818 0 Td [(;)-357(it)-349(pro)28(vides)-349(sequen)28(tial)-350(f)1(ac)-1(t)1(orization)-350(an)1(d)-350(t)1(riangular)-349(system)-350(solution)-349(for)]TJ -45.818 -13.549 Td [(single)-239(and)-239(double)-239(precision,)-258(real)-239(an)1(d)-239(com)-1(p)1(lex)-239(data.)-413(W)83(e)-239(tested)-239(v)28(ersions)-239(4.3)-239(and)-239(5.0.)]TJ 0 -13.549 Td [(If)-384(y)28(ou)-384(installed)-384(BLAS)-383(from)-384(A)83(TLAS,)-383(rem)-1(em)28(b)-28(er)-383(to)-384(de\014ne)-384(the)-384(BLASLIB)-384(v)56(ariable)]TJ 0 -13.549 Td [(in)-333(the)-334(mak)28(e.inc)-333(\014le.)]TJ -0 g 0 G -/F44 10.9091 Tf -27.273 -25.513 Td [(Sup)-32(erLU)]TJ -ET -q -1 0 0 1 143.724 326.218 cm -[]0 d 0 J 0.398 w 0 0 m 3.764 0 l S -Q -BT -/F44 10.9091 Tf 147.487 326.018 Td [(Dist)]TJ -0 g 0 G -/F15 10.9091 Tf 28.388 0 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(19)]TJ -0 g 0 G - [(])-417(A)-416(sparse)-417(LU)-416(factorization)-417(pac)28(k)55(age)-416(a)28(v)55(ailable)-416(from)-417(the)-417(same)-416(site)]TJ -55.002 -13.549 Td [(as)-366(Sup)-28(erLU;)-366(it)-367(pro)28(vides)-366(parallel)-366(factorization)-367(and)-366(triangular)-366(system)-367(solution)-366(for)]TJ 0 -13.549 Td [(double)-384(precision)-384(real)-384(and)-384(complex)-384(data.)-596(W)83(e)-384(tested)-384(v)28(ersions)-384(3.3)-384(and)-384(4.2.)-596(If)-384(y)28(ou)]TJ 0 -13.549 Td [(installed)-384(BLAS)-384(f)1(rom)-384(A)83(TLAS,)-384(remem)28(b)-28(er)-384(to)-383(de\014ne)-384(the)-384(BLASLIB)-384(v)56(ariable)-384(in)-384(the)]TJ 0 -13.549 Td [(mak)28(e.inc)-401(\014le)-401(and)-401(to)-401(add)-402(t)1(he)]TJ/F45 10.9091 Tf 142.011 0 Td [(-std=c99)]TJ/F15 10.9091 Tf 50.193 0 Td [(option)-401(to)-401(the)-401(C)-401(compiler)-401(options.)-648(Note)]TJ -192.204 -13.55 Td [(that)-432(this)-432(library)-432(requires)-433(t)1(he)-433(P)28(arMETIS)-432(library)-432(for)-432(parallel)-432(graph)-432(partitioning)]TJ 0 -13.549 Td [(and)-374(\014ll-reducing)-374(matrix)-374(ordering,)-385(a)28(v)56(ailable)-374(from)]TJ -0 1 0 0 k 0 1 0 0 K -/F45 10.9091 Tf 236.271 0 Td [(glaros.dtc.umn.edu/gkhome/)]TJ -236.271 -13.549 Td [(metis/parmetis/overview)]TJ -0 g 0 G -/F15 10.9091 Tf 131.726 0 Td [(.)]TJ/F17 11.9552 Tf -158.999 -33.494 Td [(3.3)-1125(Con\014guration)-375(options)]TJ/F15 10.9091 Tf 0 -22.05 Td [(In)-400(order)-400(to)-400(build)-400(MLD2P4,)-417(the)-400(\014rst)-400(step)-401(is)-400(to)-400(use)-400(the)]TJ/F45 10.9091 Tf 268.809 0 Td [(configure)]TJ/F15 10.9091 Tf 55.91 0 Td [(script)-400(in)-400(the)-400(main)]TJ -324.719 -13.549 Td [(directory)-333(to)-334(generate)-333(the)-333(necessary)-334(mak)28(e\014le.)]TJ 16.937 -14.299 Td [(As)-333(a)-334(minimal)-333(example)-333(consider)-334(the)-333(follo)28(wing:)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf -16.937 -26.261 Td [(./configure)-525(--with-psblas=PSB-INSTALL-DIR)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -305 0 obj -<< -/Length 4105 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(6)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [(whic)28(h)-411(assumes)-412(t)1(hat)-412(th)1(e)-412(v)56(arious)-411(MPI)-411(compilers)-411(and)-411(supp)-28(ort)-411(libraries)-411(are)-411(a)28(v)55(ailable)-411(in)]TJ 0 -13.549 Td [(the)-290(standard)-290(directories)-291(on)-290(the)-290(system,)-299(and)-290(sp)-28(eci\014es)-290(only)-290(the)-291(P)1(SBLAS)-291(install)-290(directory)]TJ 0 -13.549 Td [(\050note)-385(that)-386(the)-385(latter)-386(directory)-385(m)27(ust)-385(b)-28(e)-386(sp)-27(eci\014ed)-386(with)-385(an)]TJ/F18 10.9091 Tf 278.634 0 Td [(absolute)]TJ/F15 10.9091 Tf 42.121 0 Td [(path\051.)-601(The)-385(full)-386(set)]TJ -320.755 -13.549 Td [(of)-487(options)-487(ma)28(y)-488(b)-27(e)-487(lo)-28(ok)28(ed)-488(at)-487(b)28(y)-487(issuing)-487(the)-487(command)]TJ/F45 10.9091 Tf 273.021 0 Td [(./configure)-525(--help)]TJ/F15 10.9091 Tf 103.09 0 Td [(,)-526(whic)28(h)]TJ -376.111 -13.549 Td [(pro)-28(duces:)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 0 -27.099 Td [(`configure')-525(configures)-525(MLD2P4)-525(2.1.1)-525(to)-525(adapt)-525(to)-525(many)-525(kinds)-525(of)-525(systems.)]TJ 0 -27.098 Td [(Usage:)-525(./configure)-525([OPTION]...)-525([VAR=VALUE]...)]TJ 0 -27.099 Td [(To)-525(assign)-525(environment)-525(variables)-525(\050e.g.,)-525(CC,)-525(CFLAGS...\051,)-525(specify)-525(them)-525(as)]TJ 0 -13.549 Td [(VAR=VALUE.)-1050(See)-525(below)-525(for)-525(descriptions)-525(of)-525(some)-525(of)-525(the)-525(useful)-525(variables.)]TJ 0 -27.098 Td [(Defaults)-525(for)-525(the)-525(options)-525(are)-525(specified)-525(in)-525(brackets.)]TJ 0 -27.099 Td [(Configuration:)]TJ 11.454 -13.549 Td [(-h,)-525(--help)-7350(display)-525(this)-525(help)-525(and)-525(exit)]TJ 22.909 -13.549 Td [(--help=short)-4200(display)-525(options)-525(specific)-525(to)-525(this)-525(package)]TJ 0 -13.549 Td [(--help=recursive)-2100(display)-525(the)-525(short)-525(help)-525(of)-525(all)-525(the)-525(included)-525(packages)]TJ -22.909 -13.549 Td [(-V,)-525(--version)-5775(display)-525(version)-525(information)-525(and)-525(exit)]TJ 0 -13.55 Td [(-q,)-525(--quiet,)-525(--silent)-1575(do)-525(not)-525(print)-525(`checking)-525(...')-525(messages)]TJ 22.909 -13.549 Td [(--cache-file=FILE)-1575(cache)-525(test)-525(results)-525(in)-525(FILE)-525([disabled])]TJ -22.909 -13.549 Td [(-C,)-525(--config-cache)-3150(alias)-525(for)-525(`--cache-file=config.cache')]TJ 0 -13.549 Td [(-n,)-525(--no-create)-4725(do)-525(not)-525(create)-525(output)-525(files)]TJ 22.909 -13.549 Td [(--srcdir=DIR)-4200(find)-525(the)-525(sources)-525(in)-525(DIR)-525([configure)-525(dir)-525(or)-525(`..'])]TJ -34.363 -27.099 Td [(Installation)-525(directories:)]TJ 11.454 -13.549 Td [(--prefix=PREFIX)-4725(install)-525(architecture-independent)-525(files)-525(in)-525(PREFIX)]TJ 137.453 -13.549 Td [([/usr/local])]TJ -137.453 -13.549 Td [(--exec-prefix=EPREFIX)-1575(install)-525(architecture-dependent)-525(files)-525(in)-525(EPREFIX)]TJ 137.453 -13.549 Td [([PREFIX])]TJ -148.907 -27.099 Td [(By)-525(default,)-525(`make)-525(install')-525(will)-525(install)-525(all)-525(the)-525(files)-525(in)]TJ 0 -13.549 Td [(`/usr/local/bin',)-525(`/usr/local/lib')-525(etc.)-1050(You)-525(can)-525(specify)]TJ 0 -13.549 Td [(an)-525(installation)-525(prefix)-525(other)-525(than)-525(`/usr/local')-525(using)-525(`--prefix',)]TJ 0 -13.549 Td [(for)-525(instance)-525(`--prefix=$HOME'.)]TJ 0 -27.099 Td [(For)-525(better)-525(control,)-525(use)-525(the)-525(options)-525(below.)]TJ 0 -27.098 Td [(Fine)-525(tuning)-525(of)-525(the)-525(installation)-525(directories:)]TJ 11.454 -13.549 Td [(--bindir=DIR)-6300(user)-525(executables)-525([EPREFIX/bin])]TJ 0 -13.55 Td [(--sbindir=DIR)-5775(system)-525(admin)-525(executables)-525([EPREFIX/sbin])]TJ 0 -13.549 Td [(--libexecdir=DIR)-4200(program)-525(executables)-525([EPREFIX/libexec])]TJ 0 -13.549 Td [(--sysconfdir=DIR)-4200(read-only)-525(single-machine)-525(data)-525([PREFIX/etc])]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -206 0 obj -<< -/Type /ObjStm -/N 100 -/First 912 -/Length 14571 ->> -stream -179 0 180 146 181 298 182 443 183 594 184 746 185 896 186 1047 187 1197 188 1349 -189 1500 190 1652 191 1804 192 1961 193 2118 194 2275 195 2431 196 2586 197 2731 198 2877 -199 3024 203 3171 204 3225 200 3279 208 3372 210 3486 207 3540 222 3607 220 3813 211 3959 -212 4112 213 4264 214 4412 215 4564 216 4715 217 4871 218 5034 219 5184 11 5333 224 5386 -221 5442 246 5548 235 5754 236 5901 237 6054 238 6200 239 6347 240 6494 241 6640 242 6787 -243 6933 244 7080 245 7228 252 7308 250 7450 249 7596 254 7744 15 7798 256 7851 251 7905 -272 8024 258 8278 259 8430 260 8582 261 8730 262 8878 263 9026 275 9195 264 9364 276 9526 -265 9688 266 9852 267 9999 268 10146 269 10300 270 10452 277 10624 274 10796 19 10850 23 10903 -271 10955 294 11074 292 11288 284 11434 285 11584 286 11770 287 11918 288 12078 289 12227 297 12398 -290 12568 291 12722 298 12914 296 13106 27 13160 31 13213 293 13266 304 13385 306 13499 303 13553 -% 179 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 445.875 197.952 457.565] -/A << /S /GoTo /D (section.5) >> ->> -% 180 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 432.326 182.021 444.016] -/A << /S /GoTo /D (subsection.5.1) >> ->> -% 181 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 409.989 189.09 419.557] -/A << /S /GoTo /D (section.6) >> ->> -% 182 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 396.44 193.021 406.008] -/A << /S /GoTo /D (subsection.6.1) >> ->> -% 183 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 382.891 190.051 392.459] -/A << /S /GoTo /D (subsection.6.2) >> ->> -% 184 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 367.22 248.827 378.91] -/A << /S /GoTo /D (subsection.6.3) >> ->> -% 185 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 355.792 253.16 365.361] -/A << /S /GoTo /D (subsection.6.4) >> ->> -% 186 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 342.243 200.9 351.811] -/A << /S /GoTo /D (subsection.6.5) >> ->> -% 187 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 326.573 203.021 338.262] -/A << /S /GoTo /D (subsection.6.6) >> ->> -% 188 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 315.145 193.96 324.713] -/A << /S /GoTo /D (subsection.6.7) >> ->> -% 189 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 301.596 200.991 311.164] -/A << /S /GoTo /D (subsection.6.8) >> ->> -% 190 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [108.968 285.925 225.536 297.615] -/A << /S /GoTo /D (subsection.6.9) >> ->> -% 191 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [134.059 272.376 243.082 284.065] -/A << /S /GoTo /D (subsubsection.6.9.1) >> ->> -% 192 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [134.059 260.948 240.051 270.516] -/A << /S /GoTo /D (subsubsection.6.9.2) >> ->> -% 193 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [134.059 247.399 241.627 256.967] -/A << /S /GoTo /D (subsubsection.6.9.3) >> ->> -% 194 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [134.059 233.85 274.312 243.418] -/A << /S /GoTo /D (subsubsection.6.9.4) >> ->> -% 195 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [134.059 220.3 254.948 229.869] -/A << /S /GoTo /D (subsubsection.6.9.5) >> ->> -% 196 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 193.721 405.432 205.41] -/A << /S /GoTo /D (section.7) >> ->> -% 197 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 169.263 195.225 180.952] -/A << /S /GoTo /D (section.8) >> ->> -% 198 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 146.925 150.984 156.494] -/A << /S /GoTo /D (appendix.A) >> ->> -% 199 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 122.467 153.499 132.035] -/A << /S /GoTo /D (section*.4) >> ->> -% 203 0 obj -<< -/D [201 0 R /XYZ 92.6 752.957 null] ->> -% 204 0 obj -<< -/D [201 0 R /XYZ 93.6 722.069 null] ->> -% 200 0 obj -<< -/Font << /F15 160 0 R /F17 148 0 R /F44 205 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 208 0 obj -<< -/Type /Page -/Contents 209 0 R -/Resources 207 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 151 0 R ->> -% 210 0 obj -<< -/D [208 0 R /XYZ 85.4 752.957 null] ->> -% 207 0 obj -<< -/Font << /F19 149 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 222 0 obj -<< -/Type /Page -/Contents 223 0 R -/Resources 221 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 226 0 R -/Annots [ 220 0 R 211 0 R 212 0 R 213 0 R 214 0 R 215 0 R 216 0 R 217 0 R 218 0 R 219 0 R ] ->> -% 220 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.1) >> ->> -% 211 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [332.009 650.022 339.456 659.045] -/A << /S /GoTo /D (cite.Briggs2000) >> ->> -% 212 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [343.422 650.022 356.323 659.045] -/A << /S /GoTo /D (cite.Stuben_01) >> ->> -% 213 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [360.288 650.022 373.19 659.045] -/A << /S /GoTo /D (cite.dd2_96) >> ->> -% 214 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [479.758 515.168 487.205 524.19] -/A << /S /GoTo /D (cite.Briggs2000) >> ->> -% 215 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [491.116 515.168 504.017 524.19] -/A << /S /GoTo /D (cite.Notay2008) >> ->> -% 216 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [480.046 420.323 487.493 429.346] -/A << /S /GoTo /D (cite.BREZINA_VANEK) >> ->> -% 217 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [491.116 420.323 504.017 429.346] -/A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> ->> -% 218 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [122.62 242.467 135.522 251.49] -/A << /S /GoTo /D (cite.psblas_00) >> ->> -% 219 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [140.485 242.467 153.386 251.49] -/A << /S /GoTo /D (cite.PSBLAS3) >> ->> -% 11 0 obj -<< -/D [222 0 R /XYZ 93.6 715.095 null] ->> -% 224 0 obj -<< -/D [222 0 R /XYZ 280.58 634.895 null] ->> -% 221 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R /F22 225 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 246 0 obj -<< -/Type /Page -/Contents 247 0 R -/Resources 245 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 226 0 R -/Annots [ 235 0 R 236 0 R 237 0 R 238 0 R 239 0 R 240 0 R 241 0 R 242 0 R 243 0 R 244 0 R ] ->> -% 235 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [411.374 592.019 418.821 604.921] -/A << /S /GoTo /D (section.7) >> ->> -% 236 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [333.057 540.55 340.504 549.573] -/A << /S /GoTo /D (cite.MLD2P4_TOMS) >> ->> -% 237 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [248.99 484.232 256.437 495.921] -/A << /S /GoTo /D (section.2) >> ->> -% 238 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [259.467 470.683 266.914 482.372] -/A << /S /GoTo /D (section.3) >> ->> -% 239 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [309.136 457.133 316.583 468.823] -/A << /S /GoTo /D (section.4) >> ->> -% 240 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [325.173 430.035 332.62 441.724] -/A << /S /GoTo /D (section.5) >> ->> -% 241 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [178.729 402.937 186.176 414.626] -/A << /S /GoTo /D (section.6) >> ->> -% 242 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [336.65 389.387 344.097 401.077] -/A << /S /GoTo /D (section.7) >> ->> -% 243 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [331.001 375.838 338.449 387.528] -/A << /S /GoTo /D (section.8) >> ->> -% 244 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [432.101 362.289 442.275 373.978] -/A << /S /GoTo /D (appendix.A) >> ->> -% 245 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 252 0 obj -<< -/Type /Page -/Contents 253 0 R -/Resources 251 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 226 0 R -/Annots [ 250 0 R 249 0 R ] ->> -% 250 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.2) >> ->> -% 249 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [493.843 618.086 504.017 629.776] -/A << /S /GoTo /D (appendix.A) >> ->> -% 254 0 obj -<< -/D [252 0 R /XYZ 92.6 752.957 null] ->> -% 15 0 obj -<< -/D [252 0 R /XYZ 93.6 715.095 null] ->> -% 256 0 obj -<< -/D [252 0 R /XYZ 93.6 502.726 null] ->> -% 251 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R /F45 255 0 R /F25 257 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 272 0 obj -<< -/Type /Page -/Contents 273 0 R -/Resources 271 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 226 0 R -/Annots [ 258 0 R 259 0 R 260 0 R 261 0 R 262 0 R 263 0 R 275 0 R 264 0 R 276 0 R 265 0 R 266 0 R 267 0 R 268 0 R 269 0 R 270 0 R 277 0 R ] ->> -% 258 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [393.594 539.343 409.526 552.245] -/A << /S /GoTo /D (subsection.3.1) >> ->> -% 259 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [107.802 512.245 123.734 525.146] -/A << /S /GoTo /D (subsection.3.2) >> ->> -% 260 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [126.812 384.829 139.714 393.852] -/A << /S /GoTo /D (cite.blas3) >> ->> -% 261 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [145.384 384.829 158.286 393.852] -/A << /S /GoTo /D (cite.blas2) >> ->> -% 262 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [163.956 384.829 176.857 393.852] -/A << /S /GoTo /D (cite.blas1) >> ->> -% 263 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [434.357 368.553 499.847 381.454] -/Subtype/Link/A<> ->> -% 275 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [112.676 355.004 200.577 367.905] -/Subtype/Link/A<> ->> -% 264 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [474.946 355.004 499.847 367.905] -/Subtype/Link/A<> ->> -% 276 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [112.676 341.454 200.577 354.356] -/Subtype/Link/A<> ->> -% 265 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [357.477 246.913 479.741 258.906] -/Subtype/Link/A<> ->> -% 266 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [119.131 184.931 132.032 193.954] -/A << /S /GoTo /D (cite.MPI2) >> ->> -% 267 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [136.782 184.931 149.683 193.954] -/A << /S /GoTo /D (cite.MPI1) >> ->> -% 268 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [142.358 147.623 155.259 156.646] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 269 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [161.535 147.623 174.436 156.646] -/A << /S /GoTo /D (cite.psblas_00) >> ->> -% 270 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [434.855 144.896 499.847 157.797] -/Subtype/Link/A<> ->> -% 277 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [112.676 131.347 217.759 144.248] -/Subtype/Link/A<> ->> -% 274 0 obj -<< -/D [272 0 R /XYZ 85.4 752.957 null] ->> -% 19 0 obj -<< -/D [272 0 R /XYZ 86.4 715.095 null] ->> -% 23 0 obj -<< -/D [272 0 R /XYZ 86.4 442.92 null] ->> -% 271 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F17 148 0 R /F45 255 0 R /F44 205 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 294 0 obj -<< -/Type /Page -/Contents 295 0 R -/Resources 293 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 226 0 R -/Annots [ 292 0 R 284 0 R 285 0 R 286 0 R 287 0 R 288 0 R 289 0 R 297 0 R 290 0 R 291 0 R 298 0 R ] ->> -% 292 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.3) >> ->> -% 284 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [166.104 564.149 173.551 573.172] -/A << /S /GoTo /D (cite.UMFPACK) >> ->> -% 285 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [188.279 548.176 436.542 560.168] -/Subtype/Link/A<> ->> -% 286 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [150.104 470.891 157.551 479.914] -/A << /S /GoTo /D (cite.MUMPS) >> ->> -% 287 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [404.662 468.164 504.017 481.065] -/Subtype/Link/A<> ->> -% 288 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [150.46 404.731 163.361 413.754] -/A << /S /GoTo /D (cite.SUPERLU) >> ->> -% 289 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [396.276 402.004 507.048 414.905] -/Subtype/Link/A<> ->> -% 297 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [119.877 388.758 167.687 400.75] -/Subtype/Link/A<> ->> -% 290 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [177.909 325.022 190.811 334.045] -/A << /S /GoTo /D (cite.SUPERLUDIST) >> ->> -% 291 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [356.148 241.303 507.048 253.295] -/Subtype/Link/A<> ->> -% 298 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [119.877 227.753 253.595 239.746] -/Subtype/Link/A<> ->> -% 296 0 obj -<< -/D [294 0 R /XYZ 92.6 752.957 null] ->> -% 27 0 obj -<< -/D [294 0 R /XYZ 93.6 658.241 null] ->> -% 31 0 obj -<< -/D [294 0 R /XYZ 93.6 209.953 null] ->> -% 293 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R /F44 205 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 304 0 obj -<< -/Type /Page -/Contents 305 0 R -/Resources 303 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 226 0 R ->> -% 306 0 obj -<< -/D [304 0 R /XYZ 85.4 752.957 null] ->> -% 303 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F18 307 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> - -endstream -endobj -311 0 obj -<< -/Length 3968 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(3)]TJ -0 g 0 G - [-378(Configuring)-378(and)-377(B)-1(uilding)-377(MLD2P4)]TJ/F15 10.9091 Tf 406.997 0 Td [(7)]TJ -0 g 0 G -/F45 10.9091 Tf -395.542 -35.866 Td [(--sharedstatedir=DIR)-2100(modifiable)-525(architecture-independent)-525(data)-525([PREFIX/com])]TJ 0 -13.549 Td [(--localstatedir=DIR)-2625(modifiable)-525(single-machine)-525(data)-525([PREFIX/var])]TJ 0 -13.549 Td [(--libdir=DIR)-6300(object)-525(code)-525(libraries)-525([EPREFIX/lib])]TJ 0 -13.549 Td [(--includedir=DIR)-4200(C)-525(header)-525(files)-525([PREFIX/include])]TJ 0 -13.549 Td [(--oldincludedir=DIR)-2625(C)-525(header)-525(files)-525(for)-525(non-gcc)-525([/usr/include])]TJ 0 -13.55 Td [(--datarootdir=DIR)-3675(read-only)-525(arch.-independent)-525(data)-525(root)-525([PREFIX/share])]TJ 0 -13.549 Td [(--datadir=DIR)-5775(read-only)-525(architecture-independent)-525(data)-525([DATAROOTDIR])]TJ 0 -13.549 Td [(--infodir=DIR)-5775(info)-525(documentation)-525([DATAROOTDIR/info])]TJ 0 -13.549 Td [(--localedir=DIR)-4725(locale-dependent)-525(data)-525([DATAROOTDIR/locale])]TJ 0 -13.549 Td [(--mandir=DIR)-6300(man)-525(documentation)-525([DATAROOTDIR/man])]TJ 0 -13.55 Td [(--docdir=DIR)-6300(documentation)-525(root)-525([DATAROOTDIR/doc/mld2p4])]TJ 0 -13.549 Td [(--htmldir=DIR)-5775(html)-525(documentation)-525([DOCDIR])]TJ 0 -13.549 Td [(--dvidir=DIR)-6300(dvi)-525(documentation)-525([DOCDIR])]TJ 0 -13.549 Td [(--pdfdir=DIR)-6300(pdf)-525(documentation)-525([DOCDIR])]TJ 0 -13.549 Td [(--psdir=DIR)-6825(ps)-525(documentation)-525([DOCDIR])]TJ -11.455 -27.099 Td [(Program)-525(names:)]TJ 11.455 -13.549 Td [(--program-prefix=PREFIX)-6300(prepend)-525(PREFIX)-525(to)-525(installed)-525(program)-525(names)]TJ 0 -13.549 Td [(--program-suffix=SUFFIX)-6300(append)-525(SUFFIX)-525(to)-525(installed)-525(program)-525(names)]TJ 0 -13.549 Td [(--program-transform-name=PROGRAM)-1575(run)-525(sed)-525(PROGRAM)-525(on)-525(installed)-525(program)-525(names)]TJ -11.455 -27.099 Td [(Optional)-525(Features:)]TJ 11.455 -13.549 Td [(--disable-option-checking)-1050(ignore)-525(unrecognized)-525(--enable/--with)-525(options)]TJ 0 -13.549 Td [(--disable-FEATURE)-3675(do)-525(not)-525(include)-525(FEATURE)-525(\050same)-525(as)-525(--enable-FEATURE=no\051)]TJ 0 -13.549 Td [(--enable-FEATURE[=ARG])-1050(include)-525(FEATURE)-525([ARG=yes])]TJ 0 -13.549 Td [(--enable-silent-rules)-1575(less)-525(verbose)-525(build)-525(output)-525(\050undo:)-525("make)-525(V=1"\051)]TJ 0 -13.55 Td [(--disable-silent-rules)-1050(verbose)-525(build)-525(output)-525(\050undo:)-525("make)-525(V=0"\051)]TJ 0 -13.549 Td [(--enable-dependency-tracking)]TJ 137.453 -13.549 Td [(do)-525(not)-525(reject)-525(slow)-525(dependency)-525(extractors)]TJ -137.453 -13.549 Td [(--disable-dependency-tracking)]TJ 137.453 -13.549 Td [(speeds)-525(up)-525(one-time)-525(build)]TJ -137.453 -13.55 Td [(--enable-serial)-4725(Specify)-525(whether)-525(to)-525(enable)-525(a)-525(fake)-525(mpi)-525(library)-525(to)-525(run)]TJ 137.453 -13.549 Td [(in)-525(serial)-525(mode.)]TJ -137.453 -13.549 Td [(--enable-long-integers)-1050(Specify)-525(usage)-525(of)-525(64)-525(bits)-525(integers.)]TJ -11.455 -27.098 Td [(Optional)-525(Packages:)]TJ 11.455 -13.55 Td [(--with-PACKAGE[=ARG])-2100(use)-525(PACKAGE)-525([ARG=yes])]TJ 0 -13.549 Td [(--without-PACKAGE)-3675(do)-525(not)-525(use)-525(PACKAGE)-525(\050same)-525(as)-525(--with-PACKAGE=no\051)]TJ 0 -13.549 Td [(--with-psblas=DIR)-3675(The)-525(install)-525(directory)-525(for)-525(PSBLAS,)-525(for)-525(example,)]TJ 137.453 -13.549 Td [(--with-psblas=/opt/packages/psblas-3.5)]TJ -137.453 -13.549 Td [(--with-psblas-incdir=DIR)]TJ 137.453 -13.55 Td [(Specify)-525(the)-525(directory)-525(for)-525(PSBLAS)-525(C)-525(includes.)]TJ -137.453 -13.549 Td [(--with-psblas-moddir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(PSBLAS)-525(Fortran)-525(modules.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -317 0 obj -<< -/Length 4227 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(8)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F45 10.9091 Tf -191.811 -35.866 Td [(--with-psblas-libdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(PSBLAS)-525(library.)]TJ -137.453 -13.549 Td [(--with-ccopt)-6300(additional)-525([CCOPT])-525(flags)-525(to)-525(be)-525(added:)-525(will)-525(prepend)]TJ 137.453 -13.549 Td [(to)-525([CCOPT])]TJ -137.453 -13.549 Td [(--with-fcopt)-6300(additional)-525([FCOPT])-525(flags)-525(to)-525(be)-525(added:)-525(will)-525(prepend)]TJ 137.453 -13.55 Td [(to)-525([FCOPT])]TJ -137.453 -13.549 Td [(--with-libs)-6825(List)-525(additional)-525(link)-525(flags)-525(here.)-525(For)-525(example,)]TJ 137.453 -13.549 Td [(--with-libs=-lspecial_system_lib)-525(or)]TJ 0 -13.549 Td [(--with-libs=-L/path/to/libs)]TJ -137.453 -13.549 Td [(--with-clibs)-6300(additional)-525([CLIBS])-525(flags)-525(to)-525(be)-525(added:)-525(will)-525(prepend)]TJ 137.453 -13.55 Td [(to)-525([CLIBS])]TJ -137.453 -13.549 Td [(--with-flibs)-6300(additional)-525([FLIBS])-525(flags)-525(to)-525(be)-525(added:)-525(will)-525(prepend)]TJ 137.453 -13.549 Td [(to)-525([FLIBS])]TJ -137.453 -13.549 Td [(--with-library-path)-2625(additional)-525([LIBRARYPATH])-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.453 -13.549 Td [(prepend)-525(to)-525([LIBRARYPATH])]TJ -137.453 -13.55 Td [(--with-include-path)-2625(additional)-525([INCLUDEPATH])-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.453 -13.549 Td [(prepend)-525(to)-525([INCLUDEPATH])]TJ -137.453 -13.549 Td [(--with-module-path)-3150(additional)-525([MODULE_PATH])-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.453 -13.549 Td [(prepend)-525(to)-525([MODULE_PATH])]TJ -137.453 -13.549 Td [(--with-extra-libs)-3675(List)-525(additional)-525(link)-525(flags)-525(here.)-525(For)-525(example,)]TJ 137.453 -13.55 Td [(--with-extra-libs=-lspecial_system_lib)-525(or)]TJ 0 -13.549 Td [(--with-extra-libs=-L/path/to/libs)]TJ -137.453 -13.549 Td [(--with-blas=)-3675(use)-525(BLAS)-525(library)-525()]TJ 0 -13.549 Td [(--with-blasdir=

    )-2100(search)-525(for)-525(BLAS)-525(library)-525(in)-525()]TJ 0 -13.549 Td [(--with-lapack=)-2625(use)-525(LAPACK)-525(library)-525()]TJ 0 -13.549 Td [(--with-mumps=LIBNAME)-2100(Specify)-525(the)-525(libname)-525(for)-525(MUMPS.)-525(Default:)-525(autodetect)]TJ 137.453 -13.55 Td [(with)-525(minimum)-525("-lmumps_common)-525(-lpord")]TJ -137.453 -13.549 Td [(--with-mumpsdir=DIR)-2625(Specify)-525(the)-525(directory)-525(for)-525(MUMPS)-525(library)-525(and)]TJ 137.453 -13.549 Td [(includes.)-525(Note:)-525(you)-525(will)-525(need)-525(to)-525(add)-525(auxiliary)]TJ 0 -13.549 Td [(libraries)-525(with)-525(--extra-libs;)-525(this)-525(depends)-525(on)-525(how)]TJ 0 -13.549 Td [(MUMPS)-525(was)-525(configured)-525(and)-525(installed,)-525(at)-525(a)-525(minimum)-525(you)]TJ 0 -13.55 Td [(will)-525(need)-525(SCALAPACK)-525(and)-525(BLAS)]TJ -137.453 -13.549 Td [(--with-mumpsincdir=DIR)-1050(Specify)-525(the)-525(directory)-525(for)-525(MUMPS)-525(includes.)]TJ 0 -13.549 Td [(--with-mumpsmoddir=DIR)-1050(Specify)-525(the)-525(directory)-525(for)-525(MUMPS)-525(Fortran)-525(modules.)]TJ 0 -13.549 Td [(--with-mumpslibdir=DIR)-1050(Specify)-525(the)-525(directory)-525(for)-525(MUMPS)-525(library.)]TJ 0 -13.549 Td [(--with-umfpack=LIBNAME)-1050(Specify)-525(the)-525(library)-525(name)-525(for)-525(UMFPACK)-525(and)-525(its)-525(support)]TJ 137.453 -13.55 Td [(libraries.)-525(Default:)-525("-lumfpack)-525(-lamd")]TJ -137.453 -13.549 Td [(--with-umfpackdir=DIR)-1575(Specify)-525(the)-525(directory)-525(for)-525(UMFPACK)-525(library)-525(and)]TJ 137.453 -13.549 Td [(includes.)]TJ -137.453 -13.549 Td [(--with-umfpackincdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(UMFPACK)-525(includes.)]TJ -137.453 -13.55 Td [(--with-umfpacklibdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(UMFPACK)-525(library.)]TJ -137.453 -13.549 Td [(--with-superlu=LIBNAME)-1050(Specify)-525(the)-525(library)-525(name)-525(for)-525(SUPERLU)-525(library.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -322 0 obj -<< -/Length 3680 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(3)]TJ -0 g 0 G - [-378(Configuring)-378(and)-377(B)-1(uilding)-377(MLD2P4)]TJ/F15 10.9091 Tf 406.997 0 Td [(9)]TJ -0 g 0 G -/F45 10.9091 Tf -258.089 -35.866 Td [(Default:)-525("-lsuperlu")]TJ -137.453 -13.549 Td [(--with-superludir=DIR)-1575(Specify)-525(the)-525(directory)-525(for)-525(SUPERLU)-525(library)-525(and)]TJ 137.453 -13.549 Td [(includes.)]TJ -137.453 -13.549 Td [(--with-superluincdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLU)-525(includes.)]TJ -137.453 -13.55 Td [(--with-superlulibdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLU)-525(library.)]TJ -137.453 -13.549 Td [(--with-superludist=LIBNAME)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(libname)-525(for)-525(SUPERLUDIST)-525(library.)]TJ 0 -13.549 Td [(Requires)-525(you)-525(also)-525(specify)-525(SuperLU.)-525(Default:)]TJ 0 -13.55 Td [("-lsuperlu_dist")]TJ -137.453 -13.549 Td [(--with-superludistdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLUDIST)-525(library)-525(and)]TJ 0 -13.549 Td [(includes.)]TJ -137.453 -13.549 Td [(--with-superludistincdir=DIR)]TJ 137.453 -13.55 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLUDIST)-525(includes.)]TJ -137.453 -13.549 Td [(--with-superludistlibdir=DIR)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLUDIST)-525(library.)]TJ -148.908 -27.098 Td [(Some)-525(influential)-525(environment)-525(variables:)]TJ 11.455 -13.55 Td [(FC)-5250(Fortran)-525(compiler)-525(command)]TJ 0 -13.549 Td [(FCFLAGS)-2625(Fortran)-525(compiler)-525(flags)]TJ 0 -13.549 Td [(LDFLAGS)-2625(linker)-525(flags,)-525(e.g.)-525(-L)-525(if)-525(you)-525(have)-525(libraries)-525(in)-525(a)]TJ 68.726 -13.549 Td [(nonstandard)-525(directory)-525()]TJ -68.726 -13.549 Td [(LIBS)-4200(libraries)-525(to)-525(pass)-525(to)-525(the)-525(linker,)-525(e.g.)-525(-l)]TJ 0 -13.549 Td [(CC)-5250(C)-525(compiler)-525(command)]TJ 0 -13.55 Td [(CFLAGS)-3150(C)-525(compiler)-525(flags)]TJ 0 -13.549 Td [(CPPFLAGS)-2100(\050Objective\051)-525(C/C++)-525(preprocessor)-525(flags,)-525(e.g.)-525(-I)-525(if)]TJ 68.726 -13.549 Td [(you)-525(have)-525(headers)-525(in)-525(a)-525(nonstandard)-525(directory)-525()]TJ -68.726 -13.549 Td [(MPICC)-3675(MPI)-525(C)-525(compiler)-525(command)]TJ 0 -13.549 Td [(MPIFC)-3675(MPI)-525(Fortran)-525(compiler)-525(command)]TJ 0 -13.55 Td [(CPP)-4725(C)-525(preprocessor)]TJ -11.455 -27.098 Td [(Use)-525(these)-525(variables)-525(to)-525(override)-525(the)-525(choices)-525(made)-525(by)-525(`configure')-525(or)-525(to)-525(help)]TJ 0 -13.549 Td [(it)-525(to)-525(find)-525(libraries)-525(and)-525(programs)-525(with)-525(nonstandard)-525(names/locations.)]TJ 0 -27.099 Td [(Report)-525(bugs)-525(to)-525(.)]TJ/F15 10.9091 Tf 16.937 -26.589 Td [(F)83(or)-301(instance,)-308(if)-302(a)-302(user)-302(h)1(as)-302(built)-302(and)-301(installed)-302(PSBLAS)-302(3.5)-301(under)-302(the)]TJ/F45 10.9091 Tf 326.526 0 Td [(/opt)]TJ/F15 10.9091 Tf 26.2 0 Td [(directory)]TJ -369.663 -13.549 Td [(and)-247(is)-246(using)-247(the)-247(SuiteSp)1(arse)-247(pac)28(k)55(age)-247(\050whic)28(h)-246(includes)-247(UMFP)83(A)28(CK\051,)-247(th)1(e)-1(n)-246(MLD2P4)-247(migh)28(t)]TJ 0 -13.549 Td [(b)-28(e)-333(con\014gured)-333(with:)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 5.728 -27.608 Td [(./configure)-525(--with-psblas=/opt/psblas-3.5/)-525(\134)]TJ 0 -13.549 Td [(--with-umfpackincdir=/usr/include/suitesparse/)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -327 0 obj -<< -/Length 5497 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(10)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [(Once)-529(the)-529(con\014gure)-530(script)-529(has)-529(completed)-529(execution,)-578(it)-530(will)-529(ha)28(v)28(e)-529(ge)-1(n)1(e)-1(r)1(ate)-1(d)-529(the)-529(\014le)]TJ/F45 10.9091 Tf 0 -13.549 Td [(Make.inc)]TJ/F15 10.9091 Tf 49.144 0 Td [(whic)28(h)-305(will)-305(then)-305(b)-28(e)-305(used)-305(b)28(y)-305(all)-305(Mak)28(e\014les)-305(in)-305(the)-305(directory)-305(t)1(re)-1(e;)-314(this)-305(\014le)-305(will)-305(b)-27(e)]TJ -49.144 -13.549 Td [(copied)-333(in)-334(the)-333(install)-333(directory)-333(under)-334(the)-333(name)]TJ/F45 10.9091 Tf 223.485 0 Td [(Make.inc.MLD2P4)]TJ/F15 10.9091 Tf 85.908 0 Td [(.)]TJ -292.457 -13.549 Td [(T)83(o)-428(use)-428(the)-429(MUMPS)-428(solv)28(er)-428(pac)28(k)55(age,)-452(the)-428(user)-429(has)-428(to)-428(add)-428(the)-429(appropri)1(ate)-429(options)]TJ -16.936 -13.549 Td [(to)-342(the)-341(c)-1(on)1(\014gure)-342(script;)-346(b)28(y)-342(default)-342(w)28(e)-342(are)-341(lo)-28(oking)-342(for)-342(the)-341(libraries)]TJ/F45 10.9091 Tf 315.088 0 Td [(-ldmumps)-525(-lsmumps)]TJ -309.361 -13.55 Td [(-lzmumps)-525(-lcmumps)-525(-mumps_common)-525(-lpord)]TJ/F15 10.9091 Tf 217.634 0 Td [(.)-767(MUMPS)-441(often)-440(use)-1(s)-440(additional)-441(pac)28(k-)]TJ -223.361 -13.549 Td [(ages)-288(suc)28(h)-288(as)-287(ScaLAP)83(A)28(CK,)-288(P)28(arMETIS,)-288(SCOTCH,)-287(as)-288(w)28(ell)-288(as)-288(enabling)-287(Op)-28(enMP;)-288(in)-287(suc)27(h)]TJ 0 -13.549 Td [(cases)-235(it)-234(is)-235(necessary)-234(to)-235(add)-234(link)28(er)-235(option)1(s)-235(with)-234(the)]TJ/F45 10.9091 Tf 233.579 0 Td [(--with-extra-libs)]TJ/F15 10.9091 Tf 99.92 0 Td [(con\014gure)-234(option.)]TJ -316.563 -13.549 Td [(T)83(o)-333(build)-333(the)-334(li)1(brary)-334(the)-333(user)-333(will)-334(no)28(w)-333(en)28(ter)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf -16.936 -22.516 Td [(make)]TJ/F15 10.9091 Tf 0 -22.515 Td [(follo)28(w)28(ed)-334(\050optionally\051)-333(b)28(y)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 0 -22.516 Td [(make)-525(install)]TJ/F17 11.9552 Tf 0 -29.213 Td [(3.4)-1125(Bug)-375(rep)-31(orting)]TJ/F15 10.9091 Tf 0 -20.594 Td [(If)-333(y)28(ou)-334(\014nd)-333(an)28(y)-333(bugs)-334(in)-333(our)-333(co)-28(des,)-333(please)-334(rep)-28(ort)-333(them)-333(through)-333(our)-334(issues)-333(page)-333(on)]TJ -0 1 0 0 k 0 1 0 0 K -/F45 10.9091 Tf 0 -19.219 Td [(https://github.com/sfilippone/mld2p4-)-45(2/issues)]TJ -0 g 0 G -/F15 10.9091 Tf 0 -13.549 Td [(T)83(o)-292(enable)-293(us)-293(to)-292(trac)27(k)-292(the)-293(bug,)-301(please)-293(pro)28(vide)-292(a)-293(log)-293(from)-293(th)1(e)-293(failing)-293(application,)-300(the)-293(test)]TJ 0 -13.549 Td [(conditions,)-333(and)-333(ideally)-334(a)-333(self-con)28(tained)-334(test)-333(program)-333(repro)-28(ducing)-333(the)-333(is)-1(sue.)]TJ/F17 11.9552 Tf 0 -29.213 Td [(3.5)-1125(Example)-375(and)-375(test)-375(programs)]TJ/F15 10.9091 Tf 0 -20.595 Td [(The)-419(pac)28(k)55(age)-418(con)27(tains)-418(the)]TJ/F45 10.9091 Tf 128.338 0 Td [(examples)]TJ/F15 10.9091 Tf 50.387 0 Td [(and)]TJ/F45 10.9091 Tf 22.146 0 Td [(tests)]TJ/F15 10.9091 Tf 33.205 0 Td [(directories;)-462(b)-27(oth)-419(of)-419(them)-419(are)-419(further)]TJ -234.076 -13.549 Td [(divided)-333(in)28(to)]TJ/F45 10.9091 Tf 60.606 0 Td [(fileread)]TJ/F15 10.9091 Tf 49.454 0 Td [(and)]TJ/F45 10.9091 Tf 21.212 0 Td [(pdegen)]TJ/F15 10.9091 Tf 38 0 Td [(sub)-28(directories.)-444(Their)-333(purp)-28(ose)-333(is)-334(as)-333(follo)28(ws:)]TJ -0 g 0 G -/F45 10.9091 Tf -169.272 -22.515 Td [(examples)]TJ -0 g 0 G -/F15 10.9091 Tf 51.272 0 Td [(con)28(tains)-245(a)-244(s)-1(et)-244(of)-245(simple)-245(example)-244(programs)-245(with)-244(a)-245(prede\014ned)-245(c)28(hoice)-245(of)-244(precon-)]TJ -23.999 -13.55 Td [(ditioners,)-294(selectable)-284(via)-284(in)28(teger)-284(v)56(alues.)-428(These)-284(are)-284(in)28(tended)-284(to)-284(get)-284(an)-284(acquain)28(tance)]TJ 0 -13.549 Td [(with)-333(the)-334(m)28(ultilev)28(el)-333(preconditioners)-334(a)28(v)56(ailable)-333(in)-334(MLD2P4.)]TJ -0 g 0 G -/F45 10.9091 Tf -27.273 -22.515 Td [(tests)]TJ -0 g 0 G -/F15 10.9091 Tf 34.09 0 Td [(con)28(tains)-380(a)-380(set)-380(of)-380(more)-380(sophi)1(s)-1(ticated)-379(examples)-380(that)-380(will)-380(allo)28(w)-380(the)-380(user,)-391(via)-380(the)]TJ -6.817 -13.55 Td [(input)-286(\014les)-287(in)-286(the)]TJ/F45 10.9091 Tf 80.438 0 Td [(runs)]TJ/F15 10.9091 Tf 26.034 0 Td [(sub)-28(directories,)-296(t)1(o)-287(exp)-28(erimen)28(t)-286(with)-287(the)-286(full)-286(range)-287(of)-286(precon-)]TJ -106.472 -13.549 Td [(ditioners)-333(implemen)28(te)-1(d)-333(in)-333(the)-333(pac)27(k)56(age.)]TJ -27.273 -22.515 Td [(The)]TJ/F45 10.9091 Tf 24.239 0 Td [(fileread)]TJ/F15 10.9091 Tf 51.269 0 Td [(directories)-500(con)28(tain)-500(sample)-499(programs)-500(that)-500(read)-499(sparse)-500(matrices)-500(from)]TJ -75.508 -13.55 Td [(\014les,)-295(according)-285(to)-285(the)-285(Matrix)-285(Mark)28(et)-285(or)-285(the)-285(Harw)27(ell-Bo)-27(eing)-286(storage)-285(format;)-301(the)]TJ/F45 10.9091 Tf 378.088 0 Td [(pdegen)]TJ/F15 10.9091 Tf -378.088 -13.549 Td [(programs)-416(generate)-415(matrices)-416(in)-416(full)-415(parallel)-416(mo)-28(de)-416(from)-415(the)-416(discretization)-416(of)-415(a)-416(sample)]TJ 0 -13.549 Td [(partial)-333(di\013eren)28(tial)-334(equation.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -344 0 obj -<< -/Length 8161 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(4)]TJ -0 g 0 G - [-378(Mul)67(tigrid)-378(Ba)22(ck)22(gr)23(ound)]TJ/F15 10.9091 Tf 401.542 0 Td [(11)]TJ -0 g 0 G -/F17 14.3462 Tf -401.542 -35.866 Td [(4)-1125(Multigrid)-375(Bac)31(kground)]TJ/F15 10.9091 Tf 0 -25.431 Td [(Multigrid)-467(preconditioners,)-500(coupled)-468(with)-467(Krylo)28(v)-467(iterativ)28(e)-467(solv)27(ers,)-500(are)-467(widely)-467(use)-1(d)-467(in)]TJ 0 -13.549 Td [(the)-374(par)1(allel)-374(solution)-373(of)-374(large)-374(and)-373(sparse)-374(linear)-373(systems,)-384(b)-28(ecause)-373(of)-374(their)-373(optimalit)28(y)-374(in)]TJ 0 -13.55 Td [(the)-411(solution)-411(of)-411(linear)-411(systems)-411(arising)-411(from)-411(the)-412(d)1(isc)-1(r)1(e)-1(tization)-411(of)-411(scalar)-411(elliptic)-411(P)28(artial)]TJ 0 -13.549 Td [(Di\013eren)28(tial)-331(Equations)-330(\050PDEs\051)-331(on)-330(regular)-331(grids.)-443(Optimalit)28(y)83(,)-331(also)-331(kn)1(o)27(wn)-330(as)-331(algorithmic)]TJ 0 -13.549 Td [(scalabilit)28(y)83(,)-404(is)-389(the)-390(prop)-28(ert)28(y)-390(of)-390(ha)28(ving)-389(a)-390(computational)-390(cost)-390(p)-27(er)-390(iteration)-390(that)-390(dep)-27(ends)]TJ 0 -13.549 Td [(linearly)-291(on)-292(the)-291(problem)-292(size,)-299(and)-292(a)-291(con)28(v)27(ergence)-291(rate)-292(that)-291(is)-291(indep)-28(enden)28(t)-292(of)-291(the)-292(prob)1(le)-1(m)]TJ 0 -13.549 Td [(size.)]TJ 16.937 -14.105 Td [(Multigrid)-304(preconditioners)-304(are)-304(based)-304(on)-304(a)-304(recursiv)28(e)-304(application)-304(of)-304(a)-304(t)28(w)28(o-grid)-304(pro)-28(cess)]TJ -16.937 -13.549 Td [(consisting)-391(of)-391(smo)-28(other)-391(iterations)-391(and)-392(a)-391(coarse-space)-391(\050or)-391(coarse-lev)27(el\051)-391(correction.)-618(The)]TJ 0 -13.55 Td [(smo)-28(others)-343(ma)27(y)-343(b)-28(e)-343(either)-343(basic)-344(iterativ)28(e)-343(m)-1(eth)1(o)-28(ds,)-346(suc)28(h)-344(as)-343(the)-344(Jacobi)-343(and)-343(Gauss-Seidel)]TJ 0 -13.549 Td [(ones,)-434(or)-414(more)-414(complex)-414(subspace-correction)-414(metho)-28(ds,)-434(suc)28(h)-414(as)-414(the)-414(Sc)28(h)27(w)28(arz)-414(ones.)-686(The)]TJ 0 -13.549 Td [(coarse-space)-304(correction)-304(consists)-303(of)-304(solving,)-310(in)-303(an)-304(appropriately)-303(c)27(hosen)-303(coarse)-304(space,)-310(the)]TJ 0 -13.549 Td [(residual)-297(equation)-296(asso)-28(ciated)-297(with)-296(the)-297(appro)28(ximate)-297(solution)-296(computed)-297(b)28(y)-297(th)1(e)-297(smo)-28(other,)]TJ 0 -13.549 Td [(and)-359(of)-359(using)-359(the)-359(solution)-359(of)-359(this)-359(equation)-359(to)-359(correct)-359(the)-359(previous)-359(appro)28(ximation.)-522(The)]TJ 0 -13.55 Td [(transfer)-467(of)-467(information)-468(b)-27(et)27(w)28(een)-467(the)-467(original)-468(\050\014)1(ne\051)-468(space)-467(and)-467(the)-468(coarse)-467(one)-467(is)-468(p)-27(er-)]TJ 0 -13.549 Td [(formed)-394(b)27(y)-394(using)-394(suitable)-395(restriction)-394(and)-394(prolongation)-395(op)-27(erators.)-628(The)-394(construction)-395(of)]TJ 0 -13.549 Td [(the)-410(coarse)-409(s)-1(p)1(ac)-1(e)-409(and)-410(the)-410(corresp)-27(onding)-410(transfer)-410(op)-27(erators)-410(is)-410(carried)-409(out)-410(b)28(y)-410(applying)]TJ 0 -13.549 Td [(a)-390(so-called)-391(coarsening)-390(algorithm)-390(to)-390(the)-390(s)-1(ystem)-390(matrix.)-615(Tw)28(o)-391(main)-390(approac)28(hes)-390(can)-390(b)-28(e)]TJ 0 -13.549 Td [(used)-370(to)-369(p)-28(erform)-369(c)-1(oar)1(s)-1(enin)1(g:)-517(the)-370(geometric)-370(approac)28(h,)-378(whic)27(h)-369(exploits)-370(the)-369(kno)28(wledge)-370(of)]TJ 0 -13.55 Td [(some)-361(ph)28(ysical)-361(grid)-361(ass)-1(o)-27(ciated)-361(with)-361(the)-362(matri)1(x)-362(and)-361(requi)1(res)-362(the)-361(user)-361(to)-361(de\014ne)-361(transfer)]TJ 0 -13.549 Td [(op)-28(erators)-348(from)-349(the)-348(\014ne)-349(to)-348(the)-349(coarse)-348(lev)27(el)-348(and)-349(vi)1(c)-1(e)-348(v)28(ersa,)-353(and)-348(the)-349(algebrai)1(c)-349(approac)28(h,)]TJ 0 -13.549 Td [(whic)28(h)-282(builds)-283(the)-282(coarse-space)-282(correc)-1(ti)1(on)-283(and)-282(the)-282(asso)-28(ciate)-282(transfer)-283(op)-27(erators)-283(using)-282(only)]TJ 0 -13.549 Td [(matrix)-369(inf)1(ormation.)-551(The)-368(\014rst)-369(approac)28(h)-369(ma)28(y)-369(b)-27(e)-369(di\016cult)-369(wh)1(e)-1(n)-368(the)-369(system)-368(c)-1(omes)-368(from)]TJ 0 -13.549 Td [(discretizations)-288(on)-288(complex)-287(ge)-1(ometries;)-303(fur)1(thermore,)-297(ad)-288(ho)-28(c)-288(one-lev)28(el)-288(smo)-28(others)-288(ma)28(y)-288(b)-27(e)]TJ 0 -13.549 Td [(required)-307(to)-307(get)-306(an)-307(e\016cien)27(t)-306(in)27(terpla)28(y)-307(b)-27(et)27(w)28(een)-307(\014ne)-307(and)-306(coarse)-307(lev)28(e)-1(ls,)-312(e.g.,)-312(when)-307(matrices)]TJ 0 -13.55 Td [(with)-363(hi)1(ghly)-363(v)56(arying)-363(co)-28(e\016cien)28(ts)-363(are)-362(considered.)-532(The)-363(second)-363(appr)1(oac)27(h)-362(p)-28(erforms)-363(a)-362(fully)]TJ 0 -13.549 Td [(automatic)-349(coarsening)-350(and)-349(enforces)-349(the)-349(in)27(t)1(e)-1(rp)1(la)27(y)-349(b)-28(et)28(w)28(een)-349(\014ne)-350(and)-349(coarse)-349(lev)27(el)-349(b)28(y)-349(suit-)]TJ 0 -13.549 Td [(ably)-313(c)28(ho)-28(osing)-313(the)-313(coarse)-313(space)-313(and)-313(the)-313(coarse-to-\014ne)-313(in)28(terp)-28(olation)-313(\050see,)-317(e.g.,)-317([)]TJ -1 0 0 rg 1 0 0 RG - [(3)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-313(24)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-313(22)]TJ -0 g 0 G - [(])]TJ 0 -13.549 Td [(for)-333(details.\051)]TJ 16.937 -14.105 Td [(MLD2P4)-329(uses)-330(a)-329(pure)-330(algebraic)-329(approac)28(h,)-331(b)1(as)-1(ed)-329(on)-329(the)-330(smo)-28(othed)-329(aggregation)-330(algo-)]TJ -16.937 -13.549 Td [(rithm)-298([)]TJ -1 0 0 rg 1 0 0 RG - [(2)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-298(26)]TJ -0 g 0 G - [(],)-305(for)-298(building)-298(the)-298(sequence)-298(of)-298(coarse)-298(matrices)-298(and)-298(transfer)-298(op)-28(erators,)-305(start-)]TJ 0 -13.549 Td [(ing)-306(from)-306(the)-305(original)-306(one.)-435(A)-306(decoupled)-306(v)28(ersion)-306(of)-306(this)-306(algori)1(thm)-306(is)-306(implemen)28(ted,)-312(where)]TJ 0 -13.55 Td [(the)-316(smo)-28(othed)-316(aggregation)-315(is)-316(applied)-316(lo)-28(cally)-316(to)-316(eac)28(h)-316(submatrix)-316([)]TJ -1 0 0 rg 1 0 0 RG - [(25)]TJ -0 g 0 G - [(].)-438(A)-316(brief)-316(description)]TJ 0 -13.549 Td [(of)-333(the)-333(AMG)-333(prec)-1(on)1(ditioners)-334(implemen)28(ted)-333(in)-333(MLD2P4)-333(is)-333(giv)27(en)-333(in)-333(Sections)]TJ -0 0 1 rg 0 0 1 RG - [-333(4.1)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(4.3)]TJ -0 g 0 G - [(.)-444(F)83(or)]TJ 0 -13.549 Td [(further)-333(details)-334(th)1(e)-334(reader)-333(is)-334(r)1(e)-1(f)1(e)-1(r)1(re)-1(d)-333(to)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(4)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-333(5)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-334(7)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-333(8)]TJ -0 g 0 G - [(].)]TJ 16.937 -14.105 Td [(W)83(e)-430(note)-430(that)-430(opti)1(m)-1(al)-429(m)27(ultigrid)-430(pr)1(e)-1(cond)1(itioners)-430(do)-430(not)-430(necessarily)-430(corresp)-28(ond)-430(to)]TJ -16.937 -13.549 Td [(minim)28(um)-486(execution)-485(times)-485(in)-485(a)-486(parallel)-485(setting.)-900(Indeed,)-523(to)-486(obtain)-485(e\013ectiv)28(e)-486(parallel)]TJ 0 -13.549 Td [(m)28(ultigrid)-403(preconditioners,)-421(a)-403(tradeo\013)-403(b)-28(et)28(w)28(een)-404(the)-403(optimalit)28(y)-403(and)-403(the)-403(cost)-404(of)-403(buildi)1(ng)]TJ 0 -13.549 Td [(and)-223(applying)-223(the)-223(smo)-28(others)-223(and)-223(the)-223(coarse-space)-223(corrections)-223(m)27(ust)-223(b)-27(e)-224(ac)28(hiev)28(ed.)-408(E\013ectiv)28(e)]TJ 0 -13.55 Td [(parallel)-324(preconditioners)-324(re)-1(q)1(uire)-325(algorithmic)-324(scalabilit)28(y)-325(to)-324(b)-28(e)-324(coupled)-324(with)-325(implemen)28(ta-)]TJ 0 -13.549 Td [(tion)-270(scalabilit)28(y)83(,)-282(i.e.,)-283(a)-270(computational)-269(cost)-270(p)-28(er)-270(iteration)-270(whic)28(h)-270(remains)-270(\050almost\051)-270(constan)28(t)]TJ 0 -13.549 Td [(as)-333(the)-334(n)28(um)28(b)-28(er)-333(of)-333(parallel)-334(pro)-27(ce)-1(ssors)-333(increases.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -358 0 obj -<< -/Length 11395 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(12)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F17 11.9552 Tf -203.265 -35.866 Td [(4.1)-1125(AMG)-375(preconditioners)]TJ/F15 10.9091 Tf 0 -20.594 Td [(In)-463(order)-463(to)-463(describ)-27(e)-463(the)-463(AMG)-463(preconditioners)-463(a)28(v)56(ailable)-463(in)-463(MLD2P4,)-495(w)27(e)-463(consid)1(e)-1(r)-462(a)]TJ 0 -13.549 Td [(linear)-333(system)]TJ/F22 10.9091 Tf 186.979 -13.55 Td [(Ax)]TJ/F15 10.9091 Tf 17.447 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(b;)]TJ -0 g 0 G -/F15 10.9091 Tf 182.57 0 Td [(\0502\051)]TJ -0 g 0 G - -398.511 -19.516 Td [(where)]TJ/F22 10.9091 Tf 32.496 0 Td [(A)]TJ/F15 10.9091 Tf 12.796 0 Td [(=)-423(\050)]TJ/F22 10.9091 Tf 17.342 0 Td [(a)]TJ/F23 7.9701 Tf 5.767 -1.636 Td [(ij)]TJ/F15 10.9091 Tf 7.265 1.636 Td [(\051)]TJ/F25 10.9091 Tf 8.857 0 Td [(2)]TJ/F34 10.9091 Tf 11.888 0 Td [(R)]TJ/F23 7.9701 Tf 7.878 3.959 Td [(n)]TJ/F26 7.9701 Tf 5.139 0 Td [(\002)]TJ/F23 7.9701 Tf 6.586 0 Td [(n)]TJ/F15 10.9091 Tf 10.223 -3.959 Td [(is)-421(a)-420(nonsingular)-420(sparse)-421(matrix;)-464(for)-420(ease)-421(of)-420(presen)28(tation)-421(w)28(e)]TJ -126.237 -13.549 Td [(assume)]TJ/F22 10.9091 Tf 37.697 0 Td [(A)]TJ/F15 10.9091 Tf 11.818 0 Td [(has)-333(a)-334(symmetric)-333(sparsit)28(y)-334(pattern.)]TJ -32.579 -13.549 Td [(Let)-468(us)-469(consider)-468(as)-468(\014nest)-469(ind)1(e)-1(x)-468(space)-468(the)-468(s)-1(et)-468(of)-468(ro)28(w)-469(\050column\051)-468(indices)-468(of)]TJ/F22 10.9091 Tf 361.856 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(,)-502(i.e.,)]TJ -386.974 -13.55 Td [(\012)-377(=)]TJ/F25 10.9091 Tf 24.593 0 Td [(f)]TJ/F15 10.9091 Tf 5.454 0 Td [(1)]TJ/F22 10.9091 Tf 5.455 0 Td [(;)]TJ/F15 10.9091 Tf 4.848 0 Td [(2)]TJ/F22 10.9091 Tf 5.455 0 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(n)]TJ/F25 10.9091 Tf 30.79 0 Td [(g)]TJ/F15 10.9091 Tf 5.455 0 Td [(.)-623(An)28(y)-393(algebraic)-393(m)27(ultilev)28(el)-393(preconditioners)-393(implemen)28(ted)-393(in)-393(MLD2P4)]TJ -82.05 -13.549 Td [(generates)-333(a)-334(hierarc)28(h)28(y)-333(of)-334(index)-333(spaces)-333(and)-334(a)-333(corresp)-28(onding)-333(hierarc)28(h)28(y)-334(of)-333(matrices,)]TJ 81.377 -23.491 Td [(\012)]TJ/F20 7.9701 Tf 7.879 4.505 Td [(1)]TJ/F25 10.9091 Tf 7.762 -4.505 Td [(\021)]TJ/F15 10.9091 Tf 11.515 0 Td [(\012)]TJ/F25 10.9091 Tf 10.909 0 Td [(\033)]TJ/F15 10.9091 Tf 11.515 0 Td [(\012)]TJ/F20 7.9701 Tf 7.879 4.505 Td [(2)]TJ/F25 10.9091 Tf 7.763 -4.505 Td [(\033)]TJ/F22 10.9091 Tf 11.515 0 Td [(:)-167(:)-166(:)]TJ/F25 10.9091 Tf 15.757 0 Td [(\033)]TJ/F15 10.9091 Tf 11.516 0 Td [(\012)]TJ/F23 7.9701 Tf 7.878 4.505 Td [(nl)-12(ev)]TJ/F22 10.9091 Tf 16.597 -4.505 Td [(;)-1167(A)]TJ/F20 7.9701 Tf 23.939 4.505 Td [(1)]TJ/F25 10.9091 Tf 7.763 -4.505 Td [(\021)]TJ/F22 10.9091 Tf 11.515 0 Td [(A;)-167(A)]TJ/F20 7.9701 Tf 21.212 4.505 Td [(2)]TJ/F22 10.9091 Tf 4.732 -4.505 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(A)]TJ/F23 7.9701 Tf 32.424 4.505 Td [(nl)-12(ev)]TJ/F22 10.9091 Tf 16.597 -4.505 Td [(;)]TJ/F15 10.9091 Tf -328.044 -23.49 Td [(b)28(y)-282(using)-282(the)-282(information)-282(con)28(tained)-282(in)]TJ/F22 10.9091 Tf 180.373 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(,)-292(without)-282(assuming)-282(an)27(y)-282(kno)28(wledge)-282(of)-282(the)-282(geom-)]TJ -188.555 -13.55 Td [(etry)-295(of)-294(the)-295(problem)-294(from)-295(whic)28(h)]TJ/F22 10.9091 Tf 150.888 0 Td [(A)]TJ/F15 10.9091 Tf 11.395 0 Td [(originates.)-431(A)-295(v)28(ector)-295(space)]TJ/F34 10.9091 Tf 126.348 0 Td [(R)]TJ/F23 7.9701 Tf 7.879 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.406 Td [(k)]TJ/F15 10.9091 Tf 8.285 -2.553 Td [(is)-295(asso)-27(ciate)-1(d)-294(with)-295(\012)]TJ/F23 7.9701 Tf 94.368 3.959 Td [(k)]TJ/F15 10.9091 Tf 5.12 -3.959 Td [(,)]TJ -409.421 -13.549 Td [(where)]TJ/F22 10.9091 Tf 31.714 0 Td [(n)]TJ/F23 7.9701 Tf 6.548 -1.777 Td [(k)]TJ/F15 10.9091 Tf 8.925 1.777 Td [(is)-349(the)-349(size)-348(of)-349(\012)]TJ/F23 7.9701 Tf 71.401 3.959 Td [(k)]TJ/F15 10.9091 Tf 5.12 -3.959 Td [(.)-491(F)84(or)-349(all)]TJ/F22 10.9091 Tf 43.449 0 Td [(k)-335(<)-304(nl)-19(ev)]TJ/F15 10.9091 Tf 41.907 0 Td [(,)-353(a)-348(restriction)-349(op)-28(erator)-349(and)-348(a)-349(prolongation)]TJ -209.064 -13.549 Td [(one)-333(are)-334(built,)-333(whic)28(h)-333(connect)-334(t)28(w)28(o)-334(l)1(e)-1(v)28(els)]TJ/F22 10.9091 Tf 188.273 0 Td [(k)]TJ/F15 10.9091 Tf 9.659 0 Td [(and)]TJ/F22 10.9091 Tf 21.212 0 Td [(k)]TJ/F15 10.9091 Tf 8.447 0 Td [(+)-222(1:)]TJ/F22 10.9091 Tf -101.285 -23.491 Td [(P)]TJ/F23 7.9701 Tf 8.519 4.504 Td [(k)]TJ/F25 10.9091 Tf 8.15 -4.504 Td [(2)]TJ/F34 10.9091 Tf 10.303 0 Td [(R)]TJ/F23 7.9701 Tf 7.879 4.504 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.405 Td [(k)]TJ/F26 7.9701 Tf 4.573 1.405 Td [(\002)]TJ/F23 7.9701 Tf 6.587 0 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.405 Td [(k)]TJ/F21 5.9776 Tf 4.075 0 Td [(+1)]TJ/F22 10.9091 Tf 10.239 -3.099 Td [(;)-1167(R)]TJ/F23 7.9701 Tf 24.125 4.504 Td [(k)]TJ/F25 10.9091 Tf 8.15 -4.504 Td [(2)]TJ/F34 10.9091 Tf 10.303 0 Td [(R)]TJ/F23 7.9701 Tf 7.879 4.504 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.405 Td [(k)]TJ/F21 5.9776 Tf 4.075 0 Td [(+1)]TJ/F26 7.9701 Tf 9.741 1.405 Td [(\002)]TJ/F23 7.9701 Tf 6.587 0 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.405 Td [(k)]TJ/F15 10.9091 Tf 5.071 -3.099 Td [(;)]TJ -283.114 -23.491 Td [(the)-282(matrix)]TJ/F22 10.9091 Tf 53.146 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(k)]TJ/F20 7.9701 Tf 4.621 0 Td [(+1)]TJ/F15 10.9091 Tf 14.392 -3.959 Td [(is)-282(computed)-281(b)27(y)-281(using)-282(the)-282(previou)1(s)-282(op)-28(erators)-282(according)-281(to)-282(the)-282(Galerkin)]TJ -80.341 -13.549 Td [(approac)28(h,)-333(i.e.,)]TJ/F22 10.9091 Tf 165.163 -13.549 Td [(A)]TJ/F23 7.9701 Tf 8.182 4.504 Td [(k)]TJ/F20 7.9701 Tf 4.621 0 Td [(+1)]TJ/F15 10.9091 Tf 14.349 -4.504 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 4.504 Td [(k)]TJ/F22 10.9091 Tf 5.12 -4.504 Td [(A)]TJ/F23 7.9701 Tf 8.181 4.504 Td [(k)]TJ/F22 10.9091 Tf 5.12 -4.504 Td [(P)]TJ/F23 7.9701 Tf 8.519 4.504 Td [(k)]TJ/F22 10.9091 Tf 5.12 -4.504 Td [(:)]TJ/F15 10.9091 Tf -244.258 -19.516 Td [(In)-476(the)-477(curren)28(t)-476(implemen)28(tation)-477(of)-476(MLD2P4)-476(w)28(e)-477(ha)28(v)28(e)]TJ/F22 10.9091 Tf 261.479 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.958 Td [(k)]TJ/F15 10.9091 Tf 10.749 -3.958 Td [(=)-516(\050)]TJ/F22 10.9091 Tf 18.358 0 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.958 Td [(k)]TJ/F15 10.9091 Tf 5.119 -3.958 Td [(\051)]TJ/F23 7.9701 Tf 4.243 3.958 Td [(T)]TJ/F15 10.9091 Tf 11.801 -3.958 Td [(A)-476(smo)-28(other)-476(with)]TJ -328.636 -13.55 Td [(iteration)-441(matrix)]TJ/F22 10.9091 Tf 82.101 0 Td [(M)]TJ/F23 7.9701 Tf 11.773 3.959 Td [(k)]TJ/F15 10.9091 Tf 9.928 -3.959 Td [(is)-441(set)-441(up)-440(at)-441(eac)28(h)-441(lev)28(el)]TJ/F22 10.9091 Tf 113.517 0 Td [(k)-488(<)-457(nl)-20(ev)]TJ/F15 10.9091 Tf 45.251 0 Td [(,)-468(and)-440(a)-441(solv)28(er)-441(is)-441(set)-441(up)-440(at)-441(the)]TJ -262.57 -13.549 Td [(coarsest)-369(lev)28(el,)-378(so)-368(that)-369(they)-369(are)-369(ready)-368(for)-369(application)-369(\050for)-368(example,)-378(setting)-369(up)-368(a)-369(solv)28(er)]TJ 0 -13.549 Td [(based)-292(on)-291(the)]TJ/F22 10.9091 Tf 62.938 0 Td [(LU)]TJ/F15 10.9091 Tf 19.243 0 Td [(factorization)-292(means)-291(computing)-292(and)-291(storing)-292(the)]TJ/F22 10.9091 Tf 224.422 0 Td [(L)]TJ/F15 10.9091 Tf 10.605 0 Td [(and)]TJ/F22 10.9091 Tf 20.757 0 Td [(U)]TJ/F15 10.9091 Tf 11.819 0 Td [(factors\051.)-431(The)]TJ -349.784 -13.549 Td [(construction)-345(of)-344(the)-345(hierarc)28(h)27(y)-344(of)-345(AMG)-345(comp)-28(on)1(e)-1(n)28(ts)-345(d)1(e)-1(scrib)-27(ed)-345(so)-345(far)-345(corresp)-27(onds)-345(to)-345(the)]TJ 0 -13.549 Td [(so-called)-333(build)-334(ph)1(as)-1(e)-333(of)-333(the)-334(p)1(rec)-1(on)1(ditioner.)]TJ 16.936 -13.55 Td [(The)-359(com)-1(p)-27(onen)28(ts)-360(pro)-28(du)1(c)-1(ed)-359(in)-359(the)-360(build)-359(phase)-359(ma)27(y)-359(b)-28(e)-359(com)28(bined)-360(in)-359(sev)28(eral)-360(w)28(a)28(ys)-360(to)]TJ -16.936 -13.549 Td [(obtain)-306(di\013eren)28(t)-306(m)27(ultilev)28(el)-306(preconditioners;)-315(this)-306(is)-306(done)-307(in)-306(the)-306(application)-306(phase,)-312(i)1(.e)-1(.)1(,)-312(in)]TJ 0 -13.549 Td [(the)-391(computation)-391(of)-391(a)-391(v)27(ector)-391(of)-391(t)28(yp)-28(e)]TJ/F22 10.9091 Tf 178.081 0 Td [(w)]TJ/F15 10.9091 Tf 12.185 0 Td [(=)]TJ/F22 10.9091 Tf 12.566 0 Td [(B)]TJ/F26 7.9701 Tf 8.822 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.959 Td [(v)]TJ/F15 10.9091 Tf 5.68 0 Td [(,)-406(where)]TJ/F22 10.9091 Tf 39.631 0 Td [(B)]TJ/F15 10.9091 Tf 13.089 0 Td [(denotes)-391(the)-391(preconditioner,)]TJ -281.372 -13.549 Td [(usually)-334(with)1(in)-334(an)-334(iteration)-333(of)-334(a)-334(Kr)1(ylo)27(v)-333(solv)27(er)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(21)]TJ -0 g 0 G - [(].)-446(An)-333(example)-334(of)-333(s)-1(u)1(c)27(h)-333(a)-334(com)28(bination,)]TJ 0 -13.549 Td [(kno)28(wn)-448(as)-448(V-cycle,)-476(is)-448(giv)28(en)-448(in)-447(Figure)]TJ -0 0 1 rg 0 0 1 RG - [-448(1)]TJ -0 g 0 G - [(.)-788(In)-447(this)-448(case,)-476(a)-448(single)-448(iteration)-448(of)-447(the)-448(same)]TJ 0 -13.549 Td [(smo)-28(other)-333(is)-332(used)-333(b)-28(efore)-333(and)-332(after)-333(the)-333(the)-333(recursiv)28(e)-333(call)-333(to)-332(the)-333(V-cycle)-333(\050i.e.,)-333(in)-333(th)1(e)-333(pre-)]TJ 0 -13.55 Td [(smo)-28(othing)-409(an)1(d)-409(p)-28(ost-smo)-28(othing)-409(ph)1(as)-1(es\051;)-446(ho)28(w)27(ev)28(er,)-427(di\013eren)27(t)-408(c)27(hoices)-409(can)-408(b)-28(e)-409(p)-28(erformed.)]TJ 0 -13.549 Td [(Other)-405(cycles)-405(c)-1(an)-405(b)-27(e)-406(de\014ned;)-441(in)-405(MLD2P4,)-423(w)28(e)-405(implemen)27(ted)-405(the)-405(standard)-405(V-cycle)-405(and)]TJ 0 -13.549 Td [(W-cycle)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(3)]TJ -0 g 0 G - [(],)-334(and)-333(a)-333(v)28(e)-1(r)1(s)-1(ion)-333(of)-333(the)-333(K-cyc)-1(l)1(e)-334(describ)-28(ed)-333(in)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(20)]TJ -0 g 0 G - [(].)]TJ/F17 11.9552 Tf 0 -29.053 Td [(4.2)-1125(Smo)-31(othed)-375(Aggregation)]TJ/F15 10.9091 Tf 0 -20.595 Td [(In)-374(order)-374(to)-374(de\014ne)-374(the)-375(prolongator)]TJ/F22 10.9091 Tf 167.339 0 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.959 Td [(k)]TJ/F15 10.9091 Tf 5.12 -3.959 Td [(,)-384(used)-375(to)-374(compute)-374(the)-374(coarse-lev)28(el)-375(matrix)]TJ/F22 10.9091 Tf 204.32 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(k)]TJ/F20 7.9701 Tf 4.622 0 Td [(+1)]TJ/F15 10.9091 Tf 11.319 -3.959 Td [(,)]TJ -409.421 -13.549 Td [(MLD2P4)-319(uses)-320(the)-319(smo)-28(othed)-319(aggregation)-319(algorithm)-320(describ)-27(ed)-320(in)-319([)]TJ -1 0 0 rg 1 0 0 RG - [(2)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-319(26)]TJ -0 g 0 G - [(].)-440(The)-319(basic)-320(idea)]TJ 0 -13.549 Td [(of)-270(this)-271(algorithm)-270(is)-271(to)-270(build)-270(a)-271(coarse)-270(se)-1(t)-270(of)-270(indices)-271(\012)]TJ/F23 7.9701 Tf 243.122 3.959 Td [(k)]TJ/F20 7.9701 Tf 4.621 0 Td [(+1)]TJ/F15 10.9091 Tf 14.27 -3.959 Td [(b)28(y)-271(suitabl)1(y)-271(grouping)-270(the)-271(indices)]TJ -262.013 -13.549 Td [(of)-350(\012)]TJ/F23 7.9701 Tf 20.481 3.959 Td [(k)]TJ/F15 10.9091 Tf 8.934 -3.959 Td [(in)28(to)-350(disjoin)28(t)-350(sub)1(s)-1(ets)-349(\050aggregates\051,)-354(and)-350(to)-349(de\014ne)-350(the)-349(coarse)-1(-to-\014n)1(e)-350(space)-350(transfer)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -377 0 obj -<< -/Length 11453 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(4)]TJ -0 g 0 G - [-378(Mul)67(tigrid)-378(Ba)22(ck)22(gr)23(ound)]TJ/F15 10.9091 Tf 401.542 0 Td [(13)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G - -292.247 -42.833 Td [(pro)-28(cedure)-333(V-cycle)]TJ/F28 10.9091 Tf 85.818 8.837 Td [(\000)]TJ/F22 10.9091 Tf 5 -8.837 Td [(k)-32(;)-166(A)]TJ/F23 7.9701 Tf 19.053 3.959 Td [(k)]TJ/F22 10.9091 Tf 5.12 -3.959 Td [(;)-167(b)]TJ/F23 7.9701 Tf 9.53 3.959 Td [(k)]TJ/F22 10.9091 Tf 5.12 -3.959 Td [(;)-167(u)]TJ/F23 7.9701 Tf 11.093 3.959 Td [(k)]TJ/F28 10.9091 Tf 5.12 4.878 Td [(\001)]TJ/F15 10.9091 Tf -134.945 -28.055 Td [(if)-333(\050)]TJ/F22 10.9091 Tf 14.242 0 Td [(k)]TJ/F25 10.9091 Tf 9.053 0 Td [(6)]TJ/F15 10.9091 Tf 0 0 Td [(=)]TJ/F22 10.9091 Tf 11.516 0 Td [(nl)-20(ev)]TJ/F15 10.9091 Tf 20.776 0 Td [(\051)-333(then)]TJ/F22 10.9091 Tf -44.678 -16.393 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.958 Td [(k)]TJ/F15 10.9091 Tf 8.15 -3.958 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.958 Td [(k)]TJ/F15 10.9091 Tf 7.544 -3.958 Td [(+)]TJ/F22 10.9091 Tf 10.909 0 Td [(M)]TJ/F23 7.9701 Tf 11.773 3.958 Td [(k)]TJ/F28 10.9091 Tf 6.938 4.878 Td [(\000)]TJ/F22 10.9091 Tf 5 -8.836 Td [(b)]TJ/F23 7.9701 Tf 4.682 3.958 Td [(k)]TJ/F25 10.9091 Tf 7.544 -3.958 Td [(\000)]TJ/F22 10.9091 Tf 10.909 0 Td [(A)]TJ/F23 7.9701 Tf 8.181 3.958 Td [(k)]TJ/F22 10.9091 Tf 5.12 -3.958 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.958 Td [(k)]TJ/F28 10.9091 Tf 5.12 4.878 Td [(\001)]TJ/F22 10.9091 Tf -122.12 -25.229 Td [(b)]TJ/F23 7.9701 Tf 4.682 3.958 Td [(k)]TJ/F20 7.9701 Tf 4.622 0 Td [(+1)]TJ/F15 10.9091 Tf 14.349 -3.958 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.958 Td [(k)]TJ/F20 7.9701 Tf 4.622 0 Td [(+1)]TJ/F28 10.9091 Tf 13.137 4.878 Td [(\000)]TJ/F22 10.9091 Tf 5 -8.836 Td [(b)]TJ/F23 7.9701 Tf 4.682 3.958 Td [(k)]TJ/F25 10.9091 Tf 7.544 -3.958 Td [(\000)]TJ/F22 10.9091 Tf 10.909 0 Td [(A)]TJ/F23 7.9701 Tf 8.181 3.958 Td [(k)]TJ/F22 10.9091 Tf 5.12 -3.958 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.958 Td [(k)]TJ/F28 10.9091 Tf 5.12 4.878 Td [(\001)]TJ/F22 10.9091 Tf -114.095 -25.229 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.958 Td [(k)]TJ/F20 7.9701 Tf 4.622 0 Td [(+1)]TJ/F15 10.9091 Tf 14.349 -3.958 Td [(=)-333(V-cycle)]TJ/F28 10.9091 Tf 47.273 8.836 Td [(\000)]TJ/F22 10.9091 Tf 5 -8.836 Td [(k)]TJ/F15 10.9091 Tf 8.447 0 Td [(+)-222(1)]TJ/F22 10.9091 Tf 16.363 0 Td [(;)-167(A)]TJ/F23 7.9701 Tf 13.03 3.958 Td [(k)]TJ/F20 7.9701 Tf 4.622 0 Td [(+1)]TJ/F22 10.9091 Tf 11.319 -3.958 Td [(;)-167(b)]TJ/F23 7.9701 Tf 9.53 3.958 Td [(k)]TJ/F20 7.9701 Tf 4.622 0 Td [(+1)]TJ/F22 10.9091 Tf 11.319 -3.958 Td [(;)]TJ/F15 10.9091 Tf 4.848 0 Td [(0)]TJ/F28 10.9091 Tf 5.455 8.836 Td [(\001)]TJ/F22 10.9091 Tf -167.044 -25.229 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.958 Td [(k)]TJ/F15 10.9091 Tf 8.15 -3.958 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.958 Td [(k)]TJ/F15 10.9091 Tf 7.544 -3.958 Td [(+)]TJ/F22 10.9091 Tf 10.909 0 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.958 Td [(k)]TJ/F20 7.9701 Tf 4.622 0 Td [(+1)]TJ/F22 10.9091 Tf 11.319 -3.958 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.958 Td [(k)]TJ/F20 7.9701 Tf 4.621 0 Td [(+1)]TJ/F22 10.9091 Tf -85.934 -20.352 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.959 Td [(k)]TJ/F15 10.9091 Tf 8.15 -3.959 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.959 Td [(k)]TJ/F15 10.9091 Tf 7.544 -3.959 Td [(+)]TJ/F22 10.9091 Tf 10.909 0 Td [(M)]TJ/F23 7.9701 Tf 11.773 3.959 Td [(k)]TJ/F28 10.9091 Tf 6.938 4.878 Td [(\000)]TJ/F22 10.9091 Tf 5 -8.837 Td [(b)]TJ/F23 7.9701 Tf 4.682 3.959 Td [(k)]TJ/F25 10.9091 Tf 7.544 -3.959 Td [(\000)]TJ/F22 10.9091 Tf 10.909 0 Td [(A)]TJ/F23 7.9701 Tf 8.181 3.959 Td [(k)]TJ/F22 10.9091 Tf 5.12 -3.959 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.959 Td [(k)]TJ/F28 10.9091 Tf 5.12 4.878 Td [(\001)]TJ/F15 10.9091 Tf -133.029 -25.22 Td [(else)]TJ/F22 10.9091 Tf 10.909 -18.375 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.959 Td [(k)]TJ/F15 10.9091 Tf 8.15 -3.959 Td [(=)]TJ/F28 10.9091 Tf 11.515 8.836 Td [(\000)]TJ/F22 10.9091 Tf 5 -8.836 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(k)]TJ/F28 10.9091 Tf 5.12 4.877 Td [(\001)]TJ/F26 7.9701 Tf 5 -2.497 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 6.551 -6.339 Td [(b)]TJ/F23 7.9701 Tf 4.682 3.959 Td [(k)]TJ/F15 10.9091 Tf -77.94 -20.343 Td [(endif)]TJ 0 -16.393 Td [(return)]TJ/F22 10.9091 Tf 33.394 0 Td [(u)]TJ/F23 7.9701 Tf 6.245 3.959 Td [(k)]TJ/F15 10.9091 Tf -50.548 -20.343 Td [(end)]TJ -ET -q -1 0 0 1 195.871 714.896 cm -[]0 d 0 J 0.398 w 0 0 m 207.909 0 l S -Q -q -1 0 0 1 196.071 504.814 cm -[]0 d 0 J 0.398 w 0 0 m 0 210.082 l S -Q -q -1 0 0 1 403.581 504.814 cm -[]0 d 0 J 0.398 w 0 0 m 0 210.082 l S -Q -q -1 0 0 1 195.871 504.814 cm -[]0 d 0 J 0.398 w 0 0 m 207.909 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 165.28 486.08 Td [(Figure)-333(1:)-445(Application)-333(phase)-333(of)-333(a)-334(V-cycle)-333(preconditioner.)]TJ -0 g 0 G -0 g 0 G - -71.68 -45.436 Td [(op)-28(erator)]TJ/F22 10.9091 Tf 42.856 0 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.958 Td [(k)]TJ/F15 10.9091 Tf 7.611 -3.958 Td [(b)28(y)-229(apply)1(ing)-229(a)-228(suitable)-229(smo)-28(ot)1(he)-1(r)-228(to)-228(a)-229(simple)-228(piecewise)-229(constan)28(t)-228(prolongation)]TJ -58.986 -13.55 Td [(op)-28(erator,)-333(with)-333(the)-334(aim)-333(of)-333(impro)28(ving)-334(the)-333(qualit)28(y)-333(of)-334(the)-333(coarse-space)-334(correction.)]TJ 16.937 -13.787 Td [(Three)-333(main)-334(steps)-333(can)-333(b)-28(e)-334(i)1(den)27(ti\014ed)-333(in)-333(the)-334(smo)-27(othed)-334(aggregation)-333(pro)-28(cedure:)]TJ -0 g 0 G - -3.603 -23.466 Td [(1.)]TJ -0 g 0 G - [-500(aggregation)-333(of)-334(t)1(he)-334(indices)-333(of)-333(\012)]TJ/F23 7.9701 Tf 160.091 3.959 Td [(k)]TJ/F15 10.9091 Tf 8.756 -3.959 Td [(to)-333(obtain)-334(\012)]TJ/F23 7.9701 Tf 55.151 3.959 Td [(k)]TJ/F20 7.9701 Tf 4.622 0 Td [(+1)]TJ/F15 10.9091 Tf 11.319 -3.959 Td [(;)]TJ -0 g 0 G - -239.939 -23.467 Td [(2.)]TJ -0 g 0 G - [-500(construction)-333(of)-333(the)-334(prolongator)]TJ/F22 10.9091 Tf 166.515 0 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.959 Td [(k)]TJ/F15 10.9091 Tf 5.12 -3.959 Td [(;)]TJ -0 g 0 G - -180.154 -23.466 Td [(3.)]TJ -0 g 0 G - [-500(application)-333(of)]TJ/F22 10.9091 Tf 82.727 0 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.958 Td [(k)]TJ/F15 10.9091 Tf 8.756 -3.958 Td [(and)]TJ/F22 10.9091 Tf 21.212 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.958 Td [(k)]TJ/F15 10.9091 Tf 8.15 -3.958 Td [(=)-278(\050)]TJ/F22 10.9091 Tf 15.757 0 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.958 Td [(k)]TJ/F15 10.9091 Tf 5.12 -3.958 Td [(\051)]TJ/F23 7.9701 Tf 4.242 3.958 Td [(T)]TJ/F15 10.9091 Tf 10.241 -3.958 Td [(to)-333(build)]TJ/F22 10.9091 Tf 41.212 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.958 Td [(k)]TJ/F20 7.9701 Tf 4.622 0 Td [(+1)]TJ/F15 10.9091 Tf 11.319 -3.958 Td [(.)]TJ -243.343 -23.467 Td [(In)-407(order)-407(to)-407(p)-28(erform)-407(the)-407(coarsening)-407(s)-1(tep,)-425(the)-407(smo)-28(othed)-407(aggregation)-407(algorithm)-407(de-)]TJ -16.937 -13.549 Td [(scrib)-28(ed)-478(in)-478([)]TJ -1 0 0 rg 1 0 0 RG - [(26)]TJ -0 g 0 G - [(])-479(is)-478(used.)-879(In)-479(this)-478(algorithm,)-514(eac)27(h)-478(index)]TJ/F22 10.9091 Tf 271.801 0 Td [(j)]TJ/F25 10.9091 Tf 10.783 0 Td [(2)]TJ/F15 10.9091 Tf 12.939 0 Td [(\012)]TJ/F23 7.9701 Tf 7.879 3.959 Td [(k)]TJ/F20 7.9701 Tf 4.622 0 Td [(+1)]TJ/F15 10.9091 Tf 16.537 -3.959 Td [(corresp)-28(onds)-478(to)-478(an)]TJ -324.561 -13.549 Td [(aggregate)-374(\012)]TJ/F23 7.9701 Tf 57.445 3.958 Td [(k)]TJ 0 -7.014 Td [(j)]TJ/F15 10.9091 Tf 9.201 3.056 Td [(of)-374(\012)]TJ/F23 7.9701 Tf 20.747 3.958 Td [(k)]TJ/F15 10.9091 Tf 5.12 -3.958 Td [(,)-384(consisting)-374(of)-374(a)-374(s)-1(u)1(itably)-374(c)27(hosen)-374(index)]TJ/F22 10.9091 Tf 187.709 0 Td [(i)]TJ/F25 10.9091 Tf 7.529 0 Td [(2)]TJ/F15 10.9091 Tf 11.044 0 Td [(\012)]TJ/F23 7.9701 Tf 7.879 3.958 Td [(k)]TJ/F15 10.9091 Tf 9.201 -3.958 Td [(and)-374(indices)-374(that)-374(are)]TJ -315.875 -13.55 Td [(\050usually\051)-333(con)28(tained)-334(in)-333(a)-333(strongly-coupled)-334(n)1(e)-1(igh)28(b)-27(oro)-28(o)-28(d)-333(of)]TJ/F22 10.9091 Tf 274.122 0 Td [(i)]TJ/F15 10.9091 Tf 3.758 0 Td [(,)-333(i.e.,)]TJ -194.032 -31.214 Td [(\012)]TJ/F23 7.9701 Tf 7.879 4.505 Td [(k)]TJ 0 -7.202 Td [(j)]TJ/F25 10.9091 Tf 8.15 2.697 Td [(\032)-278(N)]TJ/F23 7.9701 Tf 22.073 4.505 Td [(k)]TJ -1.607 -7.202 Td [(i)]TJ/F15 10.9091 Tf 6.727 2.697 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(\022)]TJ/F15 10.9091 Tf 5.425 0 Td [(\051)-278(=)]TJ/F28 10.9091 Tf 18.788 15.382 Td [(\032)]TJ/F22 10.9091 Tf 8.181 -15.382 Td [(r)]TJ/F25 10.9091 Tf 8.255 0 Td [(2)]TJ/F15 10.9091 Tf 10.303 0 Td [(\012)]TJ/F23 7.9701 Tf 7.879 4.505 Td [(k)]TJ/F15 10.9091 Tf 8.15 -4.505 Td [(:)]TJ/F25 10.9091 Tf 6.061 0 Td [(j)]TJ/F22 10.9091 Tf 3.03 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 4.505 Td [(k)]TJ 0 -7.202 Td [(ir)]TJ/F25 10.9091 Tf 7.438 2.697 Td [(j)]TJ/F22 10.9091 Tf 6.061 0 Td [(>)-278(\022)]TJ/F28 10.9091 Tf 16.939 13.424 Td [(q)]TJ -ET -q -1 0 0 1 348.097 261.221 cm -[]0 d 0 J 0.436 w 0 0 m 32.469 0 l S -Q -BT -/F25 10.9091 Tf 348.097 247.579 Td [(j)]TJ/F22 10.9091 Tf 3.031 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 3.758 Td [(k)]TJ 0 -7.014 Td [(ii)]TJ/F22 10.9091 Tf 6.264 3.256 Td [(a)]TJ/F23 7.9701 Tf 5.767 3.152 Td [(k)]TJ 0 -5.849 Td [(r)-29(r)]TJ/F25 10.9091 Tf 8.611 2.697 Td [(j)]TJ/F28 10.9091 Tf 3.031 15.382 Td [(\033)]TJ/F25 10.9091 Tf 10.606 -15.382 Td [([)-222(f)]TJ/F22 10.9091 Tf 15.151 0 Td [(i)]TJ/F25 10.9091 Tf 3.758 0 Td [(g)]TJ/F22 10.9091 Tf 7.273 0 Td [(;)]TJ -0 g 0 G -/F15 10.9091 Tf 74.757 0 Td [(\0503\051)]TJ -0 g 0 G - -398.512 -31.214 Td [(for)-431(a)-430(giv)27(en)-430(threshold)]TJ/F22 10.9091 Tf 106.493 0 Td [(\022)]TJ/F25 10.9091 Tf 10.225 0 Td [(2)]TJ/F15 10.9091 Tf 12.074 0 Td [([0)]TJ/F22 10.9091 Tf 8.485 0 Td [(;)]TJ/F15 10.9091 Tf 4.848 0 Td [(1])-431(\050see)-431([)]TJ -1 0 0 rg 1 0 0 RG - [(26)]TJ -0 g 0 G - [(])-430(for)-431(the)-431(details\051.)-736(Since)-431(this)-431(algorithm)-430(has)-431(a)]TJ -142.125 -13.549 Td [(sequen)28(tial)-382(n)1(ature,)-394(a)-381(decoupled)-381(v)28(e)-1(r)1(s)-1(i)1(on)-382(of)-381(it)-381(is)-382(appli)1(e)-1(d,)-393(where)-381(eac)28(h)-382(pro)-27(ces)-1(sor)-381(indep)-28(en-)]TJ 0 -13.549 Td [(den)28(tly)-433(exe)-1(cutes)-433(the)-433(algorithm)-433(on)-434(the)-433(set)-433(of)-434(indices)-433(assigned)-433(to)-434(it)-433(in)-433(the)-433(initial)-434(data)]TJ 0 -13.549 Td [(distribution.)-442(Thi)1(s)-326(v)28(ersion)-325(is)-326(em)28(barrassingly)-325(parallel,)-327(since)-325(it)-326(do)-27(es)-326(not)-325(require)-325(an)27(y)-325(data)]TJ 0 -13.55 Td [(comm)28(unication.)-522(On)-359(the)-359(other)-359(hand,)-365(it)-360(ma)28(y)-359(pro)-28(du)1(c)-1(e)-359(some)-359(non)28(uniform)-359(aggregates)-359(and)]TJ 0 -13.549 Td [(is)-295(strongly)-295(dep)-27(enden)27(t)-294(on)-295(the)-295(n)28(um)28(b)-28(er)-295(of)-295(pro)-27(cess)-1(or)1(s)-295(and)-295(on)-295(the)-295(initial)-294(partitioning)-295(of)-295(the)]TJ 0 -13.549 Td [(matrix)]TJ/F22 10.9091 Tf 35.775 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(.)-524(Nev)28(e)-1(rt)1(hele)-1(ss,)-366(this)-360(parallel)-360(algorithm)-360(has)-360(b)-27(ee)-1(n)-359(c)27(hosen)-360(for)-359(MLD2P4,)-367(since)-360(it)]TJ -43.957 -13.549 Td [(has)-333(b)-28(een)-333(s)-1(h)1(o)27(wn)-333(to)-333(pro)-28(duce)-333(go)-28(o)-28(d)-333(results)-334(in)-333(practice)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(5)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-333(7)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-334(25)]TJ -0 g 0 G - [(].)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -392 0 obj -<< -/Length 15462 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(14)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F15 10.9091 Tf -186.329 -35.866 Td [(The)-375(prolongator)]TJ/F22 10.9091 Tf 82.192 0 Td [(P)]TJ/F23 7.9701 Tf 8.518 3.959 Td [(k)]TJ/F15 10.9091 Tf 9.216 -3.959 Td [(is)-375(built)-376(starting)-375(from)-375(a)-376(ten)28(tativ)28(e)-376(prolongator)]TJ 222.868 2.758 Td [(\026)]TJ/F22 10.9091 Tf -2.441 -2.758 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.959 Td [(k)]TJ/F25 10.9091 Tf 8.915 -3.959 Td [(2)]TJ/F34 10.9091 Tf 11.069 0 Td [(R)]TJ/F23 7.9701 Tf 7.878 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.139 -1.406 Td [(k)]TJ/F26 7.9701 Tf 4.573 1.406 Td [(\002)]TJ/F23 7.9701 Tf 6.586 0 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.406 Td [(k)]TJ/F21 5.9776 Tf 4.075 0 Td [(+1)]TJ/F15 10.9091 Tf 10.24 -2.553 Td [(,)]TJ -409.421 -13.549 Td [(de\014ned)-333(as)]TJ 115.609 -14.79 Td [(\026)]TJ/F22 10.9091 Tf -2.442 -2.757 Td [(P)]TJ/F23 7.9701 Tf 8.519 4.504 Td [(k)]TJ/F15 10.9091 Tf 8.15 -4.504 Td [(=)-278(\050)-85(\026)]TJ/F22 10.9091 Tf 15.758 0 Td [(p)]TJ/F23 7.9701 Tf 5.489 4.504 Td [(k)]TJ 0 -7.201 Td [(ij)]TJ/F15 10.9091 Tf 7.265 2.697 Td [(\051)]TJ/F22 10.9091 Tf 4.242 0 Td [(;)]TJ/F15 10.9091 Tf 16.684 0 Td [(\026)]TJ/F22 10.9091 Tf -0.926 0 Td [(p)]TJ/F23 7.9701 Tf 5.489 4.504 Td [(k)]TJ 0 -7.201 Td [(ij)]TJ/F15 10.9091 Tf 10.295 2.697 Td [(=)]TJ/F28 10.9091 Tf 11.515 15.382 Td [(\032)]TJ/F15 10.9091 Tf 13.163 -8.325 Td [(1)-1913(if)]TJ/F22 10.9091 Tf 35.721 0 Td [(i)]TJ/F25 10.9091 Tf 6.788 0 Td [(2)]TJ/F15 10.9091 Tf 10.303 0 Td [(\012)]TJ/F23 7.9701 Tf 7.879 3.959 Td [(k)]TJ 0 -7.014 Td [(j)]TJ/F22 10.9091 Tf 5.12 3.055 Td [(;)]TJ/F15 10.9091 Tf -65.811 -14.089 Td [(0)-1913(otherwise)]TJ/F22 10.9091 Tf 71.266 0 Td [(;)]TJ -0 g 0 G -/F15 10.9091 Tf 108.435 7.032 Td [(\0504\051)]TJ -0 g 0 G - -398.511 -26.829 Td [(where)-357(\012)]TJ/F23 7.9701 Tf 39.687 3.959 Td [(k)]TJ 0 -7.015 Td [(j)]TJ/F15 10.9091 Tf 9.02 3.056 Td [(is)-357(the)-358(aggregate)-357(of)-358(\012)]TJ/F23 7.9701 Tf 100.235 3.959 Td [(k)]TJ/F15 10.9091 Tf 9.019 -3.959 Td [(corresp)-28(onding)-357(to)-358(the)-357(index)]TJ/F22 10.9091 Tf 132.69 0 Td [(j)]TJ/F25 10.9091 Tf 8.586 0 Td [(2)]TJ/F15 10.9091 Tf 10.742 0 Td [(\012)]TJ/F23 7.9701 Tf 7.879 3.959 Td [(k)]TJ/F20 7.9701 Tf 4.622 0 Td [(+1)]TJ/F15 10.9091 Tf 11.318 -3.959 Td [(.)]TJ/F22 10.9091 Tf 8.669 0 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.959 Td [(k)]TJ/F15 10.9091 Tf 9.02 -3.959 Td [(is)-357(obtained)]TJ -360.006 -15.095 Td [(b)28(y)-333(applying)-334(to)]TJ 75.471 2.757 Td [(\026)]TJ/F22 10.9091 Tf -2.441 -2.757 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.959 Td [(k)]TJ/F15 10.9091 Tf 8.756 -3.959 Td [(a)-333(smo)-28(other)]TJ/F22 10.9091 Tf 56.758 0 Td [(S)]TJ/F23 7.9701 Tf 7.318 3.959 Td [(k)]TJ/F25 10.9091 Tf 8.15 -3.959 Td [(2)]TJ/F34 10.9091 Tf 10.303 0 Td [(R)]TJ/F23 7.9701 Tf 7.879 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.406 Td [(k)]TJ/F26 7.9701 Tf 4.573 1.406 Td [(\002)]TJ/F23 7.9701 Tf 6.587 0 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.406 Td [(k)]TJ/F15 10.9091 Tf 5.071 -2.553 Td [(:)]TJ/F22 10.9091 Tf -29.64 -22.041 Td [(P)]TJ/F23 7.9701 Tf 8.519 4.504 Td [(k)]TJ/F15 10.9091 Tf 8.15 -4.504 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(S)]TJ/F23 7.9701 Tf 7.318 4.504 Td [(k)]TJ/F15 10.9091 Tf 7.561 -1.746 Td [(\026)]TJ/F22 10.9091 Tf -2.441 -2.758 Td [(P)]TJ/F23 7.9701 Tf 8.519 4.504 Td [(k)]TJ/F22 10.9091 Tf 5.12 -4.504 Td [(;)]TJ/F15 10.9091 Tf -231.841 -22.041 Td [(in)-255(order)-255(to)-255(remo)27(v)28(e)-255(nonsmo)-28(oth)-255(comp)-28(onen)28(ts)-255(from)-255(the)-256(r)1(ange)-256(of)-255(the)-255(prolongator,)-271(and)-255(hence)]TJ 0 -13.549 Td [(to)-293(impro)27(v)28(e)-293(the)-294(con)28(v)28(ergence)-294(prop)-27(erties)-294(of)-293(the)-294(m)28(ultilev)28(el)-294(metho)-27(d)-294([)]TJ -1 0 0 rg 1 0 0 RG - [(2)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-293(24)]TJ -0 g 0 G - [(].)-431(A)-294(simple)-293(c)28(hoice)]TJ 0 -13.549 Td [(for)]TJ/F22 10.9091 Tf 16.697 0 Td [(S)]TJ/F23 7.9701 Tf 7.318 3.959 Td [(k)]TJ/F15 10.9091 Tf 8.756 -3.959 Td [(is)-333(the)-334(damp)-27(ed)-334(Jacobi)-333(smo)-28(other:)]TJ/F22 10.9091 Tf 118.068 -22.041 Td [(S)]TJ/F23 7.9701 Tf 7.318 4.505 Td [(k)]TJ/F15 10.9091 Tf 8.15 -4.505 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(I)]TJ/F25 10.9091 Tf 8.076 0 Td [(\000)]TJ/F22 10.9091 Tf 10.909 0 Td [(!)]TJ/F23 7.9701 Tf 7.182 4.505 Td [(k)]TJ/F15 10.9091 Tf 5.119 -4.505 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(D)]TJ/F23 7.9701 Tf 9.335 4.505 Td [(k)]TJ/F15 10.9091 Tf 5.119 -4.505 Td [(\051)]TJ/F26 7.9701 Tf 4.243 4.505 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.733 -4.505 Td [(A)]TJ/F23 7.9701 Tf 8.181 4.505 Td [(k)]TJ 0 -7.202 Td [(F)]TJ/F22 10.9091 Tf 7.034 2.697 Td [(;)]TJ/F15 10.9091 Tf -258.582 -22.04 Td [(where)]TJ/F22 10.9091 Tf 32.045 0 Td [(D)]TJ/F23 7.9701 Tf 9.335 3.958 Td [(k)]TJ/F15 10.9091 Tf 9.255 -3.958 Td [(is)-379(the)-379(diagonal)-379(matrix)-379(with)-379(the)-379(s)-1(ame)-379(diagonal)-379(en)28(tries)-379(as)]TJ/F22 10.9091 Tf 276.813 0 Td [(A)]TJ/F23 7.9701 Tf 8.181 3.958 Td [(k)]TJ/F15 10.9091 Tf 5.12 -3.958 Td [(,)]TJ/F22 10.9091 Tf 7.291 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.958 Td [(k)]TJ 0 -7.191 Td [(F)]TJ/F15 10.9091 Tf 10.896 3.233 Td [(=)-354(\050)-14(\026)]TJ/F22 10.9091 Tf 16.59 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 3.958 Td [(k)]TJ 0 -7.014 Td [(ij)]TJ/F15 10.9091 Tf 7.266 3.056 Td [(\051)-379(is)]TJ -396.74 -13.55 Td [(the)-333(\014ltered)-334(matrix)-333(de\014ned)-333(as)]TJ 48.968 -26.039 Td [(\026)]TJ/F22 10.9091 Tf -0.156 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 4.505 Td [(k)]TJ 0 -7.202 Td [(ij)]TJ/F15 10.9091 Tf 10.296 2.697 Td [(=)]TJ/F28 10.9091 Tf 11.515 15.382 Td [(\032)]TJ/F22 10.9091 Tf 13.163 -8.324 Td [(a)]TJ/F23 7.9701 Tf 5.766 3.959 Td [(k)]TJ 0 -7.015 Td [(ij)]TJ/F15 10.9091 Tf 17.228 3.056 Td [(if)]TJ/F22 10.9091 Tf 10 0 Td [(j)]TJ/F25 10.9091 Tf 8.147 0 Td [(2)-278(N)]TJ/F23 7.9701 Tf 20.862 3.959 Td [(k)]TJ -1.608 -7.015 Td [(i)]TJ/F15 10.9091 Tf 6.728 3.056 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(\022)]TJ/F15 10.9091 Tf 5.424 0 Td [(\051)]TJ/F22 10.9091 Tf 4.243 0 Td [(;)]TJ/F15 10.9091 Tf -81.032 -14.09 Td [(0)-1608(otherwise)]TJ/F22 10.9091 Tf 67.934 0 Td [(;)]TJ/F15 10.9091 Tf 27.153 7.032 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(j)]TJ/F25 10.9091 Tf 8.147 0 Td [(6)]TJ/F15 10.9091 Tf 0 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(i)]TJ/F15 10.9091 Tf 3.758 0 Td [(\051)]TJ/F22 10.9091 Tf 4.243 0 Td [(;)]TJ/F15 10.9091 Tf 26.822 0 Td [(\026)]TJ/F22 10.9091 Tf -0.156 0 Td [(a)]TJ/F23 7.9701 Tf 5.767 4.505 Td [(k)]TJ 0 -7.202 Td [(ii)]TJ/F15 10.9091 Tf 9.294 2.697 Td [(=)]TJ/F22 10.9091 Tf 11.516 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 4.505 Td [(k)]TJ 0 -7.202 Td [(ii)]TJ/F25 10.9091 Tf 8.689 2.697 Td [(\000)]TJ/F28 10.9091 Tf 10.909 10.364 Td [(X)]TJ/F23 7.9701 Tf 1.202 -23.717 Td [(j)]TJ/F26 7.9701 Tf 3.884 0 Td [(6)]TJ/F20 7.9701 Tf 0 0 Td [(=)]TJ/F23 7.9701 Tf 6.586 0 Td [(i)]TJ/F15 10.9091 Tf 4.085 13.353 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 4.505 Td [(k)]TJ 0 -7.202 Td [(ij)]TJ/F25 10.9091 Tf 9.69 2.697 Td [(\000)]TJ/F15 10.9091 Tf 11.065 0 Td [(\026)]TJ/F22 10.9091 Tf -0.156 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 4.505 Td [(k)]TJ 0 -7.202 Td [(ij)]TJ/F15 10.9091 Tf 7.265 2.697 Td [(\051)]TJ/F22 10.9091 Tf 4.243 0 Td [(;)]TJ -0 g 0 G -/F15 10.9091 Tf 39.721 0 Td [(\0505\051)]TJ -0 g 0 G - -398.512 -34.975 Td [(and)]TJ/F22 10.9091 Tf 20.68 0 Td [(!)]TJ/F23 7.9701 Tf 7.182 3.959 Td [(k)]TJ/F15 10.9091 Tf 8.224 -3.959 Td [(is)-285(an)-284(appro)28(ximation)-285(of)-284(4)]TJ/F22 10.9091 Tf 114.629 0 Td [(=)]TJ/F15 10.9091 Tf 5.455 0 Td [(\0503)]TJ/F22 10.9091 Tf 9.697 0 Td [(\032)]TJ/F23 7.9701 Tf 5.64 3.959 Td [(k)]TJ/F15 10.9091 Tf 5.12 -3.959 Td [(\051,)-294(where)]TJ/F22 10.9091 Tf 41.497 0 Td [(\032)]TJ/F23 7.9701 Tf 5.64 3.959 Td [(k)]TJ/F15 10.9091 Tf 8.224 -3.959 Td [(is)-285(the)-284(sp)-28(ectral)-285(r)1(adius)-285(of)-284(\050)]TJ/F22 10.9091 Tf 117.582 0 Td [(D)]TJ/F23 7.9701 Tf 9.335 3.959 Td [(k)]TJ/F15 10.9091 Tf 5.12 -3.959 Td [(\051)]TJ/F26 7.9701 Tf 4.242 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.959 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(k)]TJ 0 -7.192 Td [(F)]TJ/F15 10.9091 Tf 10.138 3.233 Td [([)]TJ -1 0 0 rg 1 0 0 RG - [(2)]TJ -0 g 0 G - [(].)]TJ -397.906 -13.549 Td [(In)-288(MLD2P4)-288(this)-287(appro)27(ximation)-287(is)-288(obtained)-288(b)28(y)-288(using)]TJ/F25 10.9091 Tf 250.336 0 Td [(k)]TJ/F22 10.9091 Tf 5.455 0 Td [(A)]TJ/F23 7.9701 Tf 8.181 3.959 Td [(k)]TJ 0 -7.192 Td [(F)]TJ/F25 10.9091 Tf 7.034 3.233 Td [(k)]TJ/F26 7.9701 Tf 5.454 -1.636 Td [(1)]TJ/F15 10.9091 Tf 12.107 1.636 Td [(as)-288(an)-288(estimate)-288(of)]TJ/F22 10.9091 Tf 82.683 0 Td [(\032)]TJ/F23 7.9701 Tf 5.641 3.959 Td [(k)]TJ/F15 10.9091 Tf 5.119 -3.959 Td [(.)-429(Note)]TJ -382.01 -13.549 Td [(that)-373(for)-373(systems)-374(coming)-373(from)-373(uniformly)-373(elliptic)-373(problems,)-384(\014)1(ltering)-374(the)-373(matrix)]TJ/F22 10.9091 Tf 379.26 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(k)]TJ/F15 10.9091 Tf 9.191 -3.959 Td [(has)]TJ -396.633 -13.549 Td [(little)-306(or)-306(no)-306(e\013ect,)-312(and)]TJ/F22 10.9091 Tf 106.178 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.958 Td [(k)]TJ/F15 10.9091 Tf 8.459 -3.958 Td [(can)-306(b)-28(e)-306(used)-306(instead)-306(of)]TJ/F22 10.9091 Tf 108.331 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.958 Td [(k)]TJ 0 -7.191 Td [(F)]TJ/F15 10.9091 Tf 7.033 3.233 Td [(.)-435(The)-306(latter)-306(c)27(hoice)-306(is)-306(the)-306(default)-306(in)]TJ -246.365 -13.55 Td [(MLD2P4.)]TJ/F17 11.9552 Tf 0 -28.825 Td [(4.3)-1125(Smo)-31(others)-375(and)-375(coarsest-lev)31(el)-375(solv)31(ers)]TJ/F15 10.9091 Tf 0 -20.594 Td [(The)-294(smo)-28(others)-294(implemen)28(ted)-295(i)1(n)-295(MLD2P4)-294(include)-294(the)-294(Jacobi)-294(and)-294(blo)-28(c)28(k-Jacobi)-294(metho)-28(ds,)]TJ 0 -13.549 Td [(a)-344(h)28(ybrid)-343(v)28(e)-1(r)1(s)-1(ion)-343(of)-344(the)-343(forw)28(ard)-344(and)-344(b)1(ac)27(kw)28(ard)-344(Gau)1(s)-1(s-Seidel)-343(metho)-28(ds,)-346(and)-344(the)-343(additiv)28(e)]TJ 0 -13.55 Td [(Sc)28(h)28(w)27(arz)-333(\050AS\051)-333(ones)-334(\050see,)-333(e.g.,)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(21)]TJ -0 g 0 G - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-334(22)]TJ -0 g 0 G - [(]\051.)]TJ 16.936 -13.549 Td [(The)-481(h)28(ybrid)-480(Gauss-Seidel)-481(v)28(ersion)-481(is)-480(considered)-481(b)-27(ecause)-481(the)-481(origin)1(al)-481(Gauss-Seidel)]TJ -16.936 -13.549 Td [(metho)-28(d)-364(is)-365(inheren)28(tly)-364(sequen)27(tial.)-537(A)27(t)-364(eac)28(h)-365(iteration)-364(of)-365(the)-364(h)28(ybrid)-365(v)28(ersion,)-372(eac)27(h)-364(parallel)]TJ 0 -13.549 Td [(pro)-28(cess)-452(uses)-452(the)-451(mos)-1(t)-451(recen)27(t)-451(v)55(alues)-452(of)-452(i)1(ts)-452(o)27(wn)-451(lo)-28(cal)-452(v)56(ariables)-452(and)-452(the)-452(v)56(alues)-452(of)-452(the)]TJ 0 -13.549 Td [(non-lo)-28(cal)-418(v)55(ari)1(ables)-419(computed)-418(at)-419(the)-418(previous)-418(iteration,)-440(obtained)-418(b)28(y)-419(exc)28(hanging)-418(data)]TJ 0 -13.55 Td [(with)-333(other)-334(pr)1(o)-28(cesses)-334(b)-28(efore)-333(the)-333(b)-28(eginning)-333(of)-334(th)1(e)-334(curren)28(t)-333(iteration.)]TJ 16.936 -13.549 Td [(In)-372(the)-372(AS)-372(me)-1(th)1(o)-28(ds,)-382(the)-372(index)-372(space)-373(\012)]TJ/F23 7.9701 Tf 185.618 3.959 Td [(k)]TJ/F15 10.9091 Tf 9.18 -3.959 Td [(is)-372(divided)-372(in)28(to)]TJ/F22 10.9091 Tf 72.847 0 Td [(m)]TJ/F23 7.9701 Tf 9.578 -1.777 Td [(k)]TJ/F15 10.9091 Tf 9.18 1.777 Td [(subsets)-372(\012)]TJ/F23 7.9701 Tf 46.06 3.959 Td [(k)]TJ 0 -7.014 Td [(i)]TJ/F15 10.9091 Tf 9.18 3.055 Td [(of)-372(size)]TJ/F22 10.9091 Tf 33.939 0 Td [(n)]TJ/F23 7.9701 Tf 6.548 -1.777 Td [(k)-27(;i)]TJ/F15 10.9091 Tf 10.355 1.777 Td [(,)]TJ -409.421 -13.549 Td [(p)-28(ossibly)-432(o)28(v)28(erlapping.)-740(F)83(or)-432(eac)28(h)]TJ/F22 10.9091 Tf 155.272 0 Td [(i)]TJ/F15 10.9091 Tf 8.47 0 Td [(w)28(e)-432(consider)-432(the)-432(restriction)-432(op)-28(erator)]TJ/F22 10.9091 Tf 178.985 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(k)]TJ -0.084 -7.014 Td [(i)]TJ/F25 10.9091 Tf 10.027 3.055 Td [(2)]TJ/F34 10.9091 Tf 12.095 0 Td [(R)]TJ/F23 7.9701 Tf 7.879 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.406 Td [(k)-21(;i)]TJ/F26 7.9701 Tf 9.506 1.406 Td [(\002)]TJ/F23 7.9701 Tf 6.587 0 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.406 Td [(k)]TJ/F15 10.9091 Tf -407.38 -16.102 Td [(that)-366(maps)-366(a)-365(v)27(ector)]TJ/F22 10.9091 Tf 95.448 0 Td [(x)]TJ/F23 7.9701 Tf 6.235 3.959 Td [(k)]TJ/F15 10.9091 Tf 9.11 -3.959 Td [(to)-366(the)-366(v)28(ector)]TJ/F22 10.9091 Tf 65.942 0 Td [(x)]TJ/F23 7.9701 Tf 6.235 3.959 Td [(k)]TJ 0 -7.015 Td [(i)]TJ/F15 10.9091 Tf 9.11 3.056 Td [(made)-366(of)-366(the)-365(com)-1(p)-27(onen)28(ts)-366(of)]TJ/F22 10.9091 Tf 134.56 0 Td [(x)]TJ/F23 7.9701 Tf 6.234 3.959 Td [(k)]TJ/F15 10.9091 Tf 9.111 -3.959 Td [(with)-366(indices)-366(in)]TJ -341.985 -13.549 Td [(\012)]TJ/F23 7.9701 Tf 7.879 3.959 Td [(k)]TJ 0 -7.015 Td [(i)]TJ/F15 10.9091 Tf 5.12 3.056 Td [(,)-301(and)-292(the)-293(prolongation)-292(op)-28(erator)]TJ/F22 10.9091 Tf 152.201 0 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.959 Td [(k)]TJ -1.515 -7.015 Td [(i)]TJ/F15 10.9091 Tf 9.665 3.056 Td [(=)-278(\050)]TJ/F22 10.9091 Tf 15.758 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(k)]TJ -0.084 -7.015 Td [(i)]TJ/F15 10.9091 Tf 5.204 3.056 Td [(\051)]TJ/F23 7.9701 Tf 4.242 3.959 Td [(T)]TJ/F15 10.9091 Tf 6.605 -3.959 Td [(.)-431(These)-293(op)-27(erators)-293(are)-293(then)-292(used)-293(to)-292(build)]TJ/F22 10.9091 Tf -221.961 -13.549 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.958 Td [(k)]TJ 0 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.557 3.056 Td [(=)]TJ/F22 10.9091 Tf 11.923 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.958 Td [(k)]TJ -0.084 -7.014 Td [(i)]TJ/F22 10.9091 Tf 5.204 3.056 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.958 Td [(k)]TJ/F22 10.9091 Tf 5.119 -3.958 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.958 Td [(k)]TJ -1.515 -7.014 Td [(i)]TJ/F15 10.9091 Tf 6.635 3.056 Td [(,)-361(whic)27(h)-355(is)-356(the)-356(restriction)-355(of)]TJ/F22 10.9091 Tf 133.83 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.958 Td [(k)]TJ/F15 10.9091 Tf 9.001 -3.958 Td [(to)-356(the)-355(index)-356(space)-356(\012)]TJ/F23 7.9701 Tf 99.523 3.958 Td [(k)]TJ 0 -7.014 Td [(i)]TJ/F15 10.9091 Tf 5.119 3.056 Td [(.)-512(The)-355(class)-1(ical)-355(AS)]TJ -324.744 -13.55 Td [(preconditioner)]TJ/F22 10.9091 Tf 72.182 0 Td [(M)]TJ/F23 7.9701 Tf 11.773 3.959 Td [(k)]TJ -1.19 -7.192 Td [(AS)]TJ/F15 10.9091 Tf 16.074 3.233 Td [(is)-333(de\014ned)-334(as)]TJ 38.283 -31.315 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(M)]TJ/F23 7.9701 Tf 11.773 4.504 Td [(k)]TJ -1.19 -7.201 Td [(AS)]TJ/F15 10.9091 Tf 12.437 2.697 Td [(\051)]TJ/F26 7.9701 Tf 4.242 4.504 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 7.763 -4.504 Td [(=)]TJ/F23 7.9701 Tf 13.362 14.072 Td [(m)]TJ/F24 5.9776 Tf 7.49 -1.406 Td [(k)]TJ/F28 10.9091 Tf -9.337 -2.303 Td [(X)]TJ/F23 7.9701 Tf 1.027 -23.45 Td [(i)]TJ/F20 7.9701 Tf 2.883 0 Td [(=1)]TJ/F22 10.9091 Tf 13.665 13.087 Td [(P)]TJ/F23 7.9701 Tf 8.519 4.504 Td [(k)]TJ -1.515 -7.201 Td [(i)]TJ/F15 10.9091 Tf 6.635 2.697 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(A)]TJ/F23 7.9701 Tf 8.181 4.504 Td [(k)]TJ 0 -7.201 Td [(i)]TJ/F15 10.9091 Tf 5.12 2.697 Td [(\051)]TJ/F26 7.9701 Tf 4.243 4.504 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -4.504 Td [(R)]TJ/F23 7.9701 Tf 8.368 4.504 Td [(k)]TJ -0.084 -7.201 Td [(i)]TJ/F22 10.9091 Tf 5.204 2.697 Td [(;)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -401 0 obj -<< -/Length 7392 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(4)]TJ -0 g 0 G - [-378(Mul)67(tigrid)-378(Ba)22(ck)22(gr)23(ound)]TJ/F15 10.9091 Tf 401.542 0 Td [(15)]TJ -0 g 0 G - -401.542 -35.866 Td [(where)]TJ/F22 10.9091 Tf 31.037 0 Td [(A)]TJ/F23 7.9701 Tf 8.181 3.959 Td [(k)]TJ 0 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.247 3.055 Td [(is)-287(supp)-27(osed)-287(to)-287(b)-27(e)-287(nonsingular.)-429(W)83(e)-286(observ)28(e)-287(that)-287(an)-286(appro)28(ximate)-287(in)28(v)28(e)-1(rse)-286(of)]TJ/F22 10.9091 Tf 351.685 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(k)]TJ 0 -7.014 Td [(i)]TJ/F15 10.9091 Tf -407.332 -10.494 Td [(is)-342(usually)-342(considered)-342(instead)-342(of)-342(\050)]TJ/F22 10.9091 Tf 156.503 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(k)]TJ 0 -7.014 Td [(i)]TJ/F15 10.9091 Tf 5.119 3.055 Td [(\051)]TJ/F26 7.9701 Tf 4.243 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F15 10.9091 Tf 4.733 -3.959 Td [(.)-470(The)-342(setup)-342(of)]TJ/F22 10.9091 Tf 72.445 0 Td [(M)]TJ/F23 7.9701 Tf 11.773 3.959 Td [(k)]TJ -1.19 -7.192 Td [(AS)]TJ/F15 10.9091 Tf 16.168 3.233 Td [(during)-342(the)-342(m)28(ultilev)28(el)-342(build)]TJ -284.562 -13.549 Td [(phase)-333(in)27(v)28(olv)28(es)]TJ -0 g 0 G -/F25 10.9091 Tf 16.364 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(the)-383(de\014ni)1(tion)-383(of)-383(the)-382(index)-383(subspaces)-382(\012)]TJ/F23 7.9701 Tf 188.861 3.959 Td [(k)]TJ 0 -7.014 Td [(i)]TJ/F15 10.9091 Tf 9.294 3.055 Td [(and)-383(of)-382(the)-383(corresp)-27(onding)-383(op)-28(erators)]TJ/F22 10.9091 Tf 173.536 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.959 Td [(k)]TJ -0.085 -7.014 Td [(i)]TJ/F15 10.9091 Tf -379.974 -10.494 Td [(\050and)]TJ/F22 10.9091 Tf 25.455 0 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.959 Td [(k)]TJ -1.516 -7.014 Td [(i)]TJ/F15 10.9091 Tf 6.635 3.055 Td [(\051;)]TJ -0 g 0 G -/F25 10.9091 Tf -50.002 -22.515 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(the)-333(computation)-334(of)-333(the)-333(submatrices)]TJ/F22 10.9091 Tf 173.788 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.958 Td [(k)]TJ 0 -7.014 Td [(i)]TJ/F15 10.9091 Tf 5.12 3.056 Td [(;)]TJ -0 g 0 G -/F25 10.9091 Tf -197.999 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(the)-424(computation)-425(of)-424(their)-424(in)27(v)28(erses)-424(\050usually)-425(appro)28(ximated)-424(through)-424(some)-425(form)-424(of)]TJ 0 -13.549 Td [(incomplete)-333(factorization\051.)]TJ -27.273 -22.516 Td [(The)-410(computation)-411(of)]TJ/F22 10.9091 Tf 101.006 0 Td [(z)]TJ/F23 7.9701 Tf 5.553 3.959 Td [(k)]TJ/F15 10.9091 Tf 9.551 -3.959 Td [(=)]TJ/F22 10.9091 Tf 12.916 0 Td [(M)]TJ/F23 7.9701 Tf 11.773 3.959 Td [(k)]TJ -1.19 -7.192 Td [(AS)]TJ/F22 10.9091 Tf 12.437 3.233 Td [(w)]TJ/F23 7.9701 Tf 8.104 3.959 Td [(k)]TJ/F15 10.9091 Tf 5.119 -3.959 Td [(,)-430(with)]TJ/F22 10.9091 Tf 33.407 0 Td [(w)]TJ/F23 7.9701 Tf 8.103 3.959 Td [(k)]TJ/F25 10.9091 Tf 9.551 -3.959 Td [(2)]TJ/F34 10.9091 Tf 11.704 0 Td [(R)]TJ/F23 7.9701 Tf 7.878 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.139 -1.406 Td [(k)]TJ/F15 10.9091 Tf 5.071 -2.553 Td [(,)-430(dur)1(ing)-411(the)-410(m)28(ultilev)27(el)-410(application)]TJ -246.122 -13.549 Td [(phase,)-333(requires)]TJ -0 g 0 G -/F25 10.9091 Tf 16.364 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(the)-333(restriction)-334(of)]TJ/F22 10.9091 Tf 83.455 0 Td [(w)]TJ/F23 7.9701 Tf 8.103 3.959 Td [(k)]TJ/F15 10.9091 Tf 8.756 -3.959 Td [(to)-333(the)-334(subspaces)]TJ/F34 10.9091 Tf 82 0 Td [(R)]TJ/F23 7.9701 Tf 7.879 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.406 Td [(k)-21(;i)]TJ/F15 10.9091 Tf 10.004 -2.553 Td [(,)-333(i.e.)]TJ/F22 10.9091 Tf 24.243 0 Td [(w)]TJ/F23 7.9701 Tf 8.103 3.959 Td [(k)]TJ -0.293 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.443 3.055 Td [(=)]TJ/F22 10.9091 Tf 11.516 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(k)]TJ -0.084 -7.014 Td [(i)]TJ/F22 10.9091 Tf 5.204 3.055 Td [(w)]TJ/F23 7.9701 Tf 8.103 3.959 Td [(k)]TJ/F15 10.9091 Tf 5.12 -3.959 Td [(;)]TJ -0 g 0 G -/F25 10.9091 Tf -294.966 -22.515 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(the)-333(computation)-334(of)-333(the)-333(v)28(ectors)]TJ/F22 10.9091 Tf 150.697 0 Td [(z)]TJ/F23 7.9701 Tf 5.553 3.959 Td [(k)]TJ -0.48 -7.015 Td [(i)]TJ/F15 10.9091 Tf 8.63 3.056 Td [(=)-278(\050)]TJ/F22 10.9091 Tf 15.758 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(k)]TJ 0 -7.015 Td [(i)]TJ/F15 10.9091 Tf 5.119 3.056 Td [(\051)]TJ/F26 7.9701 Tf 4.243 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.733 -3.959 Td [(w)]TJ/F23 7.9701 Tf 8.103 3.959 Td [(k)]TJ -0.293 -7.015 Td [(i)]TJ/F15 10.9091 Tf 5.413 3.056 Td [(;)]TJ -0 g 0 G -/F25 10.9091 Tf -233.153 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(the)-333(prolongation)-333(and)-334(the)-333(sum)-333(of)-334(the)-333(previous)-333(v)28(e)-1(ctors,)-333(i.e.)]TJ/F22 10.9091 Tf 277.849 0 Td [(z)]TJ/F23 7.9701 Tf 5.553 3.959 Td [(k)]TJ/F15 10.9091 Tf 8.15 -3.959 Td [(=)]TJ/F28 10.9091 Tf 11.515 8.182 Td [(P)]TJ/F23 7.9701 Tf 11.515 -3.018 Td [(m)]TJ/F24 5.9776 Tf 7.491 -1.406 Td [(k)]TJ/F23 7.9701 Tf -7.491 -7.014 Td [(i)]TJ/F20 7.9701 Tf 2.883 0 Td [(=1)]TJ/F22 10.9091 Tf 13.137 3.256 Td [(P)]TJ/F23 7.9701 Tf 8.519 3.959 Td [(k)]TJ -1.515 -7.014 Td [(i)]TJ/F22 10.9091 Tf 6.635 3.055 Td [(z)]TJ/F23 7.9701 Tf 5.553 3.959 Td [(k)]TJ -0.48 -7.014 Td [(i)]TJ/F15 10.9091 Tf 5.6 3.055 Td [(.)]TJ -382.187 -22.515 Td [(V)83(arian)28(ts)-291(of)-291(the)-291(classical)-291(AS)-291(metho)-28(d,)-299(whic)28(h)-291(use)-291(mo)-28(di\014cations)-291(of)-291(the)-291(restriction)-291(and)-291(pro-)]TJ 0 -13.549 Td [(longation)-244(op)-28(erators,)-262(are)-244(also)-244(implemen)28(ted)-244(in)-244(MLD2P4.)-415(Among)-244(them,)-262(the)-244(Restricted)-244(AS)]TJ 0 -13.55 Td [(\050RAS\051)-375(preconditi)1(one)-1(r)-374(usually)-375(outp)-27(erforms)-375(the)-375(classical)-375(AS)-374(preconditioner)-375(in)-374(terms)-375(of)]TJ 0 -13.549 Td [(con)28(v)28(erge)-1(n)1(c)-1(e)-337(rate)-337(and)-338(of)-337(computation)-338(and)-337(comm)28(unication)-338(time)-337(on)-338(parallel)-337(distributed-)]TJ 0 -13.549 Td [(memory)-309(computers,)-314(and)-310(is)-309(therefore)-309(the)-310(most)-309(widely)-309(used)-309(am)-1(on)1(g)-310(the)-309(AS)-309(precondition-)]TJ 0 -13.549 Td [(ers)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(6)]TJ -0 g 0 G - [(].)]TJ 16.937 -13.549 Td [(Direct)-427(solv)28(ers)-426(based)-427(on)-426(s)-1(p)1(arse)-427(LU)-427(factori)1(z)-1(ation)1(s)-1(,)-449(implemen)27(ted)-426(in)-427(the)-426(third-part)28(y)]TJ -16.937 -13.55 Td [(libraries)-374(rep)-27(orted)-374(in)-374(Section)]TJ -0 0 1 rg 0 0 1 RG - [-373(3.2)]TJ -0 g 0 G - [(,)-384(can)-374(b)-27(e)-374(applied)-374(as)-373(coarsest-lev)27(el)-373(solv)27(ers)-373(b)27(y)-373(MLD2P4.)]TJ 0 -13.549 Td [(Nativ)28(e)-313(inexact)-314(solv)28(ers)-313(based)-313(on)-313(incomplete)-314(LU)-313(factorizations,)-317(as)-313(w)28(ell)-314(as)-313(Jacobi,)-317(h)28(ybrid)]TJ 0 -13.549 Td [(\050forw)28(ard\051)-478(Gauss-Seidel,)-513(and)-478(blo)-28(c)28(k)-478(Jacobi)-477(preconditioners)-478(are)-477(also)-478(a)28(v)55(ailable.)-877(Direct)]TJ 0 -13.549 Td [(solv)28(ers)-279(usually)-278(lead)-279(to)-278(more)-279(e\013ectiv)28(e)-279(preconditi)1(oners)-279(in)-278(terms)-279(of)-278(algorithmic)-279(scalabilit)28(y;)]TJ 0 -13.549 Td [(ho)28(w)28(ev)27(er,)-333(this)-333(do)-28(es)-333(not)-334(guaran)28(tee)-333(parallel)-334(e\016ciency)84(.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -414 0 obj -<< -/Length 8437 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(16)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F17 14.3462 Tf -203.265 -35.866 Td [(5)-1125(Getting)-375(Started)]TJ/F15 10.9091 Tf 0 -24.802 Td [(W)83(e)-270(describ)-28(e)-270(the)-270(basic)-1(s)-270(for)-270(building)-270(and)-271(ap)1(plying)-271(MLD2P4)-270(one-lev)28(el)-271(and)-270(m)28(ultilev)28(el)-271(\050i.e.,)]TJ 0 -13.549 Td [(AMG\051)-283(preconditioners)-283(with)-283(the)-283(Krylo)27(v)-283(solv)28(ers)-283(included)-283(in)-283(PSBLAS)-283([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(].)-428(The)-283(follo)28(wing)]TJ 0 -13.549 Td [(steps)-333(are)-334(required:)]TJ -0 g 0 G - 13.333 -23.442 Td [(1.)]TJ -0 g 0 G -/F18 10.9091 Tf 13.94 0 Td [(De)51(clar)51(e)-370(the)-371(pr)51(e)51(c)51(onditioner)-370(data)-371(structur)51(e)]TJ/F15 10.9091 Tf 195.447 0 Td [(.)-487(It)-347(is)-347(a)-348(deriv)28(ed)-347(data)-348(t)28(yp)-28(e,)]TJ/F45 10.9091 Tf 131.812 0 Td [(mld_)]TJ/F18 10.9091 Tf 22.909 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(prec_)]TJ -356.542 -13.55 Td [(type)]TJ/F15 10.9091 Tf 22.908 0 Td [(,)-322(where)]TJ/F18 10.9091 Tf 37.923 0 Td [(x)]TJ/F15 10.9091 Tf 9.849 0 Td [(ma)28(y)-319(b)-28(e)]TJ/F45 10.9091 Tf 38.163 0 Td [(s)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F45 10.9091 Tf 6.538 0 Td [(d)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F45 10.9091 Tf 6.538 0 Td [(c)]TJ/F15 10.9091 Tf 9.202 0 Td [(or)]TJ/F45 10.9091 Tf 13.203 0 Td [(z)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-321(ac)-1(cord)1(ing)-319(to)-319(th)1(e)-319(basic)-319(data)-318(t)28(yp)-28(e)-319(of)-318(the)-319(sparse)]TJ -161.505 -13.549 Td [(matrix)-372(\050)]TJ/F45 10.9091 Tf 40.153 0 Td [(s)]TJ/F15 10.9091 Tf 9.79 0 Td [(=)-372(real)-373(single)-372(precision;)]TJ/F45 10.9091 Tf 114.22 0 Td [(d)]TJ/F15 10.9091 Tf 9.789 0 Td [(=)-372(real)-373(double)-372(precision;)]TJ/F45 10.9091 Tf 119.008 0 Td [(c)]TJ/F15 10.9091 Tf 9.79 0 Td [(=)-372(complex)-373(single)]TJ -302.75 -13.549 Td [(precision;)]TJ/F45 10.9091 Tf 48.807 0 Td [(z)]TJ/F15 10.9091 Tf 9.518 0 Td [(=)-347(c)-1(omp)1(le)-1(x)-347(double)-347(precision\051.)-487(This)-348(data)-347(structure)-348(is)-347(accessed)-348(b)28(y)-347(the)]TJ -58.325 -13.549 Td [(user)-333(only)-334(thr)1(ough)-334(the)-333(MLD2P4)-333(routines,)-334(fol)1(lo)27(wing)-333(an)-333(ob)-56(ject-orien)28(ted)-333(approac)28(h.)]TJ -0 g 0 G - -13.94 -23.442 Td [(2.)]TJ -0 g 0 G -/F18 10.9091 Tf 13.94 0 Td [(A)26(l)-52(l)1(o)51(c)51(ate)-444(and)-444(initialize)-444(the)-444(pr)51(e)52(c)51(onditioner)-444(data)-444(structur)51(e,)-465(ac)51(c)51(or)51(ding)-444(to)-444(a)-444(pr)51(e)52(c)51(on-)]TJ 0 -13.549 Td [(ditioner)-407(typ)52(e)-407(chosen)-407(by)-406(the)-407(user)]TJ/F15 10.9091 Tf 154.603 0 Td [(.)-604(This)-386(is)-387(p)-27(erformed)-387(b)28(y)-386(the)-387(routine)]TJ/F45 10.9091 Tf 172.699 0 Td [(init)]TJ/F15 10.9091 Tf 22.909 0 Td [(,)-400(whic)28(h)]TJ -350.211 -13.55 Td [(also)-288(sets)-288(d)1(e)-1(f)1(aults)-288(for)-288(eac)28(h)-288(preconditioner)-287(t)27(yp)-27(e)-288(selected)-288(b)28(y)-288(the)-287(use)-1(r)1(.)-430(The)-287(precondi-)]TJ 0 -13.549 Td [(tioner)-273(t)28(yp)-28(es)-273(and)-273(the)-273(d)1(e)-1(f)1(aults)-273(asso)-28(ciated)-273(with)-273(them)-273(are)-273(giv)28(en)-273(in)-273(T)83(abl)1(e)]TJ -0 0 1 rg 0 0 1 RG - [-273(1)]TJ -0 g 0 G - [(,)-285(where)-273(the)]TJ 0 -13.549 Td [(strings)-268(used)-268(b)27(y)]TJ/F45 10.9091 Tf 73.232 0 Td [(init)]TJ/F15 10.9091 Tf 25.835 0 Td [(to)-268(iden)28(tify)-268(the)-269(preconditioner)-268(t)28(yp)-28(es)-268(are)-268(also)-268(giv)27(en.)-422(Note)-269(that)]TJ -99.067 -13.549 Td [(these)-370(strings)-370(are)-371(v)56(alid)-370(also)-370(if)-370(upp)-28(ercase)-370(letters)-371(are)-370(substituted)-370(b)28(y)-370(corresp)-28(onding)]TJ 0 -13.549 Td [(lo)28(w)28(ercas)-1(e)-333(ones.)]TJ -0 g 0 G - -13.94 -23.442 Td [(3.)]TJ -0 g 0 G -/F18 10.9091 Tf 13.94 0 Td [(Mo)51(dify)-340(the)-341(sele)51(c)1(t)-1(e)52(d)-341(pr)51(e)51(c)51(onditi)1(o)-1(ner)-340(typ)51(e,)-344(by)-340(pr)51(op)51(erly)-340(setting)-341(pr)51(e)52(c)51(onditioner)-341(p)51(ar)51(am-)]TJ 0 -13.55 Td [(eters.)]TJ/F15 10.9091 Tf 31.58 0 Td [(This)-354(is)-353(p)-28(erformed)-354(b)28(y)-353(the)-354(routine)]TJ/F45 10.9091 Tf 160.936 0 Td [(set)]TJ/F15 10.9091 Tf 17.182 0 Td [(.)-505(This)-354(routine)-354(m)28(ust)-353(b)-28(e)-354(called)-354(onl)1(y)-354(if)]TJ -209.698 -13.549 Td [(the)-296(user)-296(w)28(an)27(ts)-296(to)-296(mo)-28(dify)-296(the)-296(default)-296(v)56(alues)-296(of)-297(th)1(e)-297(parameters)-296(asso)-28(ciated)-296(with)-296(the)]TJ 0 -13.549 Td [(selected)-263(pr)1(e)-1(cond)1(itioner)-263(t)28(yp)-28(e,)-276(to)-263(obtain)-262(a)-263(v)56(arian)28(t)-263(of)-262(that)-262(preconditioner.)-421(Examples)]TJ 0 -13.549 Td [(of)-306(use)-306(of)]TJ/F45 10.9091 Tf 42.808 0 Td [(set)]TJ/F15 10.9091 Tf 20.522 0 Td [(are)-306(giv)28(en)-307(in)-306(Section)]TJ -0 0 1 rg 0 0 1 RG - [-306(5.1)]TJ -0 g 0 G - [(;)-315(a)-306(complete)-306(list)-307(of)-306(all)-306(the)-306(preconditioner)-306(pa-)]TJ -63.33 -13.549 Td [(rameters)-283(and)-283(their)-283(allo)27(w)28(ed)-283(and)-283(default)-283(v)55(alues)-283(is)-283(pro)28(vided)-283(in)-283(Section)]TJ -0 0 1 rg 0 0 1 RG - [-283(6)]TJ -0 g 0 G - [(,)-294(T)84(ables)]TJ -0 0 1 rg 0 0 1 RG - [-284(2)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(8)]TJ -0 g 0 G - [(.)]TJ -0 g 0 G - -13.94 -23.442 Td [(4.)]TJ -0 g 0 G -/F18 10.9091 Tf 13.94 0 Td [(Build)-508(the)-508(pr)51(e)51(c)51(onditioner)-508(for)-508(a)-508(given)-508(matrix)]TJ/F15 10.9091 Tf 214.941 0 Td [(.)-935(If)-496(the)-497(selected)-497(preconditioner)-497(is)]TJ -214.941 -13.55 Td [(m)28(ultilev)28(el,)-334(then)-333(t)28(w)28(o)-334(steps)-333(m)28(ust)-334(b)-27(e)-334(p)-28(erformed,)-333(as)-333(sp)-28(eci\014ed)-333(next.)]TJ -0 g 0 G - 4.606 -23.442 Td [(4.1)]TJ -0 g 0 G -/F18 10.9091 Tf 19.394 0 Td [(Build)-328(the)-328(aggr)51(e)51(gation)-328(hier)51(ar)52(chy)-329(f)1(or)-329(a)-328(given)-328(matrix.)]TJ/F15 10.9091 Tf 244.224 0 Td [(This)-301(is)-301(p)-28(erformed)-301(b)28(y)-301(the)]TJ -244.224 -13.549 Td [(routine)]TJ/F45 10.9091 Tf 37.606 0 Td [(hierarchy_build)]TJ/F15 10.9091 Tf 85.908 0 Td [(.)]TJ -0 g 0 G - -142.908 -17.997 Td [(4.2)]TJ -0 g 0 G -/F18 10.9091 Tf 19.394 0 Td [(Build)-295(the)-295(pr)51(e)52(c)51(onditioner)-295(for)-295(a)-295(given)-295(matrix.)]TJ/F15 10.9091 Tf 208.934 0 Td [(This)-265(is)-265(p)-28(erformed)-265(b)28(y)-265(the)-265(routine)]TJ/F45 10.9091 Tf -208.934 -13.55 Td [(smoothers_build)]TJ/F15 10.9091 Tf 85.908 0 Td [(.)]TJ -109.908 -23.442 Td [(If)-292(the)-292(selected)-292(preconditi)1(oner)-292(is)-292(one-lev)28(el,)-301(it)-291(is)-292(built)-292(in)-292(a)-292(single)-291(ste)-1(p)1(,)-301(p)-27(erformed)-292(b)28(y)]TJ 0 -13.549 Td [(the)-333(routine)]TJ/F45 10.9091 Tf 56.394 0 Td [(bld)]TJ/F15 10.9091 Tf 17.181 0 Td [(.)]TJ -0 g 0 G - -87.515 -23.442 Td [(5.)]TJ -0 g 0 G -/F18 10.9091 Tf 13.94 0 Td [(Apply)-387(the)-388(pr)51(e)52(c)51(onditioner)-388(at)-387(e)51(ach)-387(iter)51(ation)-388(of)-387(a)-387(Krylov)-388(solver.)]TJ/F15 10.9091 Tf 300.051 0 Td [(This)-366(is)-365(p)-28(erformed)]TJ -300.051 -13.549 Td [(b)28(y)-487(the)-487(metho)-27(d)]TJ/F45 10.9091 Tf 78.657 0 Td [(apply)]TJ/F15 10.9091 Tf 28.636 0 Td [(.)-905(When)-486(using)-487(the)-487(PSBLAS)-486(Krylo)28(v)-487(solv)28(ers,)-525(this)-487(step)-487(is)]TJ -107.293 -13.549 Td [(completely)-324(transparen)28(t)-323(to)-324(the)-324(user,)-325(since)]TJ/F45 10.9091 Tf 197.842 0 Td [(apply)]TJ/F15 10.9091 Tf 32.167 0 Td [(is)-324(called)-323(b)27(y)-323(the)-324(PSBLAS)-323(routine)]TJ -230.009 -13.55 Td [(implemen)28(ting)-333(the)-334(Krylo)28(v)-333(solv)28(e)-1(r)-333(\050)]TJ/F45 10.9091 Tf 158.303 0 Td [(psb_krylov)]TJ/F15 10.9091 Tf 57.272 0 Td [(\051.)]TJ -0 g 0 G - -229.515 -23.442 Td [(6.)]TJ -0 g 0 G -/F18 10.9091 Tf 13.94 0 Td [(F)77(r)51(e)51(e)-439(the)-439(pr)51(e)51(c)51(onditioner)-438(dat)-1(a)-438(structur)51(e)]TJ/F15 10.9091 Tf 183.092 0 Td [(.)-709(This)-422(is)-421(p)-28(erformed)-421(b)27(y)-421(the)-422(routine)]TJ/F45 10.9091 Tf 176.147 0 Td [(free)]TJ/F15 10.9091 Tf 22.909 0 Td [(.)]TJ -382.148 -13.549 Td [(This)-326(step)-327(is)-326(complemen)28(tary)-326(to)-327(step)-326(1)-326(and)-326(should)-326(b)-28(e)-326(p)-28(erformed)-326(when)-327(the)-326(precon-)]TJ 0 -13.549 Td [(ditioner)-333(is)-334(no)-333(more)-333(used.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -433 0 obj -<< -/Length 9330 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(5)]TJ -0 g 0 G - [-378(Getting)-378(St)67(ar)67(ted)]TJ/F15 10.9091 Tf 401.542 0 Td [(17)]TJ -0 g 0 G - -384.605 -35.866 Td [(All)-361(the)-361(previous)-361(rou)1(tines)-361(are)-361(a)27(v)56(ailable)-361(as)-361(metho)-28(ds)-360(of)-361(the)-361(preconditioner)-361(ob)-56(j)1(e)-1(ct.)-527(A)]TJ -16.937 -13.549 Td [(detailed)-370(description)-370(of)-371(them)-370(is)-370(giv)27(en)-370(in)-370(Section)]TJ -0 0 1 rg 0 0 1 RG - [-370(6)]TJ -0 g 0 G - [(.)-556(Examples)-370(sho)28(wing)-370(the)-371(basic)-370(use)-370(of)]TJ 0 -13.549 Td [(MLD2P4)-333(are)-334(rep)-27(orted)-334(in)-333(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(5.1)]TJ -0 g 0 G - [(.)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -ET -q -1 0 0 1 93.6 642.85 cm -[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S -Q -q -1 0 0 1 93.6 629.102 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 99.578 633.167 Td [(type)]TJ -ET -q -1 0 0 1 231.54 629.102 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 237.518 633.167 Td [(string)]TJ -ET -q -1 0 0 1 294.519 629.102 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 300.497 633.167 Td [(def)89(a)22(ul)67(t)-378(preconditioner)]TJ -ET -q -1 0 0 1 538.915 629.102 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 93.6 628.903 cm -[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S -Q -q -1 0 0 1 93.6 601.605 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 99.578 619.219 Td [(No)-333(preconditioner)]TJ -ET -q -1 0 0 1 231.54 601.605 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 237.518 619.219 Td [('NONE')]TJ -ET -q -1 0 0 1 294.519 601.605 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 300.497 619.219 Td [(Considered)-507(to)-506(use)-507(the)-507(PSBLAS)-507(Kr)1(ylo)27(v)-506(solv)27(ers)]TJ 0 -13.549 Td [(with)-333(no)-334(pr)1(e)-1(cond)1(itioner.)]TJ -ET -q -1 0 0 1 538.915 601.605 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 93.6 601.406 cm -[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S -Q -q -1 0 0 1 93.6 560.559 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 99.578 591.722 Td [(Diagonal)]TJ -ET -q -1 0 0 1 231.54 560.559 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 237.518 591.722 Td [('DIAG')]TJ/F15 10.9091 Tf 41.296 0 Td [(or)]TJ/F45 10.9091 Tf -41.296 -13.549 Td [('JACOBI')]TJ -ET -q -1 0 0 1 294.519 560.559 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 300.497 591.722 Td [(Diagonal)-423(preconditioner.)-714(F)83(or)-423(an)28(y)-423(zero)-424(diagon)1(al)]TJ 0 -13.549 Td [(en)28(try)-275(of)-275(the)-275(matrix)-276(to)-275(b)-27(e)-276(p)1(re)-1(cond)1(itioned,)-287(the)-275(cor-)]TJ 0 -13.549 Td [(resp)-28(onding)-278(en)28(try)-278(of)-278(the)-278(precondit)1(ioner)-278(is)-278(set)-278(to)-278(1.)]TJ -ET -q -1 0 0 1 538.915 560.559 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 93.6 560.36 cm -[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S -Q -q -1 0 0 1 93.6 533.062 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 99.578 550.676 Td [(Gauss-Seidel)]TJ -ET -q -1 0 0 1 231.54 533.062 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 237.518 550.676 Td [('GS')]TJ -ET -q -1 0 0 1 294.519 533.062 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 300.497 550.676 Td [(Hybrid)-565(Gauss-Seidel)-565(\050forw)28(ard\051,)-623(that)-566(is,)-623(global)]TJ 0 -13.549 Td [(blo)-28(c)28(k)-333(Jacobi)-334(with)-333(Gauss-Seidel)-333(as)-334(lo)-27(cal)-334(solv)28(er.)]TJ -ET -q -1 0 0 1 538.915 533.062 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 93.6 532.863 cm -[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S -Q -q -1 0 0 1 93.6 492.016 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 99.578 523.179 Td [(Symmetrized)-333(Gauss-Seidel)]TJ -ET -q -1 0 0 1 231.54 492.016 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 237.518 523.179 Td [('FBGS')]TJ -ET -q -1 0 0 1 294.519 492.016 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 300.497 523.179 Td [(Symmetrized)-646(h)27(ybrid)-646(Gauss-Seidel,that)-646(is,)-725(for-)]TJ 0 -13.549 Td [(w)28(ard)-392(Gauss-Seidel)-392(follo)28(w)27(ed)-392(b)28(y)-392(bac)28(kw)28(ard)-392(Gauss-)]TJ 0 -13.549 Td [(Seidel.)]TJ -ET -q -1 0 0 1 538.915 492.016 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 93.6 491.817 cm -[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S -Q -q -1 0 0 1 93.6 478.068 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 99.578 482.133 Td [(Blo)-28(c)28(k)-333(Jacobi)]TJ -ET -q -1 0 0 1 231.54 478.068 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F45 10.9091 Tf 237.518 482.133 Td [('BJAC')]TJ -ET -q -1 0 0 1 294.519 478.068 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 300.497 482.133 Td [(Blo)-28(c)28(k-Jacobi)-333(with)-334(ILU\0500\051)-333(on)-333(the)-334(lo)-27(cal)-334(blo)-27(c)27(ks.)]TJ -ET -q -1 0 0 1 538.915 478.068 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 93.6 477.869 cm -[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S -Q -q -1 0 0 1 93.6 450.571 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 99.578 468.185 Td [(Additiv)28(e)-333(Sc)27(h)28(w)28(arz)]TJ -ET -q -1 0 0 1 231.54 450.571 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 237.518 468.185 Td [('AS')]TJ -ET -q -1 0 0 1 294.519 450.571 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 300.497 468.185 Td [(Additiv)28(e)-745(Sc)28(h)28(w)28(arz)-745(\050AS\051,)-745(with)-744(o)27(v)28(erlap)-744(1)-745(and)]TJ 0 -13.549 Td [(ILU\0500\051)-333(on)-334(the)-333(lo)-28(cal)-333(blo)-28(c)28(ks.)]TJ -ET -q -1 0 0 1 538.915 450.571 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 93.6 450.372 cm -[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S -Q -q -1 0 0 1 93.6 355.328 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F15 10.9091 Tf 99.578 440.688 Td [(Multilev)28(el)]TJ -ET -q -1 0 0 1 231.54 355.328 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F45 10.9091 Tf 237.518 440.688 Td [('ML')]TJ -ET -q -1 0 0 1 294.519 355.328 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F15 10.9091 Tf 300.497 440.688 Td [(V-cycle)-590(with)-589(one)-589(h)27(ybrid)-589(forw)28(ard)-590(Gau)1(s)-1(s-Seidel)]TJ 0 -13.549 Td [(\050GS\051)-246(sw)28(eep)-246(as)-245(pre-smo)-28(other)-246(and)-245(one)-246(h)28(ybrid)-246(bac)28(k-)]TJ 0 -13.549 Td [(w)28(ard)-249(GS)-249(sw)28(e)-1(ep)-249(as)-249(p)-27(os)-1(t-smo)-27(other,)-266(basic)-249(smo)-28(othed)]TJ 0 -13.549 Td [(aggregation)-645(as)-644(coarse)-1(n)1(ing)-645(algorithm,)-723(and)-644(LU)]TJ 0 -13.549 Td [(\050plus)-575(triangul)1(ar)-575(solv)28(e\051)-575(as)-575(coarsest-lev)28(el)-575(solv)28(er.)]TJ 0 -13.55 Td [(See)-449(the)-449(default)-449(v)55(alues)-449(in)-449(T)83(ables)]TJ -0 0 1 rg 0 0 1 RG - [-449(2)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(8)]TJ -0 g 0 G - [-449(for)-449(further)]TJ 0 -13.549 Td [(details)-333(of)-334(the)-333(preconditioner.)]TJ -ET -q -1 0 0 1 538.915 355.328 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -q -1 0 0 1 93.6 355.129 cm -[]0 d 0 J 0.398 w 0 0 m 445.315 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 123.31 336.395 Td [(T)83(able)-333(1:)-444(Preconditioner)-334(t)28(yp)-28(es,)-333(corresp)-28(onding)-333(strings)-333(and)-334(d)1(e)-1(f)1(ault)-334(c)28(hoices.)]TJ -0 g 0 G -0 g 0 G - -12.773 -56.375 Td [(Note)-266(that)-266(the)-266(mo)-27(dule)]TJ/F45 10.9091 Tf 104.329 0 Td [(mld_prec_mod)]TJ/F15 10.9091 Tf 68.726 0 Td [(,)-279(con)27(taini)1(ng)-266(the)-266(de\014nition)-266(of)-266(the)-266(pr)1(e)-1(cond)1(itioner)]TJ -189.992 -13.549 Td [(data)-319(t)28(yp)-28(e)-319(and)-319(the)-319(in)28(terfaces)-319(to)-319(the)-319(routines)-319(of)-319(MLD2P4,)-322(m)28(ust)-319(b)-28(e)-319(used)-319(in)-319(an)28(y)-320(p)1(rogram)]TJ 0 -13.549 Td [(calling)-358(suc)28(h)-359(routines.)-519(The)-358(mo)-28(dules)]TJ/F45 10.9091 Tf 172.419 0 Td [(psb_base_mod)]TJ/F15 10.9091 Tf 68.727 0 Td [(,)-364(for)-359(the)-358(sparse)-358(matrix)-358(and)-359(comm)28(u-)]TJ -241.146 -13.55 Td [(nication)-404(descriptor)-403(data)-404(t)28(yp)-28(es,)-421(and)]TJ/F45 10.9091 Tf 174.817 0 Td [(psb_krylov_mod)]TJ/F15 10.9091 Tf 80.181 0 Td [(,)-421(for)-404(in)28(terfacing)-404(with)-403(the)-404(Krylo)28(v)]TJ -254.998 -13.549 Td [(solv)28(ers,)-334(m)28(ust)-333(b)-28(e)-333(also)-334(used)-333(\050see)-333(Section)]TJ -0 0 1 rg 0 0 1 RG - [-334(5.1)]TJ -0 g 0 G - [(\051.)]TJ/F44 10.9091 Tf 16.937 -36.556 Td [(Remark)-513(1.)]TJ/F15 10.9091 Tf 67.379 0 Td [(Coarsest-lev)28(el)-446(solv)28(ers)-446(based)-446(on)-446(the)-446(LU)-445(factorization,)-474(suc)28(h)-446(as)-446(those)]TJ -84.316 -13.549 Td [(implemen)28(ted)-437(in)-437(UMFP)83(A)28(CK,)-437(MUMPS,)-437(Sup)-28(erLU,)-437(an)1(d)-437(Sup)-28(erLU)]TJ -ET -q -1 0 0 1 402.466 175.917 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 405.739 175.718 Td [(Dist,)-463(usually)-437(lead)-437(to)]TJ -312.139 -13.55 Td [(smaller)-462(n)28(um)28(b)-28(ers)-462(of)-462(preconditioned)-462(Krylo)28(v)-462(iterations)-462(than)-462(inexact)-462(solv)28(ers,)-495(when)-462(the)]TJ 0 -13.549 Td [(linear)-230(system)-230(comes)-230(from)-230(a)-231(standar)1(d)-231(d)1(isc)-1(retization)-230(of)-230(basic)-230(scalar)-230(elliptic)-230(PDE)-230(problems.)]TJ 0 -13.549 Td [(Ho)28(w)28(e)-1(v)28(er,)-284(this)-273(do)-28(es)-272(not)-273(necessarily)-273(corresp)-27(ond)-273(to)-272(the)-273(smallest)-273(execution)-272(time)-273(on)-272(parallel)]TJ 0 -13.549 Td [(computers.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -313 0 obj -<< -/Type /ObjStm -/N 100 -/First 900 -/Length 12970 ->> -stream -310 0 308 134 312 280 309 334 316 427 318 541 315 595 321 688 319 822 323 968 -320 1022 326 1115 324 1249 328 1435 35 1489 39 1542 325 1595 343 1701 341 1931 329 2077 -330 2230 331 2382 332 2531 333 2686 334 2848 335 3003 336 3155 337 3306 338 3456 339 3607 -340 3758 345 3911 43 3965 342 4018 357 4111 350 4285 351 4437 352 4583 353 4735 354 4886 -355 5041 359 5204 47 5258 360 5311 51 5368 356 5421 376 5618 374 5792 369 5938 370 6100 -371 6263 372 6413 373 6564 378 6720 368 6774 380 6831 381 6885 382 6939 383 6993 375 7050 -391 7208 385 7374 386 7529 387 7681 388 7837 389 7988 393 8136 394 8190 395 8247 55 8304 -390 8357 400 8567 398 8717 396 8863 397 9016 402 9168 399 9222 413 9406 404 9580 405 9734 -406 9877 407 10028 408 10175 409 10320 415 10464 59 10518 416 10571 417 10625 418 10679 419 10733 -420 10787 421 10841 412 10895 432 11014 430 11188 410 11334 411 11480 425 11630 426 11775 427 11920 -% 310 0 obj -<< -/Type /Page -/Contents 311 0 R -/Resources 309 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 314 0 R -/Annots [ 308 0 R ] ->> -% 308 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.3) >> ->> -% 312 0 obj -<< -/D [310 0 R /XYZ 92.6 752.957 null] ->> -% 309 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 316 0 obj -<< -/Type /Page -/Contents 317 0 R -/Resources 315 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 314 0 R ->> -% 318 0 obj -<< -/D [316 0 R /XYZ 85.4 752.957 null] ->> -% 315 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 321 0 obj -<< -/Type /Page -/Contents 322 0 R -/Resources 320 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 314 0 R -/Annots [ 319 0 R ] ->> -% 319 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.3) >> ->> -% 323 0 obj -<< -/D [321 0 R /XYZ 92.6 752.957 null] ->> -% 320 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 326 0 obj -<< -/Type /Page -/Contents 327 0 R -/Resources 325 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 314 0 R -/Annots [ 324 0 R ] ->> -% 324 0 obj -<< -/Type /Annot -/Border[0 0 0]/H/I/C[0 1 1] -/Rect [85.403 455.75 345.619 467.742] -/Subtype/Link/A<> ->> -% 328 0 obj -<< -/D [326 0 R /XYZ 85.4 752.957 null] ->> -% 35 0 obj -<< -/D [326 0 R /XYZ 86.4 512.931 null] ->> -% 39 0 obj -<< -/D [326 0 R /XYZ 86.4 414.685 null] ->> -% 325 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F45 255 0 R /F17 148 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 343 0 obj -<< -/Type /Page -/Contents 344 0 R -/Resources 342 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 314 0 R -/Annots [ 341 0 R 329 0 R 330 0 R 331 0 R 332 0 R 333 0 R 334 0 R 335 0 R 336 0 R 337 0 R 338 0 R 339 0 R 340 0 R ] ->> -% 341 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.4) >> ->> -% 329 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [461.862 311.325 469.309 320.347] -/A << /S /GoTo /D (cite.Briggs2000) >> ->> -% 330 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [473.761 311.325 486.663 320.347] -/A << /S /GoTo /D (cite.Stuben_01) >> ->> -% 331 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [491.116 311.325 504.017 320.347] -/A << /S /GoTo /D (cite.dd2_96) >> ->> -% 332 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [125.583 270.121 133.03 279.144] -/A << /S /GoTo /D (cite.BREZINA_VANEK) >> ->> -% 333 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [137.319 270.121 150.22 279.144] -/A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> ->> -% 334 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [394.469 243.023 407.37 252.046] -/A << /S /GoTo /D (cite.TUMINARO_TONG) >> ->> -% 335 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [449.722 227.353 465.654 239.042] -/A << /S /GoTo /D (subsection.4.1) >> ->> -% 336 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [467.298 227.353 483.23 239.042] -/A << /S /GoTo /D (subsection.4.3) >> ->> -% 337 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [283.847 215.925 291.294 224.947] -/A << /S /GoTo /D (cite.para_04) >> ->> -% 338 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [295.968 215.925 303.415 224.947] -/A << /S /GoTo /D (cite.aaecc_07) >> ->> -% 339 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [308.089 215.925 315.536 224.947] -/A << /S /GoTo /D (cite.apnum_07) >> ->> -% 340 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [320.21 215.925 327.657 224.947] -/A << /S /GoTo /D (cite.MLD2P4_TOMS) >> ->> -% 345 0 obj -<< -/D [343 0 R /XYZ 92.6 752.957 null] ->> -% 43 0 obj -<< -/D [343 0 R /XYZ 93.6 715.095 null] ->> -% 342 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 357 0 obj -<< -/Type /Page -/Contents 358 0 R -/Resources 356 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 314 0 R -/Annots [ 350 0 R 351 0 R 352 0 R 353 0 R 354 0 R 355 0 R ] ->> -% 350 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [307.765 278.566 320.667 287.589] -/A << /S /GoTo /D (cite.Saad_book) >> ->> -% 351 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [270.815 262.895 278.262 274.585] -/A << /S /GoTo /D (figure.1) >> ->> -% 352 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [130.252 210.82 137.699 219.843] -/A << /S /GoTo /D (cite.Briggs2000) >> ->> -% 353 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [347.101 210.82 360.002 219.843] -/A << /S /GoTo /D (cite.Notay2008) >> ->> -% 354 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [395.273 147.623 402.72 156.646] -/A << /S /GoTo /D (cite.BREZINA_VANEK) >> ->> -% 355 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [407.241 147.623 420.143 156.646] -/A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> ->> -% 359 0 obj -<< -/D [357 0 R /XYZ 85.4 752.957 null] ->> -% 47 0 obj -<< -/D [357 0 R /XYZ 86.4 715.095 null] ->> -% 360 0 obj -<< -/D [357 0 R /XYZ 273.379 669.993 null] ->> -% 51 0 obj -<< -/D [357 0 R /XYZ 86.4 193.984 null] ->> -% 356 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F17 148 0 R /F22 225 0 R /F23 361 0 R /F25 257 0 R /F34 362 0 R /F26 363 0 R /F20 364 0 R /F24 365 0 R /F21 366 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 376 0 obj -<< -/Type /Page -/Contents 377 0 R -/Resources 375 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 384 0 R -/Annots [ 374 0 R 369 0 R 370 0 R 371 0 R 372 0 R 373 0 R ] ->> -% 374 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.4) >> ->> -% 369 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [148.889 304.895 161.79 313.918] -/A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> ->> -% 370 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [273.884 215.369 286.786 224.392] -/A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> ->> -% 371 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [344.15 120.525 351.597 129.547] -/A << /S /GoTo /D (cite.aaecc_07) >> ->> -% 372 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [356.271 120.525 363.718 129.547] -/A << /S /GoTo /D (cite.apnum_07) >> ->> -% 373 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [368.392 120.525 381.294 129.547] -/A << /S /GoTo /D (cite.TUMINARO_TONG) >> ->> -% 378 0 obj -<< -/D [376 0 R /XYZ 92.6 752.957 null] ->> -% 368 0 obj -<< -/D [376 0 R /XYZ 213.038 499.629 null] ->> -% 380 0 obj -<< -/D [376 0 R /XYZ 93.6 406.227 null] ->> -% 381 0 obj -<< -/D [376 0 R /XYZ 93.6 382.761 null] ->> -% 382 0 obj -<< -/D [376 0 R /XYZ 93.6 359.294 null] ->> -% 383 0 obj -<< -/D [376 0 R /XYZ 177.448 261.129 null] ->> -% 375 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F28 379 0 R /F22 225 0 R /F23 361 0 R /F25 257 0 R /F20 364 0 R /F26 363 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 391 0 obj -<< -/Type /Page -/Contents 392 0 R -/Resources 390 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 384 0 R -/Annots [ 385 0 R 386 0 R 387 0 R 388 0 R 389 0 R ] ->> -% 385 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [390.76 572.489 398.207 581.512] -/A << /S /GoTo /D (cite.BREZINA_VANEK) >> ->> -% 386 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [402.446 572.489 415.348 581.512] -/A << /S /GoTo /D (cite.Stuben_01) >> ->> -% 387 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [486.339 440.295 493.787 449.318] -/A << /S /GoTo /D (cite.BREZINA_VANEK) >> ->> -% 388 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [229.191 309.58 242.093 318.603] -/A << /S /GoTo /D (cite.Saad_book) >> ->> -% 389 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [246.767 309.58 259.669 318.603] -/A << /S /GoTo /D (cite.dd2_96) >> ->> -% 393 0 obj -<< -/D [391 0 R /XYZ 85.4 752.957 null] ->> -% 394 0 obj -<< -/D [391 0 R /XYZ 199.567 686.589 null] ->> -% 395 0 obj -<< -/D [391 0 R /XYZ 135.211 489.815 null] ->> -% 55 0 obj -<< -/D [391 0 R /XYZ 86.4 372.217 null] ->> -% 390 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F22 225 0 R /F23 361 0 R /F25 257 0 R /F34 362 0 R /F24 365 0 R /F26 363 0 R /F21 366 0 R /F28 379 0 R /F20 364 0 R /F17 148 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 400 0 obj -<< -/Type /Page -/Contents 401 0 R -/Resources 399 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 384 0 R -/Annots [ 398 0 R 396 0 R 397 0 R ] ->> -% 398 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.4) >> ->> -% 396 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [112.695 387.524 120.142 396.546] -/A << /S /GoTo /D (cite.CAI_SARKIS) >> ->> -% 397 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [231.213 358.304 247.145 369.993] -/A << /S /GoTo /D (subsection.3.2) >> ->> -% 402 0 obj -<< -/D [400 0 R /XYZ 92.6 752.957 null] ->> -% 399 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F22 225 0 R /F23 361 0 R /F26 363 0 R /F20 364 0 R /F25 257 0 R /F34 362 0 R /F24 365 0 R /F28 379 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 413 0 obj -<< -/Type /Page -/Contents 414 0 R -/Resources 412 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 384 0 R -/Annots [ 404 0 R 405 0 R 406 0 R 407 0 R 408 0 R 409 0 R ] ->> -% 404 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [411.917 664.789 424.819 673.811] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 405 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [440.223 507.39 447.67 519.079] -/A << /S /GoTo /D (table.1) >> ->> -% 406 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [272.428 389.103 288.36 400.793] -/A << /S /GoTo /D (subsection.5.1) >> ->> -% 407 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [434.839 375.554 442.287 387.244] -/A << /S /GoTo /D (section.6) >> ->> -% 408 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [480.279 375.554 487.726 387.244] -/A << /S /GoTo /D (table.2) >> ->> -% 409 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [489.37 375.554 496.817 387.244] -/A << /S /GoTo /D (table.8) >> ->> -% 415 0 obj -<< -/D [413 0 R /XYZ 85.4 752.957 null] ->> -% 59 0 obj -<< -/D [413 0 R /XYZ 86.4 715.095 null] ->> -% 416 0 obj -<< -/D [413 0 R /XYZ 86.4 645.168 null] ->> -% 417 0 obj -<< -/D [413 0 R /XYZ 86.4 567.529 null] ->> -% 418 0 obj -<< -/D [413 0 R /XYZ 86.4 464.913 null] ->> -% 419 0 obj -<< -/D [413 0 R /XYZ 86.4 371.604 null] ->> -% 420 0 obj -<< -/D [413 0 R /XYZ 86.4 231.205 null] ->> -% 421 0 obj -<< -/D [413 0 R /XYZ 86.4 164.388 null] ->> -% 412 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F17 148 0 R /F18 307 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 432 0 obj -<< -/Type /Page -/Contents 433 0 R -/Resources 431 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 384 0 R -/Annots [ 430 0 R 410 0 R 411 0 R 425 0 R 426 0 R 427 0 R ] ->> -% 430 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.5) >> ->> -% 410 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [323.557 687.47 331.004 699.159] -/A << /S /GoTo /D (section.6) >> ->> -% 411 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [252.847 673.92 268.778 685.61] -/A << /S /GoTo /D (subsection.5.1) >> ->> -% 425 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [461.445 371.946 468.892 381.514] -/A << /S /GoTo /D (table.2) >> ->> -% 426 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [470.536 371.946 477.983 381.514] -/A << /S /GoTo /D (table.8) >> ->> -% 427 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [279.665 222.1 295.597 235.001] -/A << /S /GoTo /D (subsection.5.1) >> ->> - -endstream -endobj -446 0 obj -<< -/Length 8728 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(18)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F17 11.9552 Tf -203.265 -35.866 Td [(5.1)-1125(Examples)]TJ/F15 10.9091 Tf 0 -20.594 Td [(The)-262(co)-28(de)-262(rep)-28(orted)-262(in)-262(Figure)]TJ -0 0 1 rg 0 0 1 RG - [-262(2)]TJ -0 g 0 G - [-263(sho)28(ws)-262(ho)28(w)-262(to)-263(set)-262(and)-262(apply)-262(the)-262(default)-262(m)27(ultilev)28(el)-262(precon-)]TJ 0 -13.549 Td [(ditioner)-371(a)28(v)55(ailabl)1(e)-372(in)-371(the)-371(real)-371(double)-371(precision)-371(v)28(ersion)-371(of)-371(MLD2P4)-371(\050see)-371(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-371(1)]TJ -0 g 0 G - [(\051.)-558(This)]TJ 0 -13.55 Td [(preconditioner)-365(is)-364(c)27(hosen)-364(b)27(y)-364(sim)-1(p)1(ly)-365(sp)-28(ecifying)]TJ/F45 10.9091 Tf 220.847 0 Td [('ML')]TJ/F15 10.9091 Tf 26.888 0 Td [(as)-365(the)-365(second)-364(argumen)27(t)-364(of)]TJ/F45 10.9091 Tf 130.353 0 Td [(P%init)]TJ/F15 10.9091 Tf -378.088 -13.549 Td [(\050a)-306(call)-305(to)]TJ/F45 10.9091 Tf 45.76 0 Td [(P%set)]TJ/F15 10.9091 Tf 31.97 0 Td [(is)-306(not)-305(needed\051)-306(and)-305(is)-306(applied)-305(w)-1(i)1(th)-306(the)-306(CG)-305(solv)27(er)-305(pro)28(vided)-306(b)28(y)-306(PSBLAS)]TJ -77.73 -13.549 Td [(\050the)-394(matrix)-394(of)-395(the)-394(system)-394(to)-395(b)-27(e)-395(solv)28(ed)-394(is)-394(assumed)-395(to)-394(b)-28(e)-394(p)-28(ositiv)28(e)-394(de\014nite\051.)-627(As)-395(previ-)]TJ 0 -13.549 Td [(ously)-315(observ)28(ed,)-319(the)-315(mo)-28(dules)]TJ/F45 10.9091 Tf 137.03 0 Td [(psb_base_mod)]TJ/F15 10.9091 Tf 68.726 0 Td [(,)]TJ/F45 10.9091 Tf 6.507 0 Td [(mld_prec_mod)]TJ/F15 10.9091 Tf 72.164 0 Td [(and)]TJ/F45 10.9091 Tf 21.012 0 Td [(psb_krylov_mod)]TJ/F15 10.9091 Tf 83.618 0 Td [(m)28(ust)]TJ -389.057 -13.549 Td [(b)-28(e)-333(used)-333(b)27(y)-333(the)-333(example)-334(program.)]TJ 16.936 -13.55 Td [(The)-395(part)-395(of)-395(the)-395(co)-28(de)-395(concerning)-395(the)-395(reading)-395(and)-395(assem)27(blin)1(g)-396(of)-395(the)-395(sparse)-395(matrix)]TJ -16.936 -13.549 Td [(and)-457(the)-456(righ)27(t-han)1(d)-457(side)-457(v)28(ector,)-488(p)-28(erformed)-456(through)-457(the)-457(PSBLAS)-456(routines)-457(for)-457(sparse)]TJ 0 -13.549 Td [(matrix)-385(and)-385(v)28(ector)-386(managemen)28(t,)-398(is)-385(not)-385(rep)-28(orted)-385(here)-385(for)-385(brevit)28(y;)-412(t)1(he)-386(statemen)28(ts)-385(con-)]TJ 0 -13.549 Td [(cerning)-265(the)-264(deallo)-28(cation)-265(of)-264(the)-265(PSBLAS)-264(data)-265(structure)-265(are)-264(neglec)-1(ted)-264(to)-28(o.)-422(Th)1(e)-265(complete)]TJ 0 -13.549 Td [(co)-28(de)-306(can)-307(b)-27(e)-307(found)-306(in)-307(the)-306(example)-307(program)-306(\014le)]TJ/F45 10.9091 Tf 223.484 0 Td [(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 108.817 0 Td [(,)-312(in)-306(the)-307(directory)]TJ/F45 10.9091 Tf -332.301 -13.55 Td [(examples/fileread)]TJ/F15 10.9091 Tf 101.269 0 Td [(of)-358(the)-358(MLD2P4)-358(implemen)28(tation)-358(\050see)-359(Section)]TJ -0 0 1 rg 0 0 1 RG - [-358(3.5)]TJ -0 g 0 G - [(\051.)-518(A)-358(sample)-358(tes)-1(t)]TJ -101.269 -13.549 Td [(problem)-375(along)-374(with)-375(the)-375(relev)56(an)28(t)-375(input)-374(data)-375(is)-375(a)28(v)56(ailable)-375(in)]TJ/F45 10.9091 Tf 283.422 0 Td [(examples/fileread/runs)]TJ/F15 10.9091 Tf 125.999 0 Td [(.)]TJ -409.421 -13.549 Td [(F)83(or)-333(details)-333(on)-334(th)1(e)-334(use)-333(of)-334(th)1(e)-334(PSBLAS)-333(routines,)-333(see)-334(the)-333(PSBLAS)-333(User's)-334(Guide)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(].)]TJ 16.936 -13.549 Td [(The)-279(setup)-278(and)-279(application)-279(of)-278(the)-279(default)-279(m)28(ultilev)28(el)-279(preconditi)1(oner)-279(for)-279(the)-278(real)-279(single)]TJ -16.936 -13.549 Td [(precision)-494(and)-495(the)-494(complex,)-535(single)-494(and)-495(dou)1(ble)-495(precision,)-534(v)27(ersions)-494(are)-495(obtain)1(e)-1(d)-494(with)]TJ 0 -13.55 Td [(straigh)28(tforw)28(ard)-229(mo)-28(di\014cations)-229(of)-229(the)-228(previous)-229(example)-229(\050see)-229(Section)]TJ -0 0 1 rg 0 0 1 RG - [-229(6)]TJ -0 g 0 G - [-229(for)-229(details\051.)-409(If)-229(these)]TJ 0 -13.549 Td [(v)28(ersions)-334(are)-333(installed,)-333(the)-333(c)-1(or)1(res)-1(p)-27(onding)-333(c)-1(o)-27(des)-334(are)-333(a)28(v)55(ailable)-333(in)]TJ/F45 10.9091 Tf 300.455 0 Td [(examples/fileread/)]TJ/F15 10.9091 Tf 103.089 0 Td [(.)]TJ -386.608 -13.549 Td [(Di\013eren)28(t)-331(v)28(ersions)-331(of)-330(the)-331(m)28(ultilev)28(el)-331(precondit)1(ioner)-331(can)-331(b)-27(e)-331(obtained)-330(b)28(y)-331(c)28(hanging)-331(the)]TJ -16.936 -13.549 Td [(default)-357(v)55(alues)-357(of)-357(the)-358(p)1(re)-1(cond)1(itioner)-358(parameters.)-516(The)-357(c)-1(o)-27(de)-358(rep)-27(orted)-358(in)-357(Figure)]TJ -0 0 1 rg 0 0 1 RG - [-357(3)]TJ -0 g 0 G - [-357(sho)27(ws)]TJ 0 -13.549 Td [(ho)28(w)-439(to)-439(set)-439(a)-440(V-cycle)-439(preconditioner)-439(whic)28(h)-439(applies)-439(1)-439(blo)-28(c)28(k-Jacobi)-439(sw)28(eep)-440(as)-439(pre-)-439(and)]TJ 0 -13.55 Td [(p)-28(ost-smo)-28(other,)-379(and)-371(solv)28(es)-371(the)-370(coarsest-lev)28(e)-1(l)-370(system)-371(with)-370(8)-371(b)1(lo)-28(c)27(k)1(-)-1(Jacobi)-370(sw)28(eeps.)-556(Note)]TJ 0 -13.549 Td [(that)-272(th)1(e)-272(ILU\0500\051)-272(factorization)-271(\050plus)-272(triangular)-271(solv)28(e\051)-272(is)-272(used)-271(as)-272(lo)-28(cal)-271(solv)28(e)-1(r)-271(for)-272(the)-271(blo)-28(c)28(k-)]TJ 0 -13.549 Td [(Jacobi)-297(sw)28(eeps,)-304(since)-297(this)-296(is)-297(the)-297(d)1(e)-1(f)1(ault)-297(asso)-28(ciated)-297(with)-296(blo)-28(c)28(k-Jacobi)-297(and)-296(set)-297(b)28(y)]TJ/F45 10.9091 Tf 375.057 0 Td [(P%init)]TJ/F15 10.9091 Tf 34.364 0 Td [(.)]TJ -409.421 -13.549 Td [(F)83(urthermore,)-347(s)-1(p)-27(ecifying)-345(blo)-28(c)28(k-Jacobi)-345(as)-345(coarsest-lev)27(el)-345(solv)28(er)-345(implies)-345(that)-345(the)-345(coarsest-)]TJ 0 -13.549 Td [(lev)28(el)-361(matrix)-360(is)-360(distributed)-361(among)-360(the)-360(pro)-28(cesses.)-526(Figure)]TJ -0 0 1 rg 0 0 1 RG - [-360(4)]TJ -0 g 0 G - [-361(sho)28(ws)-360(ho)27(w)-360(to)-360(set)-361(a)-360(W-cycle)]TJ 0 -13.549 Td [(preconditioner)-346(whic)27(h)-346(applies)-346(2)-347(h)28(ybrid)-346(Gauss)-1(-Seid)1(e)-1(l)-346(sw)28(eeps)-347(as)-346(pre-)-347(and)-346(p)-28(ost-smo)-28(other,)]TJ 0 -13.55 Td [(and)-261(solv)28(e)-1(s)-261(the)-261(coarsest-lev)27(el)-261(system)-262(with)-261(the)-261(m)28(ultifron)28(tal)-262(LU)-261(factorization)-261(implemen)27(ted)]TJ 0 -13.549 Td [(in)-350(MUMPS.)-350(It)-350(is)-350(sp)-28(eci\014ed)-350(that)-350(the)-350(coarsest-lev)28(e)-1(l)-350(matrix)-350(is)-350(distributed,)-354(since)-350(MUMPS)]TJ 0 -13.549 Td [(can)-371(b)-28(e)-371(used)-371(on)-372(b)-27(oth)-371(replicated)-372(and)-371(distribu)1(te)-1(d)-371(matrices,)-380(and)-372(b)28(y)-371(default)-371(it)-371(is)-371(used)-372(on)]TJ 0 -13.549 Td [(replicated)-459(ones.)-821(The)-459(c)-1(o)-27(de)-459(fragmen)28(ts)-460(sho)28(wn)-459(in)-459(Figures)]TJ -0 0 1 rg 0 0 1 RG - [-459(3)]TJ -0 g 0 G - [-459(and)]TJ -0 0 1 rg 0 0 1 RG - [-459(4)]TJ -0 g 0 G - [-459(are)-459(includ)1(e)-1(d)-458(in)-459(the)]TJ 0 -13.549 Td [(example)-333(program)-334(\014le)]TJ/F45 10.9091 Tf 104 0 Td [(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 112.453 0 Td [(to)-28(o.)]TJ -199.517 -13.55 Td [(Finally)83(,)-451(Figure)]TJ -0 0 1 rg 0 0 1 RG - [-427(5)]TJ -0 g 0 G - [-428(sho)28(ws)-428(the)-428(setup)-427(of)-428(a)-427(one-le)-1(v)28(el)-427(additiv)28(e)-428(Sc)28(h)27(w)28(arz)-427(preconditioner,)]TJ -16.936 -13.549 Td [(i.e.,)-373(RAS)-364(with)-365(o)28(v)27(erlap)-364(2.)-539(Note)-365(also)-365(that)-364(a)-365(Krylo)28(v)-365(metho)-28(d)-365(di\013eren)28(t)-365(from)-364(C)-1(G)-364(m)27(ust)-364(b)-28(e)]TJ 0 -13.549 Td [(used)-294(to)-294(solv)28(e)-294(the)-294(p)1(re)-1(cond)1(itioned)-294(system,)-302(since)-294(the)-294(preconditione)-293(in)-294(nonsymmetric.)-432(Th)1(e)]TJ 0 -13.549 Td [(corresp)-28(onding)-333(example)-333(program)-334(is)-333(a)28(v)55(ailable)-333(in)-333(the)-333(\014le)]TJ/F45 10.9091 Tf 261.455 0 Td [(mld_dexample_1lev.f90)]TJ/F15 10.9091 Tf 120.271 0 Td [(.)]TJ -364.79 -13.549 Td [(F)83(or)-452(all)-452(the)-452(previous)-452(preconditi)1(oners)-1(,)-481(example)-452(programs)-452(where)-452(the)-452(sparse)-452(matrix)]TJ -16.936 -13.55 Td [(and)-370(the)-371(righ)28(t-hand)-371(side)-370(are)-371(generated)-370(b)27(y)-370(discretizing)-371(a)-370(PDE)-371(with)-370(Diric)28(hlet)-371(b)-28(oundary)]TJ 0 -13.549 Td [(conditions)-333(are)-334(also)-333(a)28(v)55(ailab)1(le)-334(in)-333(the)-333(directory)]TJ/F45 10.9091 Tf 215.061 0 Td [(examples/pdegen)]TJ/F15 10.9091 Tf 85.908 0 Td [(.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -455 0 obj -<< -/Length 3337 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(5)]TJ -0 g 0 G - [-378(Getting)-378(St)67(ar)67(ted)]TJ/F15 10.9091 Tf 401.542 0 Td [(19)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -/F45 9.9626 Tf -370.457 -30.995 Td [(use)-525(psb_base_mod)]TJ 0 -11.955 Td [(use)-525(mld_prec_mod)]TJ 0 -11.955 Td [(use)-525(psb_krylov_mod)]TJ -10.461 -11.956 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(sparse)-525(matrix)]TJ 10.461 -11.955 Td [(type\050psb_dspmat_type\051)-525(::)-525(A)]TJ -10.461 -11.955 Td [(!)-525(sparse)-525(matrix)-525(descriptor)]TJ 10.461 -11.955 Td [(type\050psb_desc_type\051)-1575(::)-525(desc_A)]TJ -10.461 -11.956 Td [(!)-525(preconditioner)]TJ 10.461 -11.955 Td [(type\050mld_dprec_type\051)-1050(::)-525(P)]TJ -10.461 -11.955 Td [(!)-525(right-hand)-525(side)-525(and)-525(solution)-525(vectors)]TJ 10.461 -11.955 Td [(type\050psb_d_vect_type\051)-525(::)-525(b,)-525(x)]TJ -10.461 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.956 Td [(!)-525(initialize)-525(the)-525(parallel)-525(environment)]TJ 10.461 -11.955 Td [(call)-525(psb_init\050ictxt\051)]TJ 0 -11.955 Td [(call)-525(psb_info\050ictxt,iam,np\051)]TJ -10.461 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(read)-525(and)-525(assemble)-525(the)-525(spd)-525(matrix)-525(A)-525(and)-525(the)-525(right-hand)-525(side)-525(b)]TJ 0 -11.956 Td [(!)-525(using)-525(PSBLAS)-525(routines)-525(for)-525(sparse)-525(matrix)-525(/)-525(vector)-525(management)]TJ 0 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(initialize)-525(the)-525(default)-525(multilevel)-525(preconditioner,)-525(i.e.)-525(V-cycle)]TJ 0 -11.955 Td [(!)-525(with)-525(basic)-525(smoothed)-525(aggregation,)-525(1)-525(hybrid)-525(forward/backward)]TJ 0 -11.956 Td [(!)-525(GS)-525(sweep)-525(as)-525(pre/post-smoother)-525(and)-525(UMFPACK)-525(as)-525(coarsest-level)]TJ 0 -11.955 Td [(!)-525(solver)]TJ 10.461 -11.955 Td [(call)-525(P%init\050'ML',info\051)]TJ -10.461 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(build)-525(the)-525(preconditioner)]TJ 10.461 -11.955 Td [(call)-525(P%hierarchy_build\050A,desc_A,info\051)]TJ 0 -11.956 Td [(call)-525(P%smoothers_build\050A,desc_A,info\051)]TJ -10.461 -23.91 Td [(!)]TJ 0 -11.955 Td [(!)-525(set)-525(the)-525(solver)-525(parameters)-525(and)-525(the)-525(initial)-525(guess)]TJ 10.461 -11.955 Td [(...)-525(...)]TJ -10.461 -11.955 Td [(!)]TJ 0 -11.956 Td [(!)-525(solve)-525(Ax=b)-525(with)-525(preconditioned)-525(CG)]TJ 10.461 -11.955 Td [(call)-525(psb_krylov\050'CG',A,P,b,x,tol,desc_A,info\051)]TJ 0 -11.955 Td [(...)-525(...)]TJ -10.461 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(deallocate)-525(the)-525(preconditioner)]TJ 10.461 -11.955 Td [(call)-525(P%free\050info\051)]TJ -10.461 -11.956 Td [(!)]TJ 0 -11.955 Td [(!)-525(deallocate)-525(other)-525(data)-525(structures)]TJ 10.461 -11.955 Td [(...)-525(...)]TJ -10.461 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(exit)-525(the)-525(parallel)-525(environment)]TJ 10.461 -11.956 Td [(call)-525(psb_exit\050ictxt\051)]TJ 0 -11.955 Td [(stop)]TJ -0 g 0 G -/F15 10.9091 Tf -29.405 -21.354 Td [(Figure)-333(2:)-445(setup)-333(and)-333(application)-333(of)-334(the)-333(default)-333(m)27(u)1(ltilev)27(el)-333(preconditioner)-333(\050example)-334(1\051.)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -ET - -endstream -endobj -460 0 obj -<< -/Length 3194 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(20)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -/F45 9.9626 Tf -182.641 -47.344 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(build)-525(a)-525(V-cycle)-525(preconditioner)-525(with)-525(1)-525(block-Jacobi)-525(sweep)-525(\050with)]TJ 0 -11.955 Td [(!)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)-525(as)-525(pre-)-525(and)-525(post-smoother,)-525(and)-525(8)-1050(block-Jacobi)]TJ 0 -11.955 Td [(!)-525(sweeps)-525(\050with)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)-525(as)-525(coarsest-level)-525(solver)]TJ 10.46 -11.956 Td [(call)-525(P%init\050'ML',info\051)]TJ 0 -11.955 Td [(call_P%set\050'SMOOTHER_TYPE','BJAC',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'COARSE_SOLVE','BJAC',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'COARSE_SWEEPS',8,info\051)]TJ 0 -11.955 Td [(call)-525(P%hierarchy_build\050A,desc_A,info\051)]TJ 0 -11.956 Td [(call)-525(P%smoothers_build\050A,desc_A,info\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ -0 g 0 G -/F15 10.9091 Tf 77.116 -18.534 Td [(Figure)-333(3:)-445(setup)-333(of)-333(a)-334(m)28(ultilev)28(el)-333(preconditioner)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -/F45 9.9626 Tf -77.116 -65.676 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(build)-525(a)-525(W-cycle)-525(preconditioner)-525(with)-525(2)-525(hybrid)-525(Gauss-Seidel)-525(sweeps)]TJ 0 -11.955 Td [(!)-525(as)-525(pre-)-525(and)-525(post-smoother,)-525(a)-525(distributed)-525(coarsest)]TJ 0 -11.955 Td [(!)-525(matrix,)-525(and)-525(MUMPS)-525(as)-525(coarsest-level)-525(solver)]TJ 10.46 -11.956 Td [(call)-525(P%init\050'ML',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'ML_CYCLE','WCYCLE',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'SMOOTHER_TYPE','FBGS',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'SMOOTHER_SWEEPS',2,info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'COARSE_SOLVE','MUMPS',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'COARSE_MAT','DIST',info\051)]TJ 0 -11.956 Td [(call)-525(P%hierarchy_build\050A,desc_A,info\051)]TJ 0 -11.955 Td [(call)-525(P%smoothers_build\050A,desc_A,info\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ -0 g 0 G -/F15 10.9091 Tf 77.116 -18.535 Td [(Figure)-333(4:)-445(setup)-333(of)-333(a)-334(m)28(ultilev)28(el)-333(preconditioner)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -/F45 9.9626 Tf -77.116 -65.675 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(set)-525(RAS)-525(with)-525(overlap)-525(2)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(local)-525(blocks)]TJ 10.46 -11.956 Td [(call)-525(P%init\050'AS',info\051)]TJ 0 -11.955 Td [(call)-525(P%set\050'SUB_OVR',2,info\051)]TJ 0 -11.955 Td [(call)-525(P%bld\050A,desc_A,info\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(solve)-525(Ax=b)-525(with)-525(preconditioned)-525(BiCGSTAB)]TJ 10.46 -11.955 Td [(call)-525(psb_krylov\050'BICGSTAB',A,P,b,x,tol,desc_A,info\051)]TJ -0 g 0 G -/F15 10.9091 Tf 46.641 -20.749 Td [(Figure)-333(5:)-445(setup)-333(of)-333(a)-334(one-lev)28(el)-333(Sc)28(h)27(w)28(arz)-333(preconditioner.)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -ET - -endstream -endobj -466 0 obj -<< -/Length 6306 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(21)]TJ -0 g 0 G -/F17 14.3462 Tf -401.542 -35.866 Td [(6)-1125(User)-375(In)31(terface)]TJ/F15 10.9091 Tf 0 -24.352 Td [(The)-325(basic)-325(user)-324(in)28(te)-1(r)1(face)-325(of)-325(MLD2P4)-325(consists)-324(of)-325(eigh)28(t)-325(metho)-28(ds.)-442(Th)1(e)-325(six)-325(metho)-28(ds)]TJ/F45 10.9091 Tf 386.512 0 Td [(init)]TJ/F15 10.9091 Tf 22.909 0 Td [(,)]TJ/F45 10.9091 Tf -409.421 -13.549 Td [(set)]TJ/F15 10.9091 Tf 17.182 0 Td [(,)]TJ/F45 10.9091 Tf 6.791 0 Td [(build)]TJ/F15 10.9091 Tf 28.636 0 Td [(,)]TJ/F45 10.9091 Tf 6.791 0 Td [(hierarchy_build)]TJ/F15 10.9091 Tf 85.908 0 Td [(,)]TJ/F45 10.9091 Tf 6.791 0 Td [(smoothers_build)]TJ/F15 10.9091 Tf 89.644 0 Td [(and)]TJ/F45 10.9091 Tf 21.311 0 Td [(apply)]TJ/F15 10.9091 Tf 32.372 0 Td [(encapsulate)-342(all)-343(the)-342(func-)]TJ -295.426 -13.549 Td [(tionalities)-392(for)-393(th)1(e)-393(setup)-392(and)-392(the)-393(application)-392(of)-392(an)28(y)-393(m)28(ultilev)28(el)-392(and)-393(one-lev)28(el)-392(precondi-)]TJ 0 -13.549 Td [(tioner)-398(implemen)28(ted)-398(in)-398(the)-399(pac)28(k)56(age.)-639(The)-398(metho)-28(d)]TJ/F45 10.9091 Tf 240.937 0 Td [(free)]TJ/F15 10.9091 Tf 27.252 0 Td [(deallo)-28(cates)-398(the)-398(preconditioner)]TJ -268.189 -13.55 Td [(data)-274(s)-1(t)1(ructure,)-287(while)]TJ/F45 10.9091 Tf 101.355 0 Td [(descr)]TJ/F15 10.9091 Tf 31.63 0 Td [(prin)28(ts)-275(a)-274(description)-275(of)-274(the)-274(prec)-1(on)1(ditioner)-275(setup)-274(b)28(y)-275(the)-274(use)-1(r)1(.)]TJ -132.985 -13.549 Td [(F)83(or)-333(bac)28(kw)28(ard)-334(compatibilit)28(y)84(,)-334(metho)-28(d)1(s)-334(are)-333(also)-334(accessible)-333(as)-333(s)-1(tan)1(d-alone)-334(subroutines.)]TJ 16.937 -13.549 Td [(F)83(or)-419(e)-1(ac)28(h)-420(metho)-27(d,)-442(the)-420(same)-420(user)-420(in)28(terface)-420(is)-420(o)28(v)28(erloaded)-420(with)-420(resp)-28(ect)-420(to)-420(the)-420(real/)]TJ -16.937 -13.549 Td [(complex)-367(case)-367(and)-367(the)-367(single/double)-366(precis)-1(i)1(on;)-384(argumen)28(ts)-367(with)-367(appropriate)-367(data)-367(t)28(yp)-28(es)]TJ 0 -13.549 Td [(m)28(ust)-334(b)-27(e)-334(passed)-333(to)-333(the)-334(metho)-28(d)1(,)-334(i.e.,)]TJ -0 g 0 G -/F25 10.9091 Tf 16.364 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(the)-463(sparse)-463(matrix)-463(data)-463(structure,)-496(con)28(taining)-463(the)-463(matrix)-463(to)-463(b)-28(e)-463(preconditioned,)]TJ 0 -13.549 Td [(m)28(ust)-424(b)-28(e)-424(of)-423(t)27(yp)-27(e)]TJ/F45 10.9091 Tf 82.798 0 Td [(psb_)]TJ/F18 10.9091 Tf 22.909 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(spmat_type)]TJ/F15 10.9091 Tf 61.896 0 Td [(with)]TJ/F18 10.9091 Tf 25.835 0 Td [(x)]TJ/F15 10.9091 Tf 10.998 0 Td [(=)]TJ/F45 10.9091 Tf 13.109 0 Td [(s)]TJ/F15 10.9091 Tf 10.351 0 Td [(for)-424(real)-424(single)-423(precision,)]TJ/F18 10.9091 Tf 121.075 0 Td [(x)]TJ/F15 10.9091 Tf 10.998 0 Td [(=)]TJ/F45 10.9091 Tf 13.108 0 Td [(d)]TJ/F15 10.9091 Tf -379.451 -13.549 Td [(for)-371(real)-371(double)-371(precision,)]TJ/F18 10.9091 Tf 123.413 0 Td [(x)]TJ/F15 10.9091 Tf 10.422 0 Td [(=)]TJ/F45 10.9091 Tf 12.532 0 Td [(c)]TJ/F15 10.9091 Tf 9.774 0 Td [(for)-371(complex)-371(single)-371(precision,)]TJ/F18 10.9091 Tf 140.11 0 Td [(x)]TJ/F15 10.9091 Tf 10.422 0 Td [(=)]TJ/F45 10.9091 Tf 12.532 0 Td [(z)]TJ/F15 10.9091 Tf 9.774 0 Td [(for)-371(complex)]TJ -328.979 -13.55 Td [(double)-333(precision;)]TJ -0 g 0 G -/F25 10.9091 Tf -10.909 -22.515 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(the)-337(preconditioner)-337(data)-337(structure)-337(m)28(ust)-337(b)-28(e)-337(of)-337(t)28(yp)-28(e)]TJ/F45 10.9091 Tf 241.776 0 Td [(mld_)]TJ/F18 10.9091 Tf 22.908 0 Td [(x)]TJ/F45 10.9091 Tf 6.375 0 Td [(prec_type)]TJ/F15 10.9091 Tf 51.544 0 Td [(,)-338(with)]TJ/F18 10.9091 Tf 31.606 0 Td [(x)]TJ/F15 10.9091 Tf 10.05 0 Td [(=)]TJ/F45 10.9091 Tf 12.162 0 Td [(s)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F45 10.9091 Tf -382.148 -13.549 Td [(d)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F45 10.9091 Tf 6.667 0 Td [(c)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F45 10.9091 Tf 6.667 0 Td [(z)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-333(according)-334(to)-333(the)-333(sparse)-334(matrix)-333(data)-333(structure;)]TJ -0 g 0 G -/F25 10.9091 Tf -41.424 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(the)-321(arra)28(ys)-321(con)27(tain)1(ing)-321(the)-322(v)28(ectors)]TJ/F22 10.9091 Tf 159.847 0 Td [(v)]TJ/F15 10.9091 Tf 9.182 0 Td [(and)]TJ/F22 10.9091 Tf 21.078 0 Td [(w)]TJ/F15 10.9091 Tf 11.606 0 Td [(in)28(v)28(olv)27(ed)-321(in)-321(the)-321(preconditioner)-321(appli)1(c)-1(a-)]TJ -201.713 -13.549 Td [(tion)]TJ/F22 10.9091 Tf 21.975 0 Td [(w)]TJ/F15 10.9091 Tf 11.134 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(B)]TJ/F26 7.9701 Tf 8.822 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.959 Td [(v)]TJ/F15 10.9091 Tf 8.866 0 Td [(m)28(ust)-292(b)-28(e)-292(of)-293(t)28(yp)-27(e)]TJ/F45 10.9091 Tf 77.053 0 Td [(psb_)]TJ/F18 10.9091 Tf 22.909 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(vect_type)]TJ/F15 10.9091 Tf 54.732 0 Td [(with)]TJ/F18 10.9091 Tf 24.399 0 Td [(x)]TJ/F15 10.9091 Tf 9.562 0 Td [(=)]TJ/F45 10.9091 Tf 11.672 0 Td [(s)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F45 10.9091 Tf 6.308 0 Td [(d)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F45 10.9091 Tf 6.307 0 Td [(c)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F45 10.9091 Tf 6.308 0 Td [(z)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-300(in)-292(a)-293(manner)]TJ -322.163 -13.549 Td [(completely)-333(analogous)-334(to)-333(the)-333(sparse)-334(matrix)-333(t)28(yp)-28(e;)]TJ -0 g 0 G -/F25 10.9091 Tf -10.909 -22.516 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(real)-450(parameters)-450(de\014ning)-450(the)-450(preconditioner)-450(m)28(ust)-450(b)-28(e)-450(d)1(e)-1(clared)-449(ac)-1(cord)1(ing)-450(to)-450(the)]TJ 0 -13.549 Td [(precision)-245(of)-246(the)-245(sparse)-246(matrix)-245(and)-245(preconditioner)-246(data)-245(structures)-245(\050se)-1(e)-245(Section)]TJ -0 0 1 rg 0 0 1 RG - [-245(6.2)]TJ -0 g 0 G - [(\051.)]TJ -27.273 -22.516 Td [(A)-333(description)-334(of)-333(eac)28(h)-333(m)-1(etho)-27(d)-334(is)-333(giv)28(en)-333(in)-334(the)-333(remainder)-333(of)-334(this)-333(section.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -472 0 obj -<< -/Length 2072 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(22)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F17 11.9552 Tf -203.265 -35.866 Td [(6.1)-1125(Metho)-31(d)-375(init)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 120.317 -20.594 Td [(call)-525(p%init\050icontx,ptype,info\051)]TJ/F15 10.9091 Tf -120.317 -25.505 Td [(This)-371(metho)-28(d)-370(allo)-28(cates)-371(and)-371(initializes)-371(the)-370(preconditioner)]TJ/F45 10.9091 Tf 272.803 0 Td [(p)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-380(according)-371(to)-371(the)-371(precondi-)]TJ -278.53 -13.549 Td [(tioner)-333(t)28(yp)-28(e)-334(c)28(hosen)-333(b)28(y)-334(the)-333(user.)]TJ/F17 11.9552 Tf 0 -33.873 Td [(Argumen)31(ts)]TJ/F45 10.9091 Tf 22.914 -15.794 Td [(icontxt)-539(integer,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 154.788 0 Td [(.)]TJ -108.817 -13.549 Td [(The)-333(comm)27(unication)-333(con)28(text.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(ptype)-1589(character\050len=*\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 206.333 0 Td [(.)]TJ -160.362 -13.549 Td [(The)-333(t)27(yp)-27(e)-334(of)-333(preconditioner.)-444(Its)-334(v)56(alues)-333(are)-334(sp)-27(e)-1(ci\014ed)-333(in)-333(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-333(1)]TJ -0 g 0 G - [(.)]TJ 0 -13.55 Td [(Note)-333(that)-334(the)-333(strings)-333(are)-334(case)-333(insensitiv)28(e.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(8)]TJ -0 g 0 G - [-333(for)-334(d)1(e)-1(tail)1(s)-1(.)]TJ -51.949 -32.961 Td [(F)83(or)-364(c)-1(ompati)1(bilit)27(y)-364(with)-365(the)-365(previous)-365(v)28(ersions)-365(of)-365(MLD2P4,)-372(this)-365(metho)-28(d)-365(can)-365(b)-27(e)-365(also)]TJ -16.936 -13.549 Td [(in)28(v)28(ok)27(ed)-333(as)-333(follo)28(ws:)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 117.454 -25.504 Td [(call)-525(mld_precinit\050p,ptype,info\051)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -484 0 obj -<< -/Length 7034 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(23)]TJ -0 g 0 G -/F17 11.9552 Tf -401.542 -35.866 Td [(6.2)-1125(Metho)-31(d)-375(set)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 63.045 -20.594 Td [(call)-525(p%set\050what,val,info)-525([,ilev,)-525(ilmax,)-525(pos,)-525(idx]\051)]TJ/F15 10.9091 Tf -63.045 -23.109 Td [(This)-439(metho)-28(d)-440(sets)-439(the)-439(parameters)-440(de\014ning)-439(the)-439(prec)-1(on)1(ditioner)]TJ/F45 10.9091 Tf 302.65 0 Td [(p)]TJ/F15 10.9091 Tf 5.727 0 Td [(.)-763(More)-439(precisely)83(,)-466(the)]TJ -308.377 -13.55 Td [(parameter)-333(iden)27(t)1(i\014ed)-334(b)28(y)]TJ/F45 10.9091 Tf 114.909 0 Td [(what)]TJ/F15 10.9091 Tf 26.546 0 Td [(is)-333(assigned)-334(the)-333(v)56(alue)-334(con)28(tained)-333(in)]TJ/F45 10.9091 Tf 163.212 0 Td [(val)]TJ/F15 10.9091 Tf 17.181 0 Td [(.)]TJ/F17 11.9552 Tf -321.848 -33.873 Td [(Argumen)31(ts)]TJ/F45 10.9091 Tf 22.914 -15.394 Td [(what)-2114(character\050len=*\051)]TJ/F15 10.9091 Tf 137.606 0 Td [(.)]TJ -91.635 -13.55 Td [(The)-262(parameter)-263(to)-262(b)-28(e)-262(set.)-421(It)-262(can)-262(b)-28(e)-263(sp)-27(eci\014ed)-263(through)-262(its)-262(name;)-286(the)-262(s)-1(tr)1(ing)]TJ 0 -13.549 Td [(is)-333(case-)-1(in)1(s)-1(ensiti)1(v)27(e.)-444(See)-334(T)84(ables)]TJ -0 0 1 rg 0 0 1 RG - [-334(2)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(8)]TJ -0 g 0 G - [(.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(val)-2639(integer)]TJ/F18 10.9091 Tf 105.136 0 Td [(or)]TJ/F45 10.9091 Tf 30.425 0 Td [(character\050len=*\051)]TJ/F18 10.9091 Tf 110.711 0 Td [(or)]TJ/F45 10.9091 Tf 30.425 0 Td [(real\050psb_spk_\051)]TJ/F18 10.9091 Tf 99.256 0 Td [(or)]TJ/F45 10.9091 Tf -329.982 -13.549 Td [(real\050psb_dpk_\051)]TJ/F15 10.9091 Tf 80.181 0 Td [(,)]TJ/F45 10.9091 Tf 6.667 0 Td [(intent\050in\051)]TJ/F15 10.9091 Tf 57.272 0 Td [(.)]TJ -144.12 -13.549 Td [(The)-306(v)56(alue)-306(of)-305(the)-306(parameter)-306(to)-305(b)-28(e)-306(set.)-435(The)-306(list)-305(of)-306(allo)28(w)28(e)-1(d)-305(v)55(alu)1(e)-1(s)-305(and)-306(the)]TJ 0 -13.55 Td [(corresp)-28(onding)-391(data)-392(t)28(yp)-28(es)-391(is)-392(giv)28(en)-391(in)-392(T)84(ables)]TJ -0 0 1 rg 0 0 1 RG - [-392(2)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(8)]TJ -0 g 0 G - [(.)-619(When)-391(the)-392(v)56(alue)-392(is)-391(of)]TJ 0 -13.549 Td [(t)28(yp)-28(e)]TJ/F45 10.9091 Tf 24.545 0 Td [(character\050len=*\051)]TJ/F15 10.9091 Tf 91.636 0 Td [(,)-333(it)-334(is)-333(also)-333(treated)-334(as)-333(case)-333(inse)-1(n)1(s)-1(i)1(tiv)27(e.)]TJ/F45 10.9091 Tf -162.152 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(8)]TJ -0 g 0 G - [-333(for)-334(details.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(ilev)-2114(integer,)-525(optional,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 212.06 0 Td [(.)]TJ -166.089 -13.549 Td [(F)83(or)-344(th)1(e)-344(m)27(ultilev)28(el)-344(preconditioner,)-346(the)-344(lev)28(el)-344(at)-344(whic)28(h)-344(the)-344(preconditioner)]TJ 0 -13.55 Td [(parameter)-404(has)-404(to)-404(b)-27(e)-404(set.)-656(The)-404(lev)27(els)-404(are)-403(n)27(um)28(b)-28(ered)-403(in)-404(increasing)-404(order)]TJ 0 -13.549 Td [(starting)-307(from)-307(the)-306(\014nest)-307(one,)-312(i.e.,)-313(lev)28(el)-307(1)-307(i)1(s)-307(the)-307(\014nest)-307(lev)28(el.)-436(If)]TJ/F45 10.9091 Tf 287.463 0 Td [(ilev)]TJ/F15 10.9091 Tf 26.256 0 Td [(is)-307(not)]TJ -313.719 -13.549 Td [(presen)28(t,)-419(the)-402(parameter)-402(iden)27(ti\014ed)-402(b)28(y)]TJ/F45 10.9091 Tf 178.631 0 Td [(what)]TJ/F15 10.9091 Tf 27.295 0 Td [(is)-402(set)-402(at)-402(all)-402(the)-402(appropriate)]TJ -205.926 -13.549 Td [(lev)28(els)-334(\050see)-333(T)83(ables)]TJ -0 0 1 rg 0 0 1 RG - [-333(2)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(8)]TJ -0 g 0 G - [(\051.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(ilmax)-1589(integer,)-525(optional,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 212.06 0 Td [(.)]TJ -166.089 -13.55 Td [(F)83(or)-608(the)-608(m)28(ultilev)28(el)-609(p)1(rec)-1(on)1(ditioner,)-677(when)-608(b)-28(oth)]TJ/F45 10.9091 Tf 236.557 0 Td [(ilev)]TJ/F15 10.9091 Tf 29.544 0 Td [(and)]TJ/F45 10.9091 Tf 24.21 0 Td [(ilmax)]TJ/F15 10.9091 Tf 35.271 0 Td [(are)]TJ -325.582 -13.549 Td [(presen)28(t,)-393(the)-381(settings)-380(are)-381(applied)-381(at)-381(all)-380(lev)27(els)]TJ/F45 10.9091 Tf 218.209 0 Td [(ilev:ilmax)]TJ/F15 10.9091 Tf 57.272 0 Td [(.)-587(When)]TJ/F45 10.9091 Tf 41.768 0 Td [(ilev)]TJ/F15 10.9091 Tf -317.249 -13.549 Td [(is)-341(presen)28(t)-341(but)]TJ/F45 10.9091 Tf 69.19 0 Td [(ilmax)]TJ/F15 10.9091 Tf 32.355 0 Td [(is)-341(not,)-343(then)-341(the)-341(default)-341(is)]TJ/F45 10.9091 Tf 125.189 0 Td [(ilmax=ilev)]TJ/F15 10.9091 Tf 57.272 0 Td [(.)-467(The)-341(lev)27(els)]TJ -284.006 -13.549 Td [(are)-331(n)28(um)27(b)-27(ered)-332(in)-331(increasing)-331(order)-331(starting)-332(from)-331(the)-331(\014nest)-331(one,)-332(i.e.,)-332(lev)28(el)]TJ 0 -13.549 Td [(1)-333(is)-334(the)-333(\014nest)-333(lev)27(el.)]TJ/F45 10.9091 Tf -45.971 -13.55 Td [(pos)-2639(charater\050len=*\051,)-525(optional,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 257.878 0 Td [(.)]TJ -211.907 -13.549 Td [(Whether)-256(the)-255(other)-256(argumen)28(ts)-256(app)1(ly)-256(only)-256(to)-255(the)-256(pre-smo)-28(other)-255(\050)]TJ/F45 10.9091 Tf 294.764 0 Td [('PRE')]TJ/F15 10.9091 Tf 28.636 0 Td [(\051)-256(or)]TJ -323.4 -13.549 Td [(to)-223(the)-223(p)-27(ost-smo)-28(other)-223(\050)]TJ/F45 10.9091 Tf 104.413 0 Td [('POST')]TJ/F15 10.9091 Tf 34.363 0 Td [(\051.)-223(If)]TJ/F45 10.9091 Tf 19.406 0 Td [(pos)]TJ/F15 10.9091 Tf 19.612 0 Td [(is)-223(not)-223(presen)28(t,)-245(the)-222(other)-223(argumen)28(ts)]TJ -177.794 -13.549 Td [(are)-349(applied)-349(to)-349(b)-28(oth)-349(smo)-28(others.)-492(If)-349(the)-349(preconditioner)-349(is)-350(one-lev)28(el)-349(or)-349(the)]TJ 0 -13.549 Td [(parameter)-447(iden)28(ti\014ed)-448(b)28(y)]TJ/F45 10.9091 Tf 118.636 0 Td [(what)]TJ/F15 10.9091 Tf 27.788 0 Td [(do)-28(es)-447(not)-447(concern)-447(the)-448(smo)-27(others,)]TJ/F45 10.9091 Tf 164.34 0 Td [(pos)]TJ/F15 10.9091 Tf 22.06 0 Td [(is)]TJ -332.824 -13.549 Td [(ignored.)]TJ/F45 10.9091 Tf -45.971 -13.55 Td [(idx)-2639(integer,)-525(optional,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 212.06 0 Td [(.)]TJ -166.089 -13.549 Td [(An)-368(auxiliary)-368(input)-368(argumen)28(t)-369(that)-368(can)-368(b)-28(e)-368(passed)-368(to)-369(the)-368(underlying)-368(ob-)]TJ 0 -13.549 Td [(jects.)]TJ -51.948 -32.961 Td [(F)83(or)-364(com)-1(p)1(atibilit)27(y)-364(with)-365(the)-365(previous)-365(v)28(ersions)-365(of)-365(MLD2P4,)-372(this)-365(metho)-28(d)-365(can)-365(b)-27(e)-365(also)]TJ -16.937 -13.549 Td [(in)28(v)28(ok)27(ed)-333(as)-333(follo)28(ws:)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 111.727 -23.109 Td [(call)-525(mld_precset\050p,what,val,info\051)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -496 0 obj -<< -/Length 7966 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(24)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [(Ho)28(w)28(ev)27(er,)-286(in)-274(this)-275(case)-274(the)-275(optional)-274(argumen)28(ts)]TJ/F45 10.9091 Tf 214.056 0 Td [(ilev)]TJ/F15 10.9091 Tf 22.908 0 Td [(,)]TJ/F45 10.9091 Tf 6.153 0 Td [(ilmax)]TJ/F15 10.9091 Tf 28.636 0 Td [(,)]TJ/F45 10.9091 Tf 6.153 0 Td [(pos)]TJ/F15 10.9091 Tf 20.175 0 Td [(and)]TJ/F45 10.9091 Tf 20.57 0 Td [(idx)]TJ/F15 10.9091 Tf 20.176 0 Td [(cannot)-274(b)-28(e)-275(used.)]TJ -321.891 -27.098 Td [(A)-417(v)56(ariet)27(y)-417(of)-417(preconditioners)-417(can)-417(b)-28(e)-417(obtained)-417(b)28(y)-417(a)-417(suitable)-417(setting)-417(of)-417(the)-417(precon-)]TJ -16.936 -13.549 Td [(ditioner)-381(p)1(arame)-1(ters.)-586(These)-381(parameters)-381(can)-380(b)-28(e)-381(logically)-380(divided)-381(in)28(to)-381(four)-380(groups,)-393(i.e.,)]TJ 0 -13.549 Td [(parameters)-333(de\014ning)]TJ -0 g 0 G - 13.333 -21.208 Td [(1.)]TJ -0 g 0 G - [-500(the)-333(t)27(yp)-27(e)-334(of)-333(m)28(ultilev)28(el)-334(cycle)-333(and)-333(ho)28(w)-334(man)28(y)-333(cycles)-334(m)28(ust)-333(b)-28(e)-334(ap)1(plied;)]TJ -0 g 0 G - 0 -21.993 Td [(2.)]TJ -0 g 0 G - [-500(the)-333(aggregation)-334(algorith)1(m;)]TJ -0 g 0 G - 0 -21.992 Td [(3.)]TJ -0 g 0 G - [-500(the)-449(coarse-space)-449(correction)-448(at)-449(the)-449(coarsest)-449(lev)28(el)-449(\050for)-448(m)27(ul)1(tilev)27(el)-448(preconditioners)]TJ 13.94 -13.55 Td [(only\051;)]TJ -0 g 0 G - -13.94 -21.992 Td [(4.)]TJ -0 g 0 G - [-500(the)-333(smo)-28(other)-333(of)-334(the)-333(m)28(ultilev)28(e)-1(l)-333(preconditioners,)-333(or)-333(the)-334(one-lev)28(el)-333(preconditioner.)]TJ -13.333 -21.208 Td [(A)-379(list)-379(of)-378(the)-379(parameters)-379(that)-379(can)-379(b)-28(e)-378(se)-1(t,)-390(along)-379(with)-378(their)-379(allo)28(w)27(ed)-378(and)-379(default)-379(v)56(alues,)]TJ 0 -13.549 Td [(is)-331(giv)27(en)-331(in)-331(T)83(ables)]TJ -0 0 1 rg 0 0 1 RG - [-331(2)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(8)]TJ -0 g 0 G - [(.)-444(F)83(or)-331(a)-331(description)-332(of)-331(the)-331(meaning)-332(of)-331(the)-331(parameters,)-332(please)-331(refer)]TJ 0 -13.55 Td [(also)-333(to)-334(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(4)]TJ -0 g 0 G - [(.)]TJ/F44 10.9091 Tf 16.936 -27.098 Td [(Remark)-361(2.)]TJ/F15 10.9091 Tf 61.979 0 Td [(A)-314(smo)-28(other)-314(is)-315(u)1(s)-1(u)1(ally)-315(obtained)-314(b)28(y)-314(com)28(bining)-315(t)28(w)28(o)-314(ob)-56(jects:)-435(a)-314(smo)-28(other)]TJ -78.915 -13.549 Td [(\050)]TJ/F45 10.9091 Tf 4.242 0 Td [(SMOOTHER_TYPE)]TJ/F15 10.9091 Tf 74.454 0 Td [(\051)-408(and)-408(a)-409(lo)-28(cal)-408(solv)28(er)-408(\050)]TJ/F45 10.9091 Tf 103.271 0 Td [(SUB_SOLVE)]TJ/F15 10.9091 Tf 51.545 0 Td [(\051,)-408(as)-409(sp)-27(e)-1(ci\014)1(e)-1(d)-408(in)-408(T)83(ables)]TJ -0 0 1 rg 0 0 1 RG - [-408(7)]TJ -0 g 0 G - [(-)]TJ -0 0 1 rg 0 0 1 RG - [(8)]TJ -0 g 0 G - [(.)-670(F)84(or)-408(e)-1(x)1(-)]TJ -233.512 -13.549 Td [(ample,)-309(the)-303(blo)-28(c)28(k-Jacobi)-303(s)-1(mo)-27(other)-303(using)-304(ILU\0500\051)-303(on)-303(the)-303(blo)-28(c)28(ks)-303(is)-303(obtained)-303(b)27(y)-303(com)28(bining)]TJ 0 -13.55 Td [(the)-357(blo)-28(c)28(k-Jacobi)-357(smo)-28(other)-357(ob)-55(ject)-357(with)-357(the)-357(ILU\0500\051)-357(solv)28(er)-357(ob)-56(ject.)-515(Similarly)83(,)-363(the)-357(h)28(ybrid)]TJ 0 -13.549 Td [(Gauss-Seidel)-297(smo)-28(other)-297(\050see)-297(Note)-296(in)-297(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-297(7)]TJ -0 g 0 G - [(\051)-297(is)-296(obtained)-297(b)28(y)-297(com)28(bining)-297(the)-297(blo)-28(c)28(k-Jacobi)]TJ 0 -13.549 Td [(smo)-28(other)-321(ob)-56(ject)-321(with)-321(a)-321(single)-322(sw)28(eep)-321(of)-321(the)-322(Gauss-Seidel)-321(solv)28(er)-321(ob)-56(ject,)-324(while)-321(the)-321(p)-28(oin)28(t-)]TJ 0 -13.549 Td [(Jacobi)-433(smo)-28(other)-432(is)-433(the)-433(result)-433(of)-433(com)28(bining)-433(the)-433(bl)1(o)-28(c)27(k-Jacobi)-432(smo)-28(other)-433(ob)-56(j)1(e)-1(ct)-432(with)-433(a)]TJ 0 -13.549 Td [(single)-404(sw)28(eep)-404(of)-404(the)-404(p)-28(oin)28(t)28(wise-Jacobi)-404(solv)27(er)-404(ob)-55(ject.)-656(Ho)27(w)28(ev)28(er,)-422(for)-404(simplicit)28(y)84(,)-422(shortcuts)]TJ 0 -13.549 Td [(are)-355(pro)28(vided)-354(to)-355(set)-355(p)-27(oin)28(t-Jacobi,)-360(h)28(ybrid)-355(\050forw)28(ard\051)-355(Gauss-Seidel,)-360(an)1(d)-355(h)28(ybrid)-355(bac)28(kw)28(ard)]TJ 0 -13.55 Td [(Gauss-Seidel,)-257(i.e.,)-258(the)-238(previous)-238(smo)-28(others)-238(can)-239(b)-27(e)-239(de\014ned)-238(b)28(y)-238(se)-1(tti)1(ng)-239(only)]TJ/F45 10.9091 Tf 337.997 0 Td [(SMOOTHER_TYPE)]TJ/F15 10.9091 Tf -337.997 -13.549 Td [(to)-333(appropriate)-333(v)55(alues)-333(\050see)-334(T)84(ables)]TJ -0 0 1 rg 0 0 1 RG - [-334(7)]TJ -0 g 0 G - [(\051,)-333(i.e.,)-333(without)-334(setting)]TJ/F45 10.9091 Tf 274.242 0 Td [(SUB_SOLVE)]TJ/F15 10.9091 Tf 55.182 0 Td [(to)-28(o.)]TJ -312.488 -13.549 Td [(The)-474(smo)-28(other)-474(and)-474(solv)28(er)-474(ob)-55(jects)-474(are)-474(arranged)-474(in)-474(a)-474(hierarc)28(hical)-474(manner.)-866(When)]TJ -16.936 -13.549 Td [(sp)-28(ecifying)-314(a)-313(smo)-28(other)-314(ob)-55(jec)-1(t,)-317(its)-314(parameters,)-318(including)-313(the)-314(lo)-28(cal)-314(solv)28(er,)-318(are)-314(set)-313(to)-314(their)]TJ 0 -13.549 Td [(default)-302(v)55(alues,)-308(and)-303(when)-302(a)-302(s)-1(ol)1(v)27(er)-302(ob)-56(ject)-302(is)-303(sp)-27(eci\014ed,)-309(its)-302(defaults)-303(are)-302(also)-303(set,)-308(o)28(v)27(erriding)]TJ 0 -13.55 Td [(in)-285(b)-28(oth)-285(cases)-285(an)28(y)-286(previous)-285(settings)-285(ev)28(en)-285(if)-286(expli)1(c)-1(it)1(ly)-286(sp)-27(ec)-1(i)1(\014ed.)-429(Therefore)-285(if)-285(the)-285(user)-285(s)-1(ets)]TJ 0 -13.549 Td [(a)-297(smo)-28(other,)-305(and)-297(wishes)-297(to)-298(use)-297(a)-297(solv)27(er)-297(di\013eren)28(t)-297(from)-298(the)-297(default)-297(one,)-305(the)-297(call)-297(to)-298(set)-297(the)]TJ 0 -13.549 Td [(solv)28(er)-334(m)28(ust)-333(come)]TJ/F18 10.9091 Tf 85.909 0 Td [(after)]TJ/F15 10.9091 Tf 26.974 0 Td [(the)-333(call)-334(to)-333(set)-333(the)-334(smo)-28(other.)]TJ -95.947 -13.549 Td [(Similar)-498(considerations)-498(apply)-498(to)-498(the)-498(p)-28(oin)28(t-Jacobi,)-540(Gauss-Seidel)-498(and)-498(blo)-28(c)28(k-Jacobi)]TJ -16.936 -13.549 Td [(coarsest-lev)28(el)-334(solv)28(ers,)-333(and)-334(shortcuts)-333(are)-333(a)28(v)55(ailable)-333(in)-333(this)-334(case)-333(to)-28(o)-333(\050see)-334(T)84(able)]TJ -0 0 1 rg 0 0 1 RG - [-334(5)]TJ -0 g 0 G - [(\051.)]TJ/F44 10.9091 Tf 16.936 -27.099 Td [(Remark)-403(3.)]TJ/F15 10.9091 Tf 63.059 0 Td [(In)-350(general,)-355(a)-350(coarsest-)-1(l)1(e)-1(v)28(el)-350(solv)28(er)-351(cannot)-350(b)-28(e)-350(used)-351(with)-350(b)-28(oth)-350(the)-350(repli-)]TJ -79.995 -13.549 Td [(cated)-487(and)-487(d)1(istributed)-487(coarsest-matrix)-487(la)28(y)28(out;)-564(therefore,)-525(setting)-487(the)-487(solv)28(er)-487(after)-486(the)]TJ 0 -13.549 Td [(la)28(y)28(out)-302(m)-1(a)28(y)-302(c)28(hange)-302(the)-302(la)27(y)28(out.)-434(Similarly)84(,)-309(setting)-302(the)-302(la)28(y)28(out)-303(after)-302(the)-302(solv)28(er)-302(ma)27(y)-302(c)28(hange)]TJ 0 -13.549 Td [(the)-333(solv)27(er.)]TJ 16.936 -13.55 Td [(More)-437(precisely)83(,)-464(UM)1(FP)83(A)28(CK)-438(and)-437(Sup)-28(erLU)-437(require)-437(the)-438(coarsest-lev)28(el)-437(m)-1(atr)1(ix)-438(to)-437(b)-28(e)]TJ -16.936 -13.549 Td [(replicated,)-470(while)-443(Sup)-28(erLU)]TJ -ET -q -1 0 0 1 214.197 135.269 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 217.47 135.07 Td [(Dist)-443(requires)-443(it)-443(to)-442(b)-28(e)-443(distributed.)-773(In)-443(these)-443(cases,)-470(setting)]TJ -131.07 -13.549 Td [(the)-445(coarsest-le)-1(v)28(el)-445(solv)28(er)-446(implies)-445(that)-445(the)-446(la)28(y)28(out)-445(is)-446(rede\014ned)-445(according)-445(to)-446(the)-445(solv)28(er,)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -515 0 obj -<< -/Length 3880 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(25)]TJ -0 g 0 G - -401.542 -35.866 Td [(o)28(vv)28(erriding)-487(an)28(y)-486(previous)-486(settings.)-904(M)1(UMPS,)-487(p)-27(oin)27(t-Jacobi,)-524(h)28(ybrid)-486(Gauss-Seidel)-487(and)]TJ 0 -13.549 Td [(blo)-28(c)28(k-Jacobi)-416(can)-417(b)-27(e)-417(app)1(lied)-417(to)-416(replicated)-416(and)-416(distributed)-416(matrice)-1(s,)-437(th)28(us)-416(their)-416(c)28(hoice)]TJ 0 -13.549 Td [(do)-28(es)-450(not)-450(mo)-28(dify)-450(an)28(y)-450(previously)-450(sp)-28(eci\014ed)-450(la)28(y)28(out.)-795(It)-450(is)-450(w)28(orth)-450(noting)-450(that,)-479(when)-450(the)]TJ 0 -13.549 Td [(matrix)-469(is)-469(replicated,)-503(the)-469(p)-28(oin)28(t-Jacobi,)-503(h)28(ybrid)-469(Gauss-Seidel)-470(and)-469(blo)-27(c)27(k-Jacobi)-469(solv)28(ers)]TJ 0 -13.549 Td [(reduce)-358(to)-357(the)-358(corresp)-27(onding)-358(lo)-27(c)-1(al)-357(solv)28(er)-358(ob)-55(jects)-358(\050see)-358(Remark)-357(2\051.)-517(F)83(or)-357(the)-358(p)-27(oin)27(t-Jacobi)]TJ 0 -13.55 Td [(and)-359(Gauss-Seidel)-359(solv)28(ers,)-366(these)-359(ob)-55(jects)-360(corresp)-27(ond)-359(to)-359(a)]TJ/F18 10.9091 Tf 268.966 0 Td [(single)]TJ/F15 10.9091 Tf 31.5 0 Td [(p)-28(oin)28(t-Jacobi)-359(sw)28(eep)-359(and)]TJ -300.466 -13.549 Td [(a)]TJ/F18 10.9091 Tf 9.091 0 Td [(single)]TJ/F15 10.9091 Tf 31.22 0 Td [(Gauss-Seidel)-333(sw)27(eep,)-333(resp)-28(ectiv)28(ely)83(,)-333(whic)28(h)-334(are)-333(v)28(ery)-333(p)-28(o)-28(or)-333(solv)28(ers)-1(.)]TJ -23.374 -13.549 Td [(On)-378(the)-377(other)-378(hand,)-389(the)-378(distribu)1(te)-1(d)-377(la)28(y)27(out)-377(can)-378(b)-28(e)-378(used)-377(w)-1(i)1(th)-378(an)28(y)-378(solv)28(er)-378(but)-378(UMF-)]TJ -16.937 -13.549 Td [(P)83(A)28(CK)-389(and)-389(Sup)-28(erLU;)-389(therefore,)-403(if)-389(an)28(y)-389(of)-389(these)-389(t)28(w)28(o)-390(solv)28(ers)-389(has)-389(already)-389(b)-28(een)-389(selected,)]TJ 0 -13.549 Td [(the)-382(coarsest-lev)27(el)-382(solv)28(er)-382(is)-382(c)27(hanged)-382(to)-382(blo)-28(c)28(k-Jacobi,)-394(with)-382(the)-383(previously)-382(c)28(hosen)-382(solv)28(er)]TJ 0 -13.55 Td [(applied)-315(to)-316(the)-315(lo)-28(cal)-316(blo)-28(c)28(ks.)-438(Lik)28(e)-1(wise,)-319(the)-315(replicated)-316(la)28(y)28(out)-316(can)-315(b)-28(e)-315(use)-1(d)-315(with)-316(an)28(y)-315(solv)28(er)]TJ 0 -13.549 Td [(but)-292(Sup)-27(erLu)]TJ -ET -q -1 0 0 1 154.287 555.294 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 157.56 555.095 Td [(Dist;)-306(therefore,)-300(if)-292(Sup)-27(erLu)]TJ -ET -q -1 0 0 1 283.008 555.294 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 286.281 555.095 Td [(Dist)-292(has)-292(b)-27(e)-1(en)-291(previously)-292(set,)-300(the)-292(coarsest-lev)27(el)]TJ -192.681 -13.549 Td [(solv)28(er)-334(is)-333(c)28(hanged)-333(to)-334(the)-333(default)-333(sequen)27(tial)-333(solv)28(er.)]TJ/F44 10.9091 Tf 16.937 -13.549 Td [(Remark)-371(4.)]TJ/F15 10.9091 Tf 62.109 0 Td [(The)-322(argumen)28(t)]TJ/F45 10.9091 Tf 71.002 0 Td [(idx)]TJ/F15 10.9091 Tf 20.698 0 Td [(can)-322(b)-28(e)-322(used)-323(to)-322(allo)28(w)-322(\014ner)-323(con)28(trol)-322(for)-322(those)-323(solv)28(ers;)]TJ -170.746 -13.549 Td [(for)-401(instance,)-417(b)27(y)-400(sp)-28(ecifying)-401(the)-401(k)28(eyw)28(ord)]TJ/F45 10.9091 Tf 194.479 0 Td [(MUMPS_IPAR_ENTRY)]TJ/F15 10.9091 Tf 96.007 0 Td [(and)-401(an)-400(appropriate)-401(v)56(alue)]TJ -290.486 -13.55 Td [(for)]TJ/F45 10.9091 Tf 17.267 0 Td [(idx)]TJ/F15 10.9091 Tf 17.181 0 Td [(,)-399(it)-385(is)-386(p)-27(ossible)-386(to)-385(se)-1(t)-385(an)28(y)-386(en)28(try)-385(in)-386(the)-385(MUMPS)-386(in)28(teger)-385(con)27(trol)-385(arra)28(y)83(.)-601(See)-386(al)1(s)-1(o)]TJ -34.448 -13.549 Td [(Sec.)]TJ -0 0 1 rg 0 0 1 RG - [-333(7)]TJ -0 g 0 G - [(.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -520 0 obj -<< -/Length 3774 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(26)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -q -0 -1 1 0 0 0 cm -0 g 0 G -0 g 0 G -0 g 0 G -q -1 0 0 1 0 86.879 cm -[]0 d 0 J 0.398 w 0 0 m 593.616 0 l S -Q -q -1 0 0 1 0 73.13 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -1 0 0 1 -292.625 -715.095 cm -BT -/F45 10.9091 Tf 298.603 792.29 Td [(what)]TJ -ET -q -1 0 0 1 406.628 788.225 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 412.605 792.29 Td [(d)22(a)67(t)66(a)-377(type)]TJ -ET -q -1 0 0 1 510.218 788.225 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F45 10.9091 Tf 516.196 792.29 Td [(val)]TJ -ET -q -1 0 0 1 590.205 788.225 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 596.183 792.29 Td [(def)89(a)22(ul)67(t)]TJ -ET -q -1 0 0 1 670.191 788.225 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 676.169 792.29 Td [(comments)]TJ -ET -q -1 0 0 1 886.241 788.225 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 292.625 788.026 cm -[]0 d 0 J 0.398 w 0 0 m 593.616 0 l S -Q -q -1 0 0 1 292.625 692.982 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F45 10.9091 Tf 298.603 778.342 Td [('ML_CYCLE')]TJ -ET -q -1 0 0 1 406.628 692.982 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F45 10.9091 Tf 412.605 778.342 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 510.218 692.982 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F45 10.9091 Tf 516.196 778.342 Td [('VCYCLE')]TJ 0 -13.549 Td [('WCYCLE')]TJ 0 -13.549 Td [('KCYCLE')]TJ 0 -13.549 Td [('MULT')]TJ 0 -13.549 Td [('ADD')]TJ -ET -q -1 0 0 1 590.205 692.982 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F45 10.9091 Tf 596.183 778.342 Td [('VCYCLE')]TJ -ET -q -1 0 0 1 670.191 692.982 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -BT -/F15 10.9091 Tf 676.169 778.342 Td [(Multilev)28(el)-231(cycle:)-393(V-cycle,)-251(W-cycle,)-251(K-cycle,)]TJ 0 -13.549 Td [(h)28(ybrid)-466(Multiplicativ)28(e)-466(Sc)28(h)27(w)28(arz,)-499(and)-466(Addi-)]TJ 0 -13.549 Td [(tiv)28(e)-334(Sc)28(h)28(w)28(arz.)]TJ 0 -13.549 Td [(Note)-586(th)1(at)-586(h)28(ybrid)-585(Multiplicativ)28(e)-586(Sc)28(h)28(w)27(arz)]TJ 0 -13.549 Td [(is)-593(equiv)55(al)1(e)-1(n)28(t)-593(to)-593(V-cycle)-593(and)-593(is)-593(included)]TJ 0 -13.55 Td [(for)-376(compatibi)1(lit)27(y)-375(with)-376(previous)-375(v)27(ersions)-375(of)]TJ 0 -13.549 Td [(MLD2P4.)]TJ -ET -q -1 0 0 1 886.241 692.982 cm -[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S -Q -q -1 0 0 1 292.625 692.783 cm -[]0 d 0 J 0.398 w 0 0 m 593.616 0 l S -Q -q -1 0 0 1 292.625 665.485 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 298.603 683.099 Td [('OUTER_SWEEPS')]TJ -ET -q -1 0 0 1 406.628 665.485 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 412.605 683.099 Td [(integer)]TJ -ET -q -1 0 0 1 510.218 665.485 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 516.196 683.099 Td [(An)28(y)-333(in)27(teger)]TJ 0 -13.549 Td [(n)28(um)28(b)-28(er)]TJ/F25 10.9091 Tf 39.727 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(1)]TJ -ET -q -1 0 0 1 590.205 665.485 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 596.183 683.099 Td [(1)]TJ -ET -q -1 0 0 1 670.191 665.485 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 676.169 683.099 Td [(Num)28(b)-28(er)-333(of)-334(m)28(ultilev)28(el)-333(cycles.)]TJ -ET -q -1 0 0 1 886.241 665.485 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 292.625 665.286 cm -[]0 d 0 J 0.398 w 0 0 m 593.616 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 373.473 634.597 Td [(T)83(able)-333(2:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(m)28(ultilev)28(el)-333(cycle)-334(and)-333(the)-333(n)28(um)27(b)-27(er)-334(of)-333(cycles)-334(t)1(o)-334(b)-28(e)-333(applied.)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -Q -0 g 0 G -0 g 0 G -0 g 0 G - -endstream -endobj -525 0 obj -<< -/Length 10624 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(27)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -q -0 1 -1 0 0 0 cm -0 g 0 G -0 g 0 G -0 g 0 G -q -1 0 0 1 0 216.592 cm -[]0 d 0 J 0.398 w 0 0 m 600.087 0 l S -Q -q -1 0 0 1 0 202.843 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -1 0 0 1 -299.826 -121.521 cm -BT -/F45 10.9091 Tf 305.803 328.429 Td [(what)]TJ -ET -q -1 0 0 1 422.332 324.364 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 428.31 328.429 Td [(d)22(a)67(t)67(a)-378(type)]TJ -ET -q -1 0 0 1 521.055 324.364 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F45 10.9091 Tf 527.032 328.429 Td [(val)]TJ -ET -q -1 0 0 1 598.207 324.364 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 604.185 328.429 Td [(def)89(a)22(ul)67(t)]TJ -ET -q -1 0 0 1 692.367 324.364 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 698.344 328.429 Td [(comments)]TJ -ET -q -1 0 0 1 899.912 324.364 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 299.826 324.165 cm -[]0 d 0 J 0.398 w 0 0 m 600.087 0 l S -Q -q -1 0 0 1 299.826 269.769 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F45 10.9091 Tf 305.803 314.481 Td [('MIN_COARSE_SIZE')]TJ -ET -q -1 0 0 1 422.332 269.769 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F45 10.9091 Tf 428.31 314.481 Td [(integer)]TJ -ET -q -1 0 0 1 521.055 269.769 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F15 10.9091 Tf 527.032 314.481 Td [(An)28(y)-334(n)28(um)28(b)-28(er)]TJ/F22 10.9091 Tf 0 -13.549 Td [(>)]TJ/F15 10.9091 Tf 11.516 0 Td [(0)]TJ -ET -q -1 0 0 1 598.207 269.769 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F25 10.9091 Tf 604.185 314.481 Td [(b)]TJ/F15 10.9091 Tf 4.848 0 Td [(40)]TJ/F21 5.9776 Tf 13.939 3.67 Td [(3)]TJ/F25 10.9091 Tf -2.407 4.188 Td [(p)]TJ -ET -q -1 0 0 1 629.656 322.557 cm -[]0 d 0 J 0.436 w 0 0 m 6.548 0 l S -Q -BT -/F22 10.9091 Tf 629.656 314.481 Td [(n)]TJ/F25 10.9091 Tf 6.548 0 Td [(c)]TJ/F15 10.9091 Tf 4.848 0 Td [(,)-363(where)]TJ/F22 10.9091 Tf 38.789 0 Td [(n)]TJ/F15 10.9091 Tf -75.656 -13.549 Td [(is)-540(the)-540(dimension)]TJ 0 -13.549 Td [(of)-511(the)-511(matrix)-510(at)]TJ 0 -13.549 Td [(the)-333(\014nest)-334(lev)28(el)]TJ -ET -q -1 0 0 1 692.367 269.769 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F15 10.9091 Tf 698.344 314.481 Td [(Coarse)-475(size)-475(threshold.)-868(The)-475(aggregation)]TJ 0 -13.549 Td [(stops)-531(if)-531(the)-530(global)-531(n)28(um)28(b)-28(er)-531(of)-531(v)56(ariables)]TJ 0 -13.549 Td [(of)-354(the)-355(computed)-354(coarsest)-355(matrix)-354(is)-354(lo)27(w)28(er)]TJ 0 -13.549 Td [(than)-249(or)-248(equal)-249(to)-248(this)-249(threshold)-248(\050see)-249(Note\051.)]TJ -ET -q -1 0 0 1 899.912 269.769 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -q -1 0 0 1 299.826 269.57 cm -[]0 d 0 J 0.398 w 0 0 m 600.087 0 l S -Q -q -1 0 0 1 299.826 201.625 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F45 10.9091 Tf 305.803 259.886 Td [('MIN_CR_RATIO')]TJ -ET -q -1 0 0 1 422.332 201.625 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F45 10.9091 Tf 428.31 259.886 Td [(real)]TJ -ET -q -1 0 0 1 521.055 201.625 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F15 10.9091 Tf 527.032 259.886 Td [(An)28(y)-334(n)28(um)28(b)-28(er)]TJ/F22 10.9091 Tf 0 -13.549 Td [(>)]TJ/F15 10.9091 Tf 11.516 0 Td [(1)]TJ -ET -q -1 0 0 1 598.207 201.625 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F15 10.9091 Tf 604.185 259.886 Td [(1.5)]TJ -ET -q -1 0 0 1 692.367 201.625 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F15 10.9091 Tf 698.344 259.886 Td [(Minim)28(um)-325(coarsening)-324(ratio.)-442(The)-324(aggrega-)]TJ 0 -13.549 Td [(tion)-480(stops)-480(if)-480(the)-480(ratio)-480(b)-27(et)27(w)28(een)-480(the)-480(ma-)]TJ 0 -13.549 Td [(trix)-364(dimensions)-364(at)-364(t)27(w)28(o)-364(consecutiv)28(e)-364(lev)27(els)]TJ 0 -13.549 Td [(is)-459(lo)28(w)28(er)-459(th)1(an)-459(or)-458(e)-1(q)1(ual)-459(to)-458(this)-459(threshold)]TJ 0 -13.55 Td [(\050see)-333(Note)-1(\051.)]TJ -ET -q -1 0 0 1 899.912 201.625 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -q -1 0 0 1 299.826 201.425 cm -[]0 d 0 J 0.398 w 0 0 m 600.087 0 l S -Q -q -1 0 0 1 299.826 160.579 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 305.803 191.742 Td [('MAX_LEVS')]TJ -ET -q -1 0 0 1 422.332 160.579 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 428.31 191.742 Td [(integer)]TJ -ET -q -1 0 0 1 521.055 160.579 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 527.032 191.742 Td [(An)28(y)-334(in)28(teger)]TJ 0 -13.549 Td [(n)28(um)28(b)-28(er)]TJ/F22 10.9091 Tf 39.728 0 Td [(>)]TJ/F15 10.9091 Tf 11.515 0 Td [(1)]TJ -ET -q -1 0 0 1 598.207 160.579 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 604.185 191.742 Td [(20)]TJ -ET -q -1 0 0 1 692.367 160.579 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 698.344 191.742 Td [(Maxim)28(um)-244(n)28(um)28(b)-28(er)-244(of)-244(lev)28(els.)-415(The)-244(aggrega-)]TJ 0 -13.549 Td [(tion)-343(stops)-343(if)-343(the)-343(n)28(um)28(b)-28(er)-343(of)-343(lev)27(els)-343(reac)28(hes)]TJ 0 -13.55 Td [(this)-333(v)55(alue)-333(\050see)-334(Note\051.)]TJ -ET -q -1 0 0 1 899.912 160.579 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 299.826 160.379 cm -[]0 d 0 J 0.398 w 0 0 m 600.087 0 l S -Q -q -1 0 0 1 299.826 92.434 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F45 10.9091 Tf 305.803 150.696 Td [('PAR_AGGR_ALG')]TJ -ET -q -1 0 0 1 422.332 92.434 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F45 10.9091 Tf 428.31 150.696 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 521.055 92.434 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F45 10.9091 Tf 527.032 150.696 Td [('DEC')]TJ/F15 10.9091 Tf 28.637 0 Td [(,)]TJ/F45 10.9091 Tf -28.637 -13.55 Td [('SYMDEC')]TJ -ET -q -1 0 0 1 598.207 92.434 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F45 10.9091 Tf 604.185 150.696 Td [('DEC')]TJ -ET -q -1 0 0 1 692.367 92.434 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F15 10.9091 Tf 698.344 150.696 Td [(P)28(arallel)-333(aggregation)-334(algorithm.)]TJ 0 -13.55 Td [(Curren)28(tly)83(,)-604(only)-550(the)-550(decoupled)-550(aggrega-)]TJ 0 -13.549 Td [(tion)-518(\050)]TJ/F45 10.9091 Tf 28.679 0 Td [(DEC)]TJ/F15 10.9091 Tf 17.182 0 Td [(\051)-518(is)-517(a)27(v)56(ailable;)-610(the)]TJ/F45 10.9091 Tf 94.568 0 Td [(SYMDEC)]TJ/F15 10.9091 Tf 40.01 0 Td [(op-)]TJ -180.439 -13.549 Td [(tion)-306(applies)-307(decoupled)-306(aggregation)-306(to)-307(the)]TJ 0 -13.549 Td [(sparsit)28(y)-334(p)1(atte)-1(r)1(n)-334(of)]TJ/F22 10.9091 Tf 92 0 Td [(A)]TJ/F15 10.9091 Tf 10.606 0 Td [(+)]TJ/F22 10.9091 Tf 10.909 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(T)]TJ/F15 10.9091 Tf 6.605 -3.959 Td [(.)]TJ -ET -q -1 0 0 1 899.912 92.434 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -q -1 0 0 1 299.826 92.235 cm -[]0 d 0 J 0.398 w 0 0 m 600.087 0 l S -Q -q -1 0 0 1 299.826 24.29 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F45 10.9091 Tf 305.803 82.551 Td [('AGGR_TYPE')]TJ -ET -q -1 0 0 1 422.332 24.29 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F45 10.9091 Tf 428.31 82.551 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 521.055 24.29 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F45 10.9091 Tf 527.032 82.551 Td [('SOC1')]TJ -ET -q -1 0 0 1 598.207 24.29 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F45 10.9091 Tf 604.185 82.551 Td [('SOC1')]TJ/F15 10.9091 Tf 34.363 0 Td [(,)]TJ/F45 10.9091 Tf 6.667 0 Td [('SOC2')]TJ -ET -q -1 0 0 1 692.367 24.29 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -BT -/F15 10.9091 Tf 698.344 82.551 Td [(T)28(yp)-28(e)-254(of)-255(aggregation)-254(algorithm:)-405(curren)28(tly)83(,)]TJ 0 -13.549 Td [(w)28(e)-355(implemen)28(t)-355(to)-355(measures)-355(of)-355(strength)-355(of)]TJ 0 -13.549 Td [(connection,)-595(the)-543(one)-542(b)28(y)-543(V)83(an)28(\024)472(ek,)-595(Mandel)]TJ 0 -13.549 Td [(and)-454(Brezina)-454([)]TJ -1 0 0 rg 1 0 0 RG - [(26)]TJ -0 g 0 G - [(],)-484(and)-454(the)-454(one)-454(b)28(y)-454(Grat-)]TJ 0 -13.55 Td [(ton)-333(et)-334(al)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(16)]TJ -0 g 0 G - [(].)]TJ -ET -q -1 0 0 1 899.912 24.29 cm -[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S -Q -q -1 0 0 1 299.826 24.09 cm -[]0 d 0 J 0.398 w 0 0 m 600.087 0 l S -Q -q -1 0 0 1 299.826 -16.756 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 305.803 14.407 Td [('AGGR_PROL')]TJ -ET -q -1 0 0 1 422.332 -16.756 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 428.31 14.407 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 521.055 -16.756 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 527.032 14.407 Td [('SMOOTHED')]TJ/F15 10.9091 Tf 57.273 0 Td [(,)]TJ/F45 10.9091 Tf -57.273 -13.549 Td [('UNSMOOTHED')]TJ -ET -q -1 0 0 1 598.207 -16.756 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 604.185 14.407 Td [('SMOOTHED')]TJ -ET -q -1 0 0 1 692.367 -16.756 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 698.344 14.407 Td [(Prolongator)-436(used)-435(b)27(y)-435(the)-436(aggregation)-436(al-)]TJ 0 -13.549 Td [(gorithm:)-609(smo)-28(othed)-416(or)-416(unsmo)-28(oth)1(e)-1(d)-415(\050i.e.,)]TJ 0 -13.55 Td [(ten)28(tativ)28(e)-334(prolongator\051.)]TJ -ET -q -1 0 0 1 899.912 -16.756 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 299.826 -16.956 cm -[]0 d 0 J 0.398 w 0 0 m 600.087 0 l S -Q -q -1 0 0 1 299.826 -30.704 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F44 10.9091 Tf 305.803 -26.639 Td [(Note.)]TJ/F15 10.9091 Tf 35.053 0 Td [(The)-333(aggregation)-334(algorithm)-333(stops)-333(when)-334(at)-333(least)-333(one)-334(of)-333(the)-333(follo)28(wing)-334(criteria)-333(is)-333(met:)-445(the)-333(coarse)-334(size)-333(threshold,)-333(the)]TJ -ET -q -1 0 0 1 899.912 -30.704 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 299.826 -44.253 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 305.803 -40.189 Td [(minim)28(um)-334(coarsening)-333(ratio,)-333(or)-333(the)-334(maxim)28(um)-333(n)27(u)1(m)27(b)-27(e)-1(r)-333(of)-333(lev)28(els)-334(is)-333(reac)28(hed.)-445(Therefore,)-333(the)-333(actual)-334(n)28(um)28(b)-28(er)-333(of)-333(lev)27(els)-333(ma)28(y)-334(b)-27(e)]TJ -ET -q -1 0 0 1 899.912 -44.253 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 299.826 -57.802 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 305.803 -53.738 Td [(smaller)-333(than)-334(the)-333(sp)-28(eci\014ed)-333(maxim)28(um)-334(n)28(um)28(b)-28(er)-333(of)-333(lev)27(els.)]TJ -ET -q -1 0 0 1 899.912 -57.802 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 299.826 -58.002 cm -[]0 d 0 J 0.398 w 0 0 m 600.087 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 459.779 -88.691 Td [(T)83(able)-333(3:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(aggregation)-333(algorithm.)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -Q -0 g 0 G -0 g 0 G -0 g 0 G - -endstream -endobj -531 0 obj -<< -/Length 6126 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(28)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -q -0 -1 1 0 0 0 cm -0 g 0 G -0 g 0 G -0 g 0 G -q -1 0 0 1 0 108.207 cm -[]0 d 0 J 0.398 w 0 0 m 598.736 0 l S -Q -q -1 0 0 1 0 94.458 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -1 0 0 1 -292.625 -715.095 cm -BT -/F45 10.9091 Tf 298.603 813.618 Td [(what)]TJ -ET -q -1 0 0 1 412.297 809.553 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 418.275 813.618 Td [(d)22(a)67(t)67(a)-378(type)]TJ -ET -q -1 0 0 1 531.27 809.553 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F45 10.9091 Tf 537.248 813.618 Td [(val)]TJ -ET -q -1 0 0 1 614.092 809.553 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 620.069 813.618 Td [(def)89(a)22(ul)67(t)]TJ -ET -q -1 0 0 1 691.244 809.553 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 697.221 813.618 Td [(comments)]TJ -ET -q -1 0 0 1 891.361 809.553 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 292.625 809.354 cm -[]0 d 0 J 0.398 w 0 0 m 598.736 0 l S -Q -q -1 0 0 1 292.625 754.958 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F45 10.9091 Tf 298.603 799.671 Td [('AGGR_ORD')]TJ -ET -q -1 0 0 1 412.297 754.958 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F45 10.9091 Tf 418.275 799.671 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 531.27 754.958 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F45 10.9091 Tf 537.248 799.671 Td [('NATURAL')]TJ 0 -13.55 Td [('DEGREE')]TJ -ET -q -1 0 0 1 614.092 754.958 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F45 10.9091 Tf 620.069 799.671 Td [('NATURAL')]TJ -ET -q -1 0 0 1 691.244 754.958 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -BT -/F15 10.9091 Tf 697.221 799.671 Td [(Initial)-314(ordering)-313(of)-314(indices)-314(for)-314(the)-314(aggre-)]TJ 0 -13.55 Td [(gation)-372(algor)1(ithm:)-521(either)-372(natural)-371(order-)]TJ 0 -13.549 Td [(ing)-414(or)-415(sorted)-414(b)28(y)-414(descending)-415(d)1(e)-1(gr)1(e)-1(es)-414(of)]TJ 0 -13.549 Td [(the)-333(no)-28(des)-333(in)-334(the)-333(matrix)-333(graph.)]TJ -ET -q -1 0 0 1 891.361 754.958 cm -[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S -Q -q -1 0 0 1 292.625 754.759 cm -[]0 d 0 J 0.398 w 0 0 m 598.736 0 l S -Q -q -1 0 0 1 292.625 713.912 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 298.603 745.075 Td [('AGGR_THRESH')]TJ -ET -q -1 0 0 1 412.297 713.912 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 418.275 745.075 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ -ET -q -1 0 0 1 467.652 745.275 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 470.998 745.075 Td [(p)51(ar)51(ameter)]TJ/F45 10.9091 Tf 48.568 0 Td [(\051)]TJ -ET -q -1 0 0 1 531.27 713.912 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 537.248 745.075 Td [(An)28(y)-333(re)-1(al)]TJ 0 -13.549 Td [(n)28(um)28(b)-28(er)]TJ/F25 10.9091 Tf 38.745 0 Td [(2)]TJ/F15 10.9091 Tf 10.303 0 Td [([0)]TJ/F22 10.9091 Tf 8.485 0 Td [(;)]TJ/F15 10.9091 Tf 4.848 0 Td [(1])]TJ -ET -q -1 0 0 1 614.092 713.912 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 620.069 745.075 Td [(0.01)]TJ -ET -q -1 0 0 1 691.244 713.912 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 697.221 745.075 Td [(The)-412(thres)-1(h)1(old)]TJ/F22 10.9091 Tf 72.12 0 Td [(\022)]TJ/F15 10.9091 Tf 9.924 0 Td [(in)-412(the)-413(aggregation)-412(al-)]TJ -82.044 -13.549 Td [(gorithm,)-300(see)-292(\050)]TJ -0 0 1 rg 0 0 1 RG - [(3)]TJ -0 g 0 G - [(\051)-292(in)-292(Sec)-1(ti)1(on)]TJ -0 0 1 rg 0 0 1 RG - [-292(4.2)]TJ -0 g 0 G - [(.)-431(See)-292(also)]TJ 0 -13.549 Td [(the)-333(note)-334(at)-333(the)-333(b)-28(ottom)-333(of)-334(this)-333(table.)]TJ -ET -q -1 0 0 1 891.361 713.912 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 292.625 713.713 cm -[]0 d 0 J 0.398 w 0 0 m 598.736 0 l S -Q -q -1 0 0 1 292.625 672.866 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 298.603 704.029 Td [('AGGR_FILTER')]TJ -ET -q -1 0 0 1 412.297 672.866 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 418.275 704.029 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 531.27 672.866 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 537.248 704.029 Td [('FILTER')]TJ 0 -13.549 Td [('NOFILTER')]TJ -ET -q -1 0 0 1 614.092 672.866 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F45 10.9091 Tf 620.069 704.029 Td [('NOFILTER')]TJ -ET -q -1 0 0 1 691.244 672.866 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -BT -/F15 10.9091 Tf 697.221 704.029 Td [(Matrix)-233(used)-232(in)-233(computing)-233(the)-232(smo)-28(othed)]TJ 0 -13.549 Td [(prolongator:)-1734(\014ltered)-979(or)-978(un\014ltered)]TJ 0 -13.549 Td [(\050see)-333(\050)]TJ -0 0 1 rg 0 0 1 RG - [(5)]TJ -0 g 0 G - [(\051)-334(in)-333(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(4.2)]TJ -0 g 0 G - [(\051.)]TJ -ET -q -1 0 0 1 891.361 672.866 cm -[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S -Q -q -1 0 0 1 292.625 672.667 cm -[]0 d 0 J 0.398 w 0 0 m 598.736 0 l S -Q -q -1 0 0 1 292.625 658.918 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F44 10.9091 Tf 298.603 662.983 Td [(Note.)]TJ/F15 10.9091 Tf 35.053 0 Td [(Di\013eren)28(t)-334(th)1(res)-1(h)1(olds)-334(at)-333(di\013eren)28(t)-334(lev)28(els,)-333(suc)27(h)-333(as)-333(those)-334(used)-333(in)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(26)]TJ -0 g 0 G - [(,)-333(Sec)-1(ti)1(on)-334(5.1],)-333(can)-333(b)-28(e)-333(e)-1(asily)-333(set)-333(b)28(y)-334(in)28(v)28(oking)-333(the)-334(rou-)]TJ -ET -q -1 0 0 1 891.361 658.918 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 292.625 645.369 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 298.603 649.434 Td [(tine)]TJ/F45 10.9091 Tf 21.818 0 Td [(set)]TJ/F15 10.9091 Tf 20.818 0 Td [(with)-333(the)-334(parameter)]TJ/F45 10.9091 Tf 95.818 0 Td [(ilev)]TJ/F15 10.9091 Tf 22.909 0 Td [(.)]TJ -ET -q -1 0 0 1 891.361 645.369 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 292.625 645.17 cm -[]0 d 0 J 0.398 w 0 0 m 598.736 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 423.488 613.875 Td [(T)83(able)-333(4:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(aggregation)-333(algorithm)-333(\050con)28(tin)28(ued\051.)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -Q -0 g 0 G -0 g 0 G -0 g 0 G - -endstream -endobj -537 0 obj -<< -/Length 9225 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(29)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -q -0 1 -1 0 0 0 cm -0 g 0 G -0 g 0 G -0 g 0 G -q -1 0 0 1 0 195.67 cm -[]0 d 0 J 0.398 w 0 0 m 602.12 0 l S -Q -q -1 0 0 1 0 181.922 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -1 0 0 1 -299.826 -121.521 cm -BT -/F45 10.9091 Tf 305.803 307.508 Td [(what)]TJ -ET -q -1 0 0 1 422.332 303.443 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 428.31 307.508 Td [(d)22(a)67(t)67(a)-378(type)]TJ -ET -q -1 0 0 1 525.922 303.443 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F45 10.9091 Tf 531.9 307.508 Td [(val)]TJ -ET -q -1 0 0 1 586.067 303.443 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 592.044 307.508 Td [(def)89(a)22(ul)67(t)]TJ -ET -q -1 0 0 1 646.211 303.443 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 652.188 307.508 Td [(comments)]TJ -ET -q -1 0 0 1 901.945 303.443 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 299.826 303.244 cm -[]0 d 0 J 0.398 w 0 0 m 602.12 0 l S -Q -q -1 0 0 1 299.826 275.946 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 305.803 293.56 Td [('COARSE_MAT')]TJ -ET -q -1 0 0 1 422.332 275.946 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 428.31 293.56 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 525.922 275.946 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 531.9 293.56 Td [('DIST')]TJ 0 -13.549 Td [('REPL')]TJ -ET -q -1 0 0 1 586.067 275.946 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 592.044 293.56 Td [('REPL')]TJ -ET -q -1 0 0 1 646.211 275.946 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 652.188 293.56 Td [(Coarsest)-290(matrix)-291(la)28(y)28(out:)-423(distributed)-290(among)-290(the)-290(pro-)]TJ 0 -13.549 Td [(cesses)-334(or)-333(replicated)-333(on)-334(eac)28(h)-333(of)-333(them.)]TJ -ET -q -1 0 0 1 901.945 275.946 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 299.826 275.747 cm -[]0 d 0 J 0.398 w 0 0 m 602.12 0 l S -Q -q -1 0 0 1 299.826 85.859 cm -[]0 d 0 J 0.398 w 0 0 m 0 189.689 l S -Q -BT -/F45 10.9091 Tf 305.803 266.063 Td [('COARSE_SOLVE')]TJ -ET -q -1 0 0 1 422.332 85.859 cm -[]0 d 0 J 0.398 w 0 0 m 0 189.689 l S -Q -BT -/F45 10.9091 Tf 428.31 266.063 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 525.922 85.859 cm -[]0 d 0 J 0.398 w 0 0 m 0 189.689 l S -Q -BT -/F45 10.9091 Tf 531.9 266.063 Td [('MUMPS')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.549 Td [('SLU')]TJ 0 -13.549 Td [('SLUDIST')]TJ 0 -13.55 Td [('JACOBI')]TJ 0 -13.549 Td [('GS')]TJ 0 -13.549 Td [('BJAC')]TJ -ET -q -1 0 0 1 586.067 85.859 cm -[]0 d 0 J 0.398 w 0 0 m 0 189.689 l S -Q -BT -/F15 10.9091 Tf 592.044 266.063 Td [(See)-333(Note.)]TJ -ET -q -1 0 0 1 646.211 85.859 cm -[]0 d 0 J 0.398 w 0 0 m 0 189.689 l S -Q -BT -/F15 10.9091 Tf 652.188 266.063 Td [(Solv)28(er)-535(used)-534(at)-535(the)-535(coarsest)-534(lev)27(el:)-847(sequen)28(tial)-534(LU)]TJ 0 -13.549 Td [(from)-407(MUMPS,)-406(UMFP)83(A)28(CK,)-407(or)-407(Sup)-28(erLU)-406(\050plus)-407(tri-)]TJ 0 -13.549 Td [(angular)-546(solv)28(e\051;)-652(distribu)1(ted)-546(LU)-546(from)-545(MUMPS)-546(or)]TJ 0 -13.549 Td [(Sup)-28(erLU)]TJ -ET -q -1 0 0 1 695.449 225.615 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 698.722 225.415 Td [(Dist)-319(\050plus)-319(triangular)-319(solv)28(e\051;)-324(p)-28(oin)28(t-Jacobi,)]TJ -46.534 -13.549 Td [(h)28(ybrid)-333(Gauss-Seidel)-334(or)-333(blo)-28(c)28(k-Jacobi.)]TJ 0 -13.549 Td [(Note)-359(that)]TJ/F45 10.9091 Tf 50.551 0 Td [(UMF)]TJ/F15 10.9091 Tf 21.094 0 Td [(and)]TJ/F45 10.9091 Tf 21.487 0 Td [(SLU)]TJ/F15 10.9091 Tf 21.094 0 Td [(require)-359(t)1(he)-359(coarsest)-359(matrix)]TJ -114.226 -13.549 Td [(to)-320(b)-27(e)-320(replicated,)]TJ/F45 10.9091 Tf 81.13 0 Td [(SLUDIST)]TJ/F15 10.9091 Tf 40.09 0 Td [(,)]TJ/F45 10.9091 Tf 6.519 0 Td [(JACOBI)]TJ/F15 10.9091 Tf 34.363 0 Td [(,)]TJ/F45 10.9091 Tf 6.518 0 Td [(GS)]TJ/F15 10.9091 Tf 14.942 0 Td [(and)]TJ/F45 10.9091 Tf 21.064 0 Td [(BJAC)]TJ/F15 10.9091 Tf 26.396 0 Td [(re-)]TJ -231.022 -13.549 Td [(quire)-418(it)-419(to)-419(b)-27(e)-419(distributed,)-440(an)1(d)]TJ/F45 10.9091 Tf 152.598 0 Td [(MUMPS)]TJ/F15 10.9091 Tf 33.201 0 Td [(can)-419(b)-27(e)-419(used)]TJ -185.799 -13.549 Td [(with)-535(either)-535(a)-534(replicated)-535(or)-535(a)-535(distributed)-534(matrix.)]TJ 0 -13.55 Td [(When)-425(an)28(y)-425(of)-426(th)1(e)-426(previous)-425(solv)28(ers)-425(is)-425(sp)-28(eci\014ed,)-448(the)]TJ 0 -13.549 Td [(matrix)-333(la)28(y)28(out)-333(is)-332(set)-333(to)-333(a)-332(default)-333(v)56(alue)-333(whic)28(h)-333(allo)28(ws)]TJ 0 -13.549 Td [(the)-411(use)-411(of)-410(the)-411(solv)27(er)-410(\050see)-411(Remark)-411(3,)-430(p.)-411(24\051.)-677(Note)]TJ 0 -13.549 Td [(also)-389(th)1(at)-389(UMFP)83(A)28(CK)-388(and)-389(Sup)-27(erLU)]TJ -ET -q -1 0 0 1 824.279 103.672 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 827.552 103.473 Td [(Dist)-389(ar)1(e)-389(a)28(v)55(ail-)]TJ -175.364 -13.549 Td [(able)-333(only)-334(in)-333(double)-333(precision.)]TJ -ET -q -1 0 0 1 901.945 85.859 cm -[]0 d 0 J 0.398 w 0 0 m 0 189.689 l S -Q -q -1 0 0 1 299.826 85.66 cm -[]0 d 0 J 0.398 w 0 0 m 602.12 0 l S -Q -q -1 0 0 1 299.826 4.165 cm -[]0 d 0 J 0.398 w 0 0 m 0 81.295 l S -Q -BT -/F45 10.9091 Tf 305.803 75.976 Td [('COARSE_SUBSOLVE')]TJ -ET -q -1 0 0 1 422.332 4.165 cm -[]0 d 0 J 0.398 w 0 0 m 0 81.295 l S -Q -BT -/F45 10.9091 Tf 428.31 75.976 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 525.922 4.165 cm -[]0 d 0 J 0.398 w 0 0 m 0 81.295 l S -Q -BT -/F45 10.9091 Tf 531.9 75.976 Td [('ILU')]TJ 0 -13.549 Td [('ILUT')]TJ 0 -13.55 Td [('MILU')]TJ 0 -13.549 Td [('MUMPS')]TJ 0 -13.549 Td [('SLU')]TJ 0 -13.549 Td [('UMF')]TJ -ET -q -1 0 0 1 586.067 4.165 cm -[]0 d 0 J 0.398 w 0 0 m 0 81.295 l S -Q -BT -/F15 10.9091 Tf 592.044 75.976 Td [(See)-333(Note.)]TJ -ET -q -1 0 0 1 646.211 4.165 cm -[]0 d 0 J 0.398 w 0 0 m 0 81.295 l S -Q -BT -/F15 10.9091 Tf 652.188 75.976 Td [(Solv)28(er)-332(for)-332(the)-333(diagonal)-332(blo)-27(c)27(ks)-332(of)-332(the)-332(coarse)-333(matrix,)]TJ 0 -13.549 Td [(in)-279(case)-279(the)-279(blo)-28(c)28(k)-279(Jacobi)-279(solv)28(er)-279(is)-279(c)28(hosen)-279(as)-279(coarsest-)]TJ 0 -13.55 Td [(lev)28(el)-397(solv)28(er:)-572(ILU\050)]TJ/F22 10.9091 Tf 85.354 0 Td [(p)]TJ/F15 10.9091 Tf 5.488 0 Td [(\051,)-413(ILU\050)]TJ/F22 10.9091 Tf 34.958 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.277 0 Td [(\051,)-413(MILU\050)]TJ/F22 10.9091 Tf 44.957 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051,)-413(LU)-397(from)]TJ -190.523 -13.549 Td [(MUMPS,)-360(Sup)-28(erLU)-360(or)-361(UMFP)84(A)28(CK)-361(\050plus)-360(triangular)]TJ 0 -13.549 Td [(solv)28(e\051.)-885(Note)-481(that)-480(UMFP)84(A)27(CK)-480(and)-480(Sup)-27(e)-1(r)1(LU)]TJ -ET -q -1 0 0 1 872.786 21.978 cm -[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S -Q -BT -/F15 10.9091 Tf 876.059 21.779 Td [(Dist)]TJ -223.871 -13.549 Td [(are)-333(a)27(v)56(ailable)-333(only)-334(in)-333(double)-333(precision.)]TJ -ET -q -1 0 0 1 901.945 4.165 cm -[]0 d 0 J 0.398 w 0 0 m 0 81.295 l S -Q -q -1 0 0 1 299.826 3.966 cm -[]0 d 0 J 0.398 w 0 0 m 602.12 0 l S -Q -q -1 0 0 1 299.826 -9.783 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F44 10.9091 Tf 305.803 -5.718 Td [(Note.)]TJ/F15 10.9091 Tf 35.053 0 Td [(Defaults)-333(for)]TJ/F45 10.9091 Tf 59.94 0 Td [(COARSE)]TJ -ET -q -1 0 0 1 435.846 -5.519 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S -Q -BT -/F45 10.9091 Tf 439.283 -5.718 Td [(SOLVE)]TJ/F15 10.9091 Tf 32.272 0 Td [(and)]TJ/F45 10.9091 Tf 21.212 0 Td [(COARSE)]TJ -ET -q -1 0 0 1 527.818 -5.519 cm -[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S -Q -BT -/F45 10.9091 Tf 531.254 -5.718 Td [(SUBSOLVE)]TJ/F15 10.9091 Tf 49.454 0 Td [(are)-333(c)27(hosen)-333(in)-333(the)-334(f)1(ollo)27(wing)-333(order:)]TJ -ET -q -1 0 0 1 901.945 -9.783 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 299.826 -23.332 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 305.803 -19.267 Td [(single)-333(precision)-334(v)28(ersion)-333({)]TJ/F45 10.9091 Tf 122.364 0 Td [(MUMPS)]TJ/F15 10.9091 Tf 32.272 0 Td [(if)-333(installed,)-334(then)]TJ/F45 10.9091 Tf 81.576 0 Td [(SLU)]TJ/F15 10.9091 Tf 20.818 0 Td [(if)-333(installed,)]TJ/F45 10.9091 Tf 56.728 0 Td [(ILU)]TJ/F15 10.9091 Tf 20.818 0 Td [(otherwise;)]TJ -ET -q -1 0 0 1 901.945 -23.332 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 299.826 -36.881 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F15 10.9091 Tf 305.803 -32.816 Td [(double)-333(precision)-334(v)28(ersion)-333({)]TJ/F45 10.9091 Tf 127.152 0 Td [(UMF)]TJ/F15 10.9091 Tf 20.818 0 Td [(if)-333(installed,)-334(t)1(he)-1(n)]TJ/F45 10.9091 Tf 81.576 0 Td [(MUMPS)]TJ/F15 10.9091 Tf 32.272 0 Td [(if)-333(installed,)-334(th)1(e)-1(n)]TJ/F45 10.9091 Tf 81.576 0 Td [(SLU)]TJ/F15 10.9091 Tf 20.818 0 Td [(if)-333(installed,)]TJ/F45 10.9091 Tf 56.727 0 Td [(ILU)]TJ/F15 10.9091 Tf 20.818 0 Td [(otherwise.)]TJ -ET -q -1 0 0 1 901.945 -36.881 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 299.826 -37.08 cm -[]0 d 0 J 0.398 w 0 0 m 602.12 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 410.84 -67.769 Td [(T)83(able)-333(5:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(coarse-space)-333(correction)-333(at)-334(the)-333(coarsest)-334(lev)28(el.)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -Q -0 g 0 G -0 g 0 G -0 g 0 G - -endstream -endobj -541 0 obj -<< -/Length 4941 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(30)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -q -0 -1 1 0 0 0 cm -0 g 0 G -0 g 0 G -0 g 0 G -q -1 0 0 1 2.209 67.858 cm -[]0 d 0 J 0.398 w 0 0 m 589.156 0 l S -Q -q -1 0 0 1 2.209 54.11 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -1 0 0 1 -292.625 -715.095 cm -BT -/F45 10.9091 Tf 300.812 773.27 Td [(what)]TJ -ET -q -1 0 0 1 417.341 769.205 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 423.318 773.27 Td [(d)22(a)67(t)66(a)-377(type)]TJ -ET -q -1 0 0 1 536.314 769.205 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F45 10.9091 Tf 542.292 773.27 Td [(val)]TJ -ET -q -1 0 0 1 604.962 769.205 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 610.94 773.27 Td [(def)89(a)22(ul)67(t)]TJ -ET -q -1 0 0 1 659.437 769.205 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -BT -/F42 10.9091 Tf 665.415 773.27 Td [(comments)]TJ -ET -q -1 0 0 1 883.991 769.205 cm -[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S -Q -q -1 0 0 1 294.834 769.006 cm -[]0 d 0 J 0.398 w 0 0 m 589.156 0 l S -Q -q -1 0 0 1 294.834 741.708 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 300.812 759.322 Td [('COARSE_SWEEPS')]TJ -ET -q -1 0 0 1 417.341 741.708 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 423.318 759.322 Td [(integer)]TJ -ET -q -1 0 0 1 536.314 741.708 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 542.292 759.322 Td [(An)28(y)-333(in)27(teger)]TJ 0 -13.549 Td [(n)28(um)28(b)-28(er)]TJ/F22 10.9091 Tf 39.723 0 Td [(>)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ -ET -q -1 0 0 1 604.962 741.708 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 610.94 759.322 Td [(10)]TJ -ET -q -1 0 0 1 659.437 741.708 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 665.415 759.322 Td [(Num)28(b)-28(er)-354(of)-354(sw)28(eeps)-354(when)]TJ/F45 10.9091 Tf 119.533 0 Td [(JACOBI)]TJ/F15 10.9091 Tf 34.363 0 Td [(,)]TJ/F45 10.9091 Tf 6.891 0 Td [(GS)]TJ/F15 10.9091 Tf 15.314 0 Td [(or)]TJ/F45 10.9091 Tf 13.588 0 Td [(BJAC)]TJ/F15 10.9091 Tf -189.689 -13.549 Td [(is)-333(c)27(hosen)-333(as)-333(coarsest-lev)27(el)-333(solv)28(er.)]TJ -ET -q -1 0 0 1 883.991 741.708 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 294.834 741.509 cm -[]0 d 0 J 0.398 w 0 0 m 589.156 0 l S -Q -q -1 0 0 1 294.834 714.211 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 300.812 731.825 Td [('COARSE_FILLIN')]TJ -ET -q -1 0 0 1 417.341 714.211 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 423.318 731.825 Td [(integer)]TJ -ET -q -1 0 0 1 536.314 714.211 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 542.292 731.825 Td [(An)28(y)-333(in)27(teger)]TJ 0 -13.549 Td [(n)28(um)28(b)-28(er)]TJ/F25 10.9091 Tf 39.723 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ -ET -q -1 0 0 1 604.962 714.211 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 610.94 731.825 Td [(0)]TJ -ET -q -1 0 0 1 659.437 714.211 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 665.415 731.825 Td [(Fill-in)-333(lev)28(el)]TJ/F22 10.9091 Tf 57.424 0 Td [(p)]TJ/F15 10.9091 Tf 9.125 0 Td [(of)-333(the)-334(ILU)-333(factorizations.)]TJ -ET -q -1 0 0 1 883.991 714.211 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 294.834 714.012 cm -[]0 d 0 J 0.398 w 0 0 m 589.156 0 l S -Q -q -1 0 0 1 294.834 686.714 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 300.812 704.328 Td [('COARSE_ILUTHRS')]TJ -ET -q -1 0 0 1 417.341 686.714 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F45 10.9091 Tf 423.318 704.328 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ -ET -q -1 0 0 1 472.696 704.527 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 476.041 704.328 Td [(p)51(ar)51(ameter)]TJ/F45 10.9091 Tf 48.568 0 Td [(\051)]TJ -ET -q -1 0 0 1 536.314 686.714 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 542.292 704.328 Td [(An)28(y)-333(real)]TJ 0 -13.549 Td [(n)28(um)28(b)-28(er)]TJ/F25 10.9091 Tf 39.723 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ -ET -q -1 0 0 1 604.962 686.714 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 610.94 704.328 Td [(0)]TJ -ET -q -1 0 0 1 659.437 686.714 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -BT -/F15 10.9091 Tf 665.415 704.328 Td [(Drop)-473(tolerance)]TJ/F22 10.9091 Tf 77.501 0 Td [(t)]TJ/F15 10.9091 Tf 9.099 0 Td [(in)-473(the)-473(ILU\050)]TJ/F22 10.9091 Tf 57.744 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051)-473(factoriza-)]TJ -158.62 -13.549 Td [(tion.)]TJ -ET -q -1 0 0 1 883.991 686.714 cm -[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S -Q -q -1 0 0 1 294.834 686.515 cm -[]0 d 0 J 0.398 w 0 0 m 589.156 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 374.549 655.22 Td [(T)83(able)-333(6:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(coarse-space)-333(correction)-333(at)-334(the)-333(coarsest)-334(l)1(e)-1(v)28(el)-333(\050con)28(tin)28(ued\051.)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -Q -0 g 0 G -0 g 0 G -0 g 0 G - -endstream -endobj -435 0 obj -<< -/Type /ObjStm -/N 100 -/First 898 -/Length 12333 ->> -stream -434 0 422 54 431 111 445 217 428 423 429 569 436 713 437 865 438 1018 439 1165 -440 1309 441 1455 442 1601 443 1743 447 1888 63 1942 444 1995 454 2101 452 2235 456 2381 -448 2435 453 2492 459 2585 461 2699 449 2753 450 2810 451 2867 458 2924 465 3017 463 3159 -462 3305 467 3456 67 3510 464 3563 471 3734 468 3876 469 4021 473 4168 71 4222 470 4275 -483 4381 481 4571 474 4717 475 4862 476 5007 477 5152 478 5297 479 5444 480 5589 485 5733 -75 5787 482 5840 495 5959 486 6149 487 6292 488 6434 489 6580 490 6724 491 6869 492 7013 -493 7158 497 7303 498 7357 499 7411 500 7465 501 7519 494 7573 514 7692 512 7834 504 7980 -516 8125 513 8179 519 8298 521 8412 423 8466 518 8525 524 8631 522 8781 505 8927 506 9090 -526 9242 527 9296 523 9354 530 9512 507 9678 508 9828 509 9980 510 10128 511 10278 532 10440 -533 10494 529 10553 536 10698 534 10832 538 10978 503 11032 535 11089 540 11208 542 11322 543 11376 -% 434 0 obj -<< -/D [432 0 R /XYZ 92.6 752.957 null] ->> -% 422 0 obj -<< -/D [432 0 R /XYZ 166.644 349.945 null] ->> -% 431 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F45 255 0 R /F44 205 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 445 0 obj -<< -/Type /Page -/Contents 446 0 R -/Resources 444 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 384 0 R -/Annots [ 428 0 R 429 0 R 436 0 R 437 0 R 438 0 R 439 0 R 440 0 R 441 0 R 442 0 R 443 0 R ] ->> -% 428 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [220.251 680.424 227.698 692.114] -/A << /S /GoTo /D (figure.2) >> ->> -% 429 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [457.77 666.269 465.218 679.171] -/A << /S /GoTo /D (table.1) >> ->> -% 436 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [404.565 517.228 420.497 530.129] -/A << /S /GoTo /D (subsection.3.5) >> ->> -% 437 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [464.571 492.857 477.472 501.88] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 438 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [397.562 449.482 405.009 462.383] -/A << /S /GoTo /D (section.6) >> ->> -% 439 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [460.805 409.44 468.252 421.13] -/A << /S /GoTo /D (figure.3) >> ->> -% 440 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [355.295 328.145 362.742 339.835] -/A << /S /GoTo /D (figure.4) >> ->> -% 441 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [360.507 260.399 367.954 272.089] -/A << /S /GoTo /D (figure.3) >> ->> -% 442 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [393.552 260.399 401 272.089] -/A << /S /GoTo /D (figure.4) >> ->> -% 443 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [178.322 233.301 185.769 244.99] -/A << /S /GoTo /D (figure.5) >> ->> -% 447 0 obj -<< -/D [445 0 R /XYZ 85.4 752.957 null] ->> -% 63 0 obj -<< -/D [445 0 R /XYZ 86.4 715.095 null] ->> -% 444 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F17 148 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 454 0 obj -<< -/Type /Page -/Contents 455 0 R -/Resources 453 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 457 0 R -/Annots [ 452 0 R ] ->> -% 452 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.5) >> ->> -% 456 0 obj -<< -/D [454 0 R /XYZ 92.6 752.957 null] ->> -% 448 0 obj -<< -/D [454 0 R /XYZ 143.038 103.443 null] ->> -% 453 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 459 0 obj -<< -/Type /Page -/Contents 460 0 R -/Resources 458 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 457 0 R ->> -% 461 0 obj -<< -/D [459 0 R /XYZ 85.4 752.957 null] ->> -% 449 0 obj -<< -/D [459 0 R /XYZ 231.898 568.121 null] ->> -% 450 0 obj -<< -/D [459 0 R /XYZ 231.898 340.449 null] ->> -% 451 0 obj -<< -/D [459 0 R /XYZ 211.883 170.338 null] ->> -% 458 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 465 0 obj -<< -/Type /Page -/Contents 466 0 R -/Resources 464 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 457 0 R -/Annots [ 463 0 R 462 0 R ] ->> -% 463 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 462 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [483.843 382.76 499.775 395.662] -/A << /S /GoTo /D (subsection.6.2) >> ->> -% 467 0 obj -<< -/D [465 0 R /XYZ 92.6 752.957 null] ->> -% 67 0 obj -<< -/D [465 0 R /XYZ 93.6 715.095 null] ->> -% 464 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R /F45 255 0 R /F25 257 0 R /F18 307 0 R /F22 225 0 R /F26 363 0 R /F20 364 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 471 0 obj -<< -/Type /Page -/Contents 472 0 R -/Resources 470 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 457 0 R -/Annots [ 468 0 R 469 0 R ] ->> -% 468 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [443.652 549.113 451.099 562.746] -/A << /S /GoTo /D (table.1) >> ->> -% 469 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [395.046 508.465 402.493 522.098] -/A << /S /GoTo /D (section.8) >> ->> -% 473 0 obj -<< -/D [471 0 R /XYZ 85.4 752.957 null] ->> -% 71 0 obj -<< -/D [471 0 R /XYZ 86.4 715.095 null] ->> -% 470 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F17 148 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 483 0 obj -<< -/Type /Page -/Contents 484 0 R -/Resources 482 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 457 0 R -/Annots [ 481 0 R 474 0 R 475 0 R 476 0 R 477 0 R 478 0 R 479 0 R 480 0 R ] ->> -% 481 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 474 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [306.337 565.456 313.784 579.089] -/A << /S /GoTo /D (table.2) >> ->> -% 475 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [315.428 565.456 322.875 579.089] -/A << /S /GoTo /D (table.8) >> ->> -% 476 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [376.234 513.203 383.681 524.892] -/A << /S /GoTo /D (table.2) >> ->> -% 477 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [385.325 513.203 392.772 524.892] -/A << /S /GoTo /D (table.8) >> ->> -% 478 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [402.247 470.612 409.694 484.245] -/A << /S /GoTo /D (section.8) >> ->> -% 479 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [246.822 389.317 254.269 403.556] -/A << /S /GoTo /D (table.2) >> ->> -% 480 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [255.913 389.317 263.36 403.556] -/A << /S /GoTo /D (table.8) >> ->> -% 485 0 obj -<< -/D [483 0 R /XYZ 92.6 752.957 null] ->> -% 75 0 obj -<< -/D [483 0 R /XYZ 93.6 715.095 null] ->> -% 482 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R /F45 255 0 R /F18 307 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 495 0 obj -<< -/Type /Page -/Contents 496 0 R -/Resources 494 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 457 0 R -/Annots [ 486 0 R 487 0 R 488 0 R 489 0 R 490 0 R 491 0 R 492 0 R 493 0 R ] ->> -% 486 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [171.802 511.33 179.249 523.02] -/A << /S /GoTo /D (table.2) >> ->> -% 487 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [180.892 511.33 188.34 523.02] -/A << /S /GoTo /D (table.8) >> ->> -% 488 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [158.797 499.902 166.245 509.47] -/A << /S /GoTo /D (section.4) >> ->> -% 489 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [438.34 456.527 445.787 469.429] -/A << /S /GoTo /D (table.7) >> ->> -% 490 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [447.431 456.527 454.878 469.429] -/A << /S /GoTo /D (table.8) >> ->> -% 491 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [285.485 415.88 292.932 428.781] -/A << /S /GoTo /D (table.7) >> ->> -% 492 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [246.252 334.585 253.699 347.486] -/A << /S /GoTo /D (table.7) >> ->> -% 493 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [449.707 226.191 457.154 239.093] -/A << /S /GoTo /D (table.5) >> ->> -% 497 0 obj -<< -/D [495 0 R /XYZ 85.4 752.957 null] ->> -% 498 0 obj -<< -/D [495 0 R /XYZ 86.4 644.381 null] ->> -% 499 0 obj -<< -/D [495 0 R /XYZ 86.4 622.389 null] ->> -% 500 0 obj -<< -/D [495 0 R /XYZ 86.4 600.396 null] ->> -% 501 0 obj -<< -/D [495 0 R /XYZ 86.4 564.248 null] ->> -% 494 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F45 255 0 R /F44 205 0 R /F18 307 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 514 0 obj -<< -/Type /Page -/Contents 515 0 R -/Resources 513 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 517 0 R -/Annots [ 512 0 R 504 0 R ] ->> -% 512 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 504 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [115.028 486.353 122.475 495.8] -/A << /S /GoTo /D (section.7) >> ->> -% 516 0 obj -<< -/D [514 0 R /XYZ 92.6 752.957 null] ->> -% 513 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F18 307 0 R /F44 205 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 519 0 obj -<< -/Type /Page -/Contents 520 0 R -/Resources 518 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 517 0 R ->> -% 521 0 obj -<< -/D [519 0 R /XYZ 85.4 752.957 null] ->> -% 423 0 obj -<< -/D [519 0 R /XYZ -3855.021 590.914 null] ->> -% 518 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F45 255 0 R /F25 257 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 524 0 obj -<< -/Type /Page -/Contents 525 0 R -/Resources 523 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 517 0 R -/Annots [ 522 0 R 505 0 R 506 0 R ] ->> -% 522 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 505 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [371.416 585.797 380.439 599.695] -/A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> ->> -% 506 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [384.966 566.316 393.988 580.214] -/A << /S /GoTo /D (cite.GrHeJi:16) >> ->> -% 526 0 obj -<< -/D [524 0 R /XYZ 92.6 752.957 null] ->> -% 527 0 obj -<< -/D [524 0 R /XYZ 496.319 4405.505 null] ->> -% 523 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F45 255 0 R /F22 225 0 R /F25 257 0 R /F21 366 0 R /F23 361 0 R /F44 205 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 530 0 obj -<< -/Type /Page -/Contents 531 0 R -/Resources 529 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 517 0 R -/Annots [ 507 0 R 508 0 R 509 0 R 510 0 R 511 0 R ] ->> -% 507 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [305.333 237.711 318.234 246.154] -/A << /S /GoTo /D (equation.4.3) >> ->> -% 508 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [305.333 166.335 318.234 183.263] -/A << /S /GoTo /D (subsection.4.2) >> ->> -% 509 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [249.4 276.931 263.639 285.374] -/A << /S /GoTo /D (equation.4.5) >> ->> -% 510 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [249.4 204.203 263.639 221.132] -/A << /S /GoTo /D (subsection.4.2) >> ->> -% 511 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [239.517 367.769 248.54 381.667] -/A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> ->> -% 532 0 obj -<< -/D [530 0 R /XYZ 85.4 752.957 null] ->> -% 533 0 obj -<< -/D [530 0 R /XYZ -3875.743 540.899 null] ->> -% 529 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F45 255 0 R /F18 307 0 R /F25 257 0 R /F22 225 0 R /F44 205 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 536 0 obj -<< -/Type /Page -/Contents 537 0 R -/Resources 535 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 517 0 R -/Annots [ 534 0 R ] ->> -% 534 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 538 0 obj -<< -/D [536 0 R /XYZ 92.6 752.957 null] ->> -% 503 0 obj -<< -/D [536 0 R /XYZ 475.567 285.353 null] ->> -% 535 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F45 255 0 R /F22 225 0 R /F44 205 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 540 0 obj -<< -/Type /Page -/Contents 541 0 R -/Resources 539 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 517 0 R ->> -% 542 0 obj -<< -/D [540 0 R /XYZ 85.4 752.957 null] ->> -% 543 0 obj -<< -/D [540 0 R /XYZ -3834.398 589.839 null] ->> - -endstream -endobj -548 0 obj -<< -/Length 7639 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(31)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -q -0 1 -1 0 0 0 cm -0 g 0 G -0 g 0 G -0 g 0 G -q -1 0 0 1 3.954 157.513 cm -[]0 d 0 J 0.398 w 0 0 m 585.666 0 l S -Q -q -1 0 0 1 3.954 145.359 cm -[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S -Q -1 0 0 1 -299.826 -121.521 cm -BT -/F45 9.9626 Tf 309.757 270.467 Td [(what)]TJ -ET -q -1 0 0 1 417.782 266.88 cm -[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S -Q -BT -/F42 9.9626 Tf 423.76 270.467 Td [(d)22(a)67(t)66(a)-377(type)]TJ -ET -q -1 0 0 1 513.423 266.88 cm -[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S -Q -BT -/F45 9.9626 Tf 519.401 270.467 Td [(val)]TJ -ET -q -1 0 0 1 579.236 266.88 cm -[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S -Q -BT -/F42 9.9626 Tf 585.214 270.467 Td [(def)89(a)22(ul)67(t)]TJ -ET -q -1 0 0 1 693.239 266.88 cm -[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S -Q -BT -/F42 9.9626 Tf 699.216 270.467 Td [(comments)]TJ -ET -q -1 0 0 1 889.446 266.88 cm -[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S -Q -q -1 0 0 1 303.78 266.681 cm -[]0 d 0 J 0.398 w 0 0 m 585.666 0 l S -Q -q -1 0 0 1 303.78 194.75 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F45 9.9626 Tf 309.757 258.113 Td [('SMOOTHER_TYPE')]TJ -ET -q -1 0 0 1 417.782 194.75 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F45 9.9626 Tf 423.76 258.113 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 513.423 194.75 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F45 9.9626 Tf 519.401 258.113 Td [('JACOBI')]TJ 0 -11.955 Td [('GS')]TJ 0 -11.955 Td [('BGS')]TJ 0 -11.956 Td [('BJAC')]TJ 0 -11.955 Td [('AS')]TJ -ET -q -1 0 0 1 579.236 194.75 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F45 9.9626 Tf 585.214 258.113 Td [('FBGS')]TJ -ET -q -1 0 0 1 693.239 194.75 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F15 9.9626 Tf 699.216 258.113 Td [(T)28(yp)-28(e)-765(of)-766(smo)-27(other)-766(used)-765(in)-765(the)-765(m)27(ul)1(ti-)]TJ 0 -11.955 Td [(lev)28(el)-419(pr)1(e)-1(cond)1(itioner:)-615(p)-27(oin)27(t-Jacobi,)-439(h)28(ybrid)]TJ 0 -11.955 Td [(\050forw)28(ard\051)-519(Gauss-Seidel,)-566(h)28(ybrid)-519(bac)28(kw)27(ard)]TJ 0 -11.956 Td [(Gauss-Seidel,)-558(blo)-28(c)28(k-Jacobi,)-558(and)-513(Additiv)28(e)]TJ 0 -11.955 Td [(Sc)28(h)28(w)27(arz.)]TJ 0 -11.955 Td [(It)-333(is)-334(ignored)-333(b)28(y)-333(one)-1(-lev)28(el)-333(preconditioners.)]TJ -ET -q -1 0 0 1 889.446 194.75 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -q -1 0 0 1 303.78 194.551 cm -[]0 d 0 J 0.398 w 0 0 m 585.666 0 l S -Q -q -1 0 0 1 303.78 86.755 cm -[]0 d 0 J 0.398 w 0 0 m 0 107.597 l S -Q -BT -/F45 9.9626 Tf 309.757 185.983 Td [('SUB_SOLVE')]TJ -ET -q -1 0 0 1 417.782 86.755 cm -[]0 d 0 J 0.398 w 0 0 m 0 107.597 l S -Q -BT -/F45 9.9626 Tf 423.76 185.983 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 513.423 86.755 cm -[]0 d 0 J 0.398 w 0 0 m 0 107.597 l S -Q -BT -/F45 9.9626 Tf 519.401 185.983 Td [('JACOBI')]TJ 0 -11.955 Td [('GS')]TJ 0 -11.955 Td [('BGS')]TJ 0 -11.955 Td [('ILU')]TJ 0 -11.955 Td [('ILUT')]TJ 0 -11.956 Td [('MILU')]TJ 0 -11.955 Td [('MUMPS')]TJ 0 -11.955 Td [('SLU')]TJ 0 -11.955 Td [('UMF')]TJ -ET -q -1 0 0 1 579.236 86.755 cm -[]0 d 0 J 0.398 w 0 0 m 0 107.597 l S -Q -BT -/F45 9.9626 Tf 585.214 185.983 Td [(GS)]TJ/F15 9.9626 Tf 13.397 0 Td [(and)]TJ/F45 9.9626 Tf 18.987 0 Td [(BGS)]TJ/F15 9.9626 Tf 18.627 0 Td [(for)-295(pre-)-294(and)]TJ -51.011 -11.955 Td [(p)-28(ost-smo)-28(others)-417(of)-417(m)27(ul-)]TJ 0 -11.955 Td [(tilev)28(el)-677(pr)1(e)-1(cond)1(itioners,)]TJ 0 -11.955 Td [(resp)-28(ectiv)28(ely)]TJ/F45 9.9626 Tf 0 -11.955 Td [(ILU)]TJ/F15 9.9626 Tf 25.851 0 Td [(for)-1020(blo)-28(c)28(k-Jacobi)]TJ -25.851 -11.956 Td [(and)-676(Addi)1(tiv)27(e)-675(Sc)27(h)28(w)28(arz)]TJ 0 -11.955 Td [(one-lev)28(el)-685(precondition-)]TJ 0 -11.955 Td [(ers)]TJ -ET -q -1 0 0 1 693.239 86.755 cm -[]0 d 0 J 0.398 w 0 0 m 0 107.597 l S -Q -BT -/F15 9.9626 Tf 699.216 185.983 Td [(The)-719(lo)-28(cal)-720(solv)28(er)-719(to)-720(b)-28(e)-719(used)-719(with)-720(the)]TJ 0 -11.955 Td [(smo)-28(other)-458(or)-458(one-lev)27(el)-458(preconditioner)-458(\050see)]TJ 0 -11.955 Td [(Remark)-383(2,)-395(page)-383(24\051:)-544(p)-27(oin)27(t-Jacobi,)-395(h)28(ybrid)]TJ 0 -11.955 Td [(\050forw)28(ard\051)-519(Gauss-Seidel,)-566(h)28(ybrid)-519(bac)28(kw)27(ard)]TJ 0 -11.955 Td [(Gauss-Seidel,)-364(ILU\050)]TJ/F22 9.9626 Tf 82.539 0 Td [(p)]TJ/F15 9.9626 Tf 5.012 0 Td [(\051,)-364(ILU\050)]TJ/F22 9.9626 Tf 31.439 0 Td [(p;)-167(t)]TJ/F15 9.9626 Tf 13.037 0 Td [(\051,)-364(MILU\050)]TJ/F22 9.9626 Tf 40.571 0 Td [(p)]TJ/F15 9.9626 Tf 5.013 0 Td [(\051,)]TJ -177.611 -11.956 Td [(LU)-708(from)-709(MUM)1(PS,)-709(Sup)-28(erLU)-708(or)-708(UMF-)]TJ 0 -11.955 Td [(P)83(A)28(CK)-487(\050plus)-486(triangular)-487(solv)28(e\051.)-906(See)-487(Note)]TJ 0 -11.955 Td [(for)-333(details)-334(on)-333(h)28(ybrid)-333(Gauss-Seidel.)]TJ -ET -q -1 0 0 1 889.446 86.755 cm -[]0 d 0 J 0.398 w 0 0 m 0 107.597 l S -Q -q -1 0 0 1 303.78 86.556 cm -[]0 d 0 J 0.398 w 0 0 m 585.666 0 l S -Q -q -1 0 0 1 303.78 26.581 cm -[]0 d 0 J 0.398 w 0 0 m 0 59.776 l S -Q -BT -/F45 9.9626 Tf 309.757 77.988 Td [('SMOOTHER_SWEEPS')]TJ -ET -q -1 0 0 1 417.782 26.581 cm -[]0 d 0 J 0.398 w 0 0 m 0 59.776 l S -Q -BT -/F45 9.9626 Tf 423.76 77.988 Td [(integer)]TJ -ET -q -1 0 0 1 513.423 26.581 cm -[]0 d 0 J 0.398 w 0 0 m 0 59.776 l S -Q -BT -/F15 9.9626 Tf 519.401 77.988 Td [(An)28(y)-333(in)27(teger)]TJ 0 -11.955 Td [(n)28(um)28(b)-28(er)]TJ/F25 9.9626 Tf 36.28 0 Td [(\025)]TJ/F15 9.9626 Tf 10.516 0 Td [(0)]TJ -ET -q -1 0 0 1 579.236 26.581 cm -[]0 d 0 J 0.398 w 0 0 m 0 59.776 l S -Q -BT -/F15 9.9626 Tf 585.214 77.988 Td [(1)]TJ -ET -q -1 0 0 1 693.239 26.581 cm -[]0 d 0 J 0.398 w 0 0 m 0 59.776 l S -Q -BT -/F15 9.9626 Tf 699.216 77.988 Td [(Num)28(b)-28(er)-325(of)-325(sw)28(eeps)-325(of)-325(the)-325(smo)-28(other)-325(or)-325(one-)]TJ 0 -11.955 Td [(lev)28(el)-240(preconditioner.)-413(In)-240(the)-239(m)27(ultilev)28(el)-240(case,)]TJ 0 -11.955 Td [(no)-491(pre-smother)-491(or)-491(p)-28(ost-smo)-28(other)-491(is)-491(used)]TJ 0 -11.955 Td [(if)-375(this)-374(parameter)-375(is)-375(set)-374(to)-375(0)-375(t)1(o)-1(gether)-374(with)]TJ/F45 9.9626 Tf 0 -11.955 Td [(pos='PRE')]TJ/F15 9.9626 Tf 50.394 0 Td [(or)]TJ/F45 9.9626 Tf 12.205 0 Td [(pos='POST)]TJ/F15 9.9626 Tf 47.073 0 Td [(,)-333(resp)-28(ectiv)28(ely)83(.)]TJ -ET -q -1 0 0 1 889.446 26.581 cm -[]0 d 0 J 0.398 w 0 0 m 0 59.776 l S -Q -q -1 0 0 1 303.78 26.382 cm -[]0 d 0 J 0.398 w 0 0 m 585.666 0 l S -Q -q -1 0 0 1 303.78 2.272 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F45 9.9626 Tf 309.757 17.814 Td [('SUB_OVR')]TJ -ET -q -1 0 0 1 417.782 2.272 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F45 9.9626 Tf 423.76 17.814 Td [(integer)]TJ -ET -q -1 0 0 1 513.423 2.272 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 519.401 17.814 Td [(An)28(y)-333(in)27(teger)]TJ 0 -11.955 Td [(n)28(um)28(b)-28(er)]TJ/F25 9.9626 Tf 36.28 0 Td [(\025)]TJ/F15 9.9626 Tf 10.516 0 Td [(0)]TJ -ET -q -1 0 0 1 579.236 2.272 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 585.214 17.814 Td [(1)]TJ -ET -q -1 0 0 1 693.239 2.272 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 699.216 17.814 Td [(Num)28(b)-28(er)-647(of)-646(o)28(v)28(e)-1(r)1(lap)-647(la)28(y)28(ers,)-725(for)-647(Additiv)28(e)]TJ 0 -11.955 Td [(Sc)28(h)28(w)27(arz)-333(only)83(.)]TJ -ET -q -1 0 0 1 889.446 2.272 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -q -1 0 0 1 303.78 2.073 cm -[]0 d 0 J 0.398 w 0 0 m 585.666 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 382.719 -28.616 Td [(T)83(able)-333(7:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(smo)-27(other)-334(or)-333(the)-333(details)-334(of)-333(the)-333(one-lev)28(e)-1(l)-333(preconditioner.)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 299.826 121.521 cm -Q -0 g 0 G -0 g 0 G -0 g 0 G - -endstream -endobj -553 0 obj -<< -/Length 10231 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(32)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -q -0 -1 1 0 0 0 cm -0 g 0 G -0 g 0 G -0 g 0 G -q -1 0 0 1 8.269 164.097 cm -[]0 d 0 J 0.398 w 0 0 m 577.037 0 l S -Q -q -1 0 0 1 8.269 151.943 cm -[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S -Q -1 0 0 1 -292.625 -715.095 cm -BT -/F45 9.9626 Tf 306.872 870.625 Td [(what)]TJ -ET -q -1 0 0 1 397.889 867.038 cm -[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S -Q -BT -/F42 9.9626 Tf 403.866 870.625 Td [(d)22(a)67(t)66(a)-377(type)]TJ -ET -q -1 0 0 1 507.577 867.038 cm -[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S -Q -BT -/F45 9.9626 Tf 513.555 870.625 Td [(val)]TJ -ET -q -1 0 0 1 590.399 867.038 cm -[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S -Q -BT -/F42 9.9626 Tf 596.376 870.625 Td [(def)89(a)22(ul)67(t)]TJ -ET -q -1 0 0 1 664.716 867.038 cm -[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S -Q -BT -/F42 9.9626 Tf 670.693 870.625 Td [(comments)]TJ -ET -q -1 0 0 1 877.931 867.038 cm -[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S -Q -q -1 0 0 1 300.894 866.839 cm -[]0 d 0 J 0.398 w 0 0 m 577.037 0 l S -Q -q -1 0 0 1 300.894 794.908 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F45 9.9626 Tf 306.872 858.271 Td [('SUB_RESTR')]TJ -ET -q -1 0 0 1 397.889 794.908 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F45 9.9626 Tf 403.866 858.271 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 507.577 794.908 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F45 9.9626 Tf 513.555 858.271 Td [('HALO')]TJ 0 -11.955 Td [('NONE')]TJ -ET -q -1 0 0 1 590.399 794.908 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F45 9.9626 Tf 596.376 858.271 Td [('HALO')]TJ -ET -q -1 0 0 1 664.716 794.908 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F15 9.9626 Tf 670.693 858.271 Td [(T)28(yp)-28(e)-733(of)-733(restriction)-733(op)-28(erator,)-833(for)-733(Additiv)28(e)]TJ 0 -11.955 Td [(Sc)28(h)28(w)27(arz)-271(only:)]TJ/F45 9.9626 Tf 63.303 0 Td [(HALO)]TJ/F15 9.9626 Tf 23.622 0 Td [(for)-271(taking)-271(in)28(to)-272(accoun)28(t)-271(the)]TJ -86.925 -11.955 Td [(o)28(v)28(e)-1(r)1(lap,)]TJ/F45 9.9626 Tf 37.388 0 Td [(NONE)]TJ/F15 9.9626 Tf 24.242 0 Td [(for)-333(neglecting)-334(it.)]TJ -61.63 -11.956 Td [(Note)-367(that)]TJ/F45 9.9626 Tf 46.337 0 Td [(HALO)]TJ/F15 9.9626 Tf 24.58 0 Td [(m)28(ust)-367(b)-28(e)-367(c)27(hosen)-367(for)-367(the)-367(classi-)]TJ -70.917 -11.955 Td [(cal)-399(Addditiv)28(e)-399(Sc)28(h)28(w)27(ar)1(z)-399(smo)-28(other)-399(and)-399(its)-399(RAS)]TJ 0 -11.955 Td [(v)56(arian)27(t.)]TJ -ET -q -1 0 0 1 877.931 794.908 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -q -1 0 0 1 300.894 794.709 cm -[]0 d 0 J 0.398 w 0 0 m 577.037 0 l S -Q -q -1 0 0 1 300.894 722.779 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F45 9.9626 Tf 306.872 786.141 Td [('SUB_PROL')]TJ -ET -q -1 0 0 1 397.889 722.779 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F45 9.9626 Tf 403.866 786.141 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 507.577 722.779 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F45 9.9626 Tf 513.555 786.141 Td [('SUM')]TJ 0 -11.955 Td [('NONE')]TJ -ET -q -1 0 0 1 590.399 722.779 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F45 9.9626 Tf 596.376 786.141 Td [('NONE')]TJ -ET -q -1 0 0 1 664.716 722.779 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -BT -/F15 9.9626 Tf 670.693 786.141 Td [(T)28(yp)-28(e)-534(of)-533(prolongation)-534(op)-27(erator,)-584(for)-534(Add)1(itiv)27(e)]TJ 0 -11.955 Td [(Sc)28(h)28(w)27(arz)-253(on)1(ly:)]TJ/F45 9.9626 Tf 63.028 0 Td [(SUM)]TJ/F15 9.9626 Tf 18.209 0 Td [(for)-253(adding)-252(the)-253(con)28(tributions)]TJ -81.237 -11.955 Td [(from)-333(the)-334(o)28(v)28(erlap,)]TJ/F45 9.9626 Tf 78.097 0 Td [(NONE)]TJ/F15 9.9626 Tf 24.242 0 Td [(for)-333(neglecting)-334(them.)]TJ -102.339 -11.955 Td [(Note)-322(that)]TJ/F45 9.9626 Tf 45.431 0 Td [(SUM)]TJ/F15 9.9626 Tf 18.896 0 Td [(m)28(ust)-322(b)-28(e)-321(c)27(hosen)-321(for)-322(the)-322(classical)]TJ -64.327 -11.955 Td [(Additiv)28(e)-436(S)1(c)27(h)28(w)28(arz)-436(smo)-27(other,)-461(and)]TJ/F45 9.9626 Tf 149.166 0 Td [(NONE)]TJ/F15 9.9626 Tf 25.258 0 Td [(for)-435(its)]TJ -174.424 -11.956 Td [(RAS)-333(v)55(arian)28(t.)]TJ -ET -q -1 0 0 1 877.931 722.779 cm -[]0 d 0 J 0.398 w 0 0 m 0 71.731 l S -Q -q -1 0 0 1 300.894 722.58 cm -[]0 d 0 J 0.398 w 0 0 m 577.037 0 l S -Q -q -1 0 0 1 300.894 698.47 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F45 9.9626 Tf 306.872 714.012 Td [('SUB_FILLIN')]TJ -ET -q -1 0 0 1 397.889 698.47 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F45 9.9626 Tf 403.866 714.012 Td [(integer)]TJ -ET -q -1 0 0 1 507.577 698.47 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 513.555 714.012 Td [(An)28(y)-333(in)27(teger)]TJ 0 -11.955 Td [(n)28(um)28(b)-28(er)]TJ/F25 9.9626 Tf 36.281 0 Td [(\025)]TJ/F15 9.9626 Tf 10.516 0 Td [(0)]TJ -ET -q -1 0 0 1 590.399 698.47 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 596.376 714.012 Td [(0)]TJ -ET -q -1 0 0 1 664.716 698.47 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 670.693 714.012 Td [(Fill-in)-389(lev)28(el)]TJ/F22 9.9626 Tf 53.553 0 Td [(p)]TJ/F15 9.9626 Tf 8.888 0 Td [(of)-389(the)-389(incomplete)-389(LU)-389(factoriza-)]TJ -62.441 -11.955 Td [(tions.)]TJ -ET -q -1 0 0 1 877.931 698.47 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -q -1 0 0 1 300.894 698.271 cm -[]0 d 0 J 0.398 w 0 0 m 577.037 0 l S -Q -q -1 0 0 1 300.894 674.161 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F45 9.9626 Tf 306.872 689.703 Td [('SUB_ILUTHRS')]TJ -ET -q -1 0 0 1 397.889 674.161 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F45 9.9626 Tf 403.866 689.703 Td [(real\050)]TJ/F18 9.9626 Tf 26.152 0 Td [(kind)]TJ -ET -q -1 0 0 1 448.96 689.902 cm -[]0 d 0 J 0.398 w 0 0 m 3.055 0 l S -Q -BT -/F18 9.9626 Tf 452.015 689.703 Td [(p)51(ar)51(ameter)]TJ/F45 9.9626 Tf 44.354 0 Td [(\051)]TJ -ET -q -1 0 0 1 507.577 674.161 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 513.555 689.703 Td [(An)28(y)-722(real)-722(n)28(um-)]TJ 0 -11.955 Td [(b)-28(er)]TJ/F25 9.9626 Tf 17.462 0 Td [(\025)]TJ/F15 9.9626 Tf 10.516 0 Td [(0)]TJ -ET -q -1 0 0 1 590.399 674.161 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 596.376 689.703 Td [(0)]TJ -ET -q -1 0 0 1 664.716 674.161 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 670.693 689.703 Td [(Drop)-314(tolerance)]TJ/F22 9.9626 Tf 67.612 0 Td [(t)]TJ/F15 9.9626 Tf 6.726 0 Td [(in)-314(the)-314(ILU\050)]TJ/F22 9.9626 Tf 49.568 0 Td [(p;)-167(t)]TJ/F15 9.9626 Tf 13.038 0 Td [(\051)-314(factorization.)]TJ -ET -q -1 0 0 1 877.931 674.161 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -q -1 0 0 1 300.894 638.296 cm -[]0 d 0 J 0.398 w 0 0 m 0 35.866 l S -Q -BT -/F45 9.9626 Tf 306.872 665.793 Td [('MUMPS_LOC_GLOB')]TJ -ET -q -1 0 0 1 397.889 638.296 cm -[]0 d 0 J 0.398 w 0 0 m 0 35.866 l S -Q -BT -/F45 9.9626 Tf 403.866 665.793 Td [(character\050len=*\051)]TJ -ET -q -1 0 0 1 507.577 638.296 cm -[]0 d 0 J 0.398 w 0 0 m 0 35.866 l S -Q -BT -/F45 9.9626 Tf 513.555 665.793 Td [(LOCAL)]TJ -ET -q -1 0 0 1 540.334 665.992 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F45 9.9626 Tf 543.472 665.793 Td [(SOLVER')]TJ -29.917 -11.956 Td [(GLOBAL)]TJ -ET -q -1 0 0 1 545.564 654.037 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F45 9.9626 Tf 548.703 653.837 Td [(SOLVER')]TJ -ET -q -1 0 0 1 590.399 638.296 cm -[]0 d 0 J 0.398 w 0 0 m 0 35.866 l S -Q -BT -/F45 9.9626 Tf 596.376 665.793 Td [(GLOBAL)]TJ -ET -q -1 0 0 1 628.386 665.992 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F45 9.9626 Tf 631.524 665.793 Td [(SOLVER')]TJ -ET -q -1 0 0 1 664.716 638.296 cm -[]0 d 0 J 0.398 w 0 0 m 0 35.866 l S -Q -BT -/F15 9.9626 Tf 670.693 665.793 Td [(Whether)-543(MUMPS)-543(should)-543(b)-28(e)-543(used)-543(as)-543(a)-543(dis-)]TJ 0 -11.956 Td [(tributed)-280(solv)28(er,)-290(or)-280(as)-280(a)-280(serial)-279(solv)27(er)-279(acting)-280(only)]TJ 0 -11.955 Td [(on)-283(the)-282(part)-283(of)-282(the)-283(matrix)-282(lo)-28(cal)-283(to)-282(eac)28(h)-283(pro)-28(cess.)]TJ -ET -q -1 0 0 1 877.931 638.296 cm -[]0 d 0 J 0.398 w 0 0 m 0 35.866 l S -Q -q -1 0 0 1 300.894 614.385 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F45 9.9626 Tf 306.872 629.927 Td [('MUMPS_IPAR_ENTRY')]TJ -ET -q -1 0 0 1 397.889 614.385 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F45 9.9626 Tf 403.866 629.927 Td [(integer)]TJ -ET -q -1 0 0 1 507.577 614.385 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 513.555 629.927 Td [(An)28(y)-2333(in)28(teger)]TJ 0 -11.955 Td [(n)28(um)28(b)-28(er)]TJ -ET -q -1 0 0 1 590.399 614.385 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 596.376 629.927 Td [(0)]TJ -ET -q -1 0 0 1 664.716 614.385 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 670.693 629.927 Td [(Set)-490(an)-490(en)28(try)-490(in)-490(the)-490(MUMPS)-489(in)28(tege)-1(r)-489(con)27(trol)]TJ 0 -11.955 Td [(arra)28(y)83(,)-261(as)-243(c)28(hosen)-243(via)-243(the)]TJ/F45 9.9626 Tf 101.278 0 Td [(idx)]TJ/F15 9.9626 Tf 18.111 0 Td [(optional)-243(argumen)28(t.)]TJ -ET -q -1 0 0 1 877.931 614.385 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -q -1 0 0 1 300.894 590.475 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F45 9.9626 Tf 306.872 606.017 Td [('MUMPS_RPAR_ENTRY')]TJ -ET -q -1 0 0 1 397.889 590.475 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F45 9.9626 Tf 403.866 606.017 Td [(real)]TJ -ET -q -1 0 0 1 507.577 590.475 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 513.555 606.017 Td [(An)28(y)-722(real)-722(n)28(um-)]TJ 0 -11.955 Td [(b)-28(er)]TJ -ET -q -1 0 0 1 590.399 590.475 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 596.376 606.017 Td [(0)]TJ -ET -q -1 0 0 1 664.716 590.475 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -BT -/F15 9.9626 Tf 670.693 606.017 Td [(Set)-289(an)-289(en)28(try)-289(in)-289(the)-289(MUMPS)-289(real)-289(con)27(trol)-289(arra)28(y)83(,)]TJ 0 -11.955 Td [(as)-333(c)27(hosen)-333(via)-333(the)]TJ/F45 9.9626 Tf 77.598 0 Td [(idx)]TJ/F15 9.9626 Tf 19.012 0 Td [(optional)-333(argumen)28(t.)]TJ -ET -q -1 0 0 1 877.931 590.475 cm -[]0 d 0 J 0.398 w 0 0 m 0 23.91 l S -Q -q -1 0 0 1 300.894 590.276 cm -[]0 d 0 J 0.398 w 0 0 m 577.037 0 l S -Q -0 g 0 G -BT -/F15 10.9091 Tf 348.852 558.981 Td [(T)83(able)-333(8:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(smo)-27(other)-334(or)-333(the)-333(details)-334(of)-333(the)-333(one-lev)28(e)-1(l)-333(preconditioner)-333(\050con)28(tin)28(ued\051.)]TJ -0 g 0 G -0 g 0 G -ET -1 0 0 1 292.625 715.095 cm -Q -0 g 0 G -0 g 0 G -0 g 0 G - -endstream -endobj -561 0 obj -<< -/Length 2792 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(33)]TJ -0 g 0 G -/F17 11.9552 Tf -401.542 -35.866 Td [(6.3)-1125(Metho)-31(d)-375(hierarc)31(h)31(y)]TJ -ET -q -1 0 0 1 230.363 704.336 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F17 11.9552 Tf 234.398 704.136 Td [(build)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf -40.526 -20.594 Td [(call)-525(p%hierarchy_build\050a,desc_a,info\051)]TJ/F15 10.9091 Tf -100.272 -25.505 Td [(This)-430(metho)-28(d)-430(bu)1(ilds)-430(the)-430(hierarc)28(h)27(y)-429(of)-430(matrices)-430(and)-430(restriction/prolongation)-430(op)-28(erator)1(s)]TJ 0 -13.549 Td [(for)-436(th)1(e)-436(m)28(ultilev)28(e)-1(l)-435(preconditioner)]TJ/F45 10.9091 Tf 162.128 0 Td [(p)]TJ/F15 10.9091 Tf 5.728 0 Td [(,)-461(according)-436(to)-435(the)-436(requiremen)28(ts)-436(made)-435(b)28(y)-436(the)-435(user)]TJ -167.856 -13.549 Td [(through)-333(the)-334(metho)-27(ds)]TJ/F45 10.9091 Tf 104.031 0 Td [(init)]TJ/F15 10.9091 Tf 26.545 0 Td [(and)]TJ/F45 10.9091 Tf 21.212 0 Td [(set)]TJ/F15 10.9091 Tf 17.182 0 Td [(.)]TJ/F17 11.9552 Tf -168.97 -33.873 Td [(Argumen)31(ts)]TJ/F45 10.9091 Tf 22.914 -15.794 Td [(a)-3689(type\050psb_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(spmat_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 131.726 0 Td [(.)]TJ -189.645 -13.549 Td [(The)-501(sparse)-501(matrix)-501(structure)-501(con)28(taining)-501(th)1(e)-501(lo)-28(cal)-501(part)-501(of)-501(the)-501(matrix)]TJ 0 -13.549 Td [(to)-470(b)-28(e)-469(preconditioned.)-854(Note)-470(that)]TJ/F18 10.9091 Tf 166.818 0 Td [(x)]TJ/F15 10.9091 Tf 11.5 0 Td [(m)28(ust)-470(b)-28(e)-470(c)28(hosen)-470(according)-470(to)-469(the)]TJ -178.318 -13.55 Td [(real/complex,)-534(single/doubl)1(e)-494(precision)-494(v)28(ersion)-493(of)-494(MLD2P4)-493(under)-494(use.)]TJ 0 -13.549 Td [(See)-333(the)-334(PSBLAS)-333(User's)-333(Guide)-334(for)-333(details)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(].)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(desc_a)-1064(type\050psb_desc_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 223.515 0 Td [(.)]TJ -177.544 -13.549 Td [(The)-354(comm)28(unication)-354(descriptor)-354(of)]TJ/F45 10.9091 Tf 162.836 0 Td [(a)]TJ/F15 10.9091 Tf 5.727 0 Td [(.)-506(See)-354(the)-354(PSBLAS)-354(User's)-353(Guide)-354(for)]TJ -168.563 -13.549 Td [(details)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(].)]TJ/F45 10.9091 Tf -45.971 -13.55 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(8)]TJ -0 g 0 G - [-333(for)-334(details.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -570 0 obj -<< -/Length 4654 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(34)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F17 11.9552 Tf -203.265 -35.866 Td [(6.4)-1125(Metho)-31(d)-375(smo)-32(others)]TJ -ET -q -1 0 0 1 228.466 704.336 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F17 11.9552 Tf 232.501 704.136 Td [(build)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf -108.828 -20.594 Td [(call)-525(p%smoothers_build\050a,desc_a,p,info[,amold,vmold,imold]\051)]TJ/F15 10.9091 Tf -37.273 -25.505 Td [(This)-326(metho)-28(d)-326(builds)-327(the)-326(smo)-28(others)-326(and)-327(th)1(e)-327(coarsest-lev)28(el)-327(solv)28(ers)-326(for)-327(the)-326(m)28(ultilev)28(el)-327(pre-)]TJ 0 -13.549 Td [(conditioner)]TJ/F45 10.9091 Tf 57.841 0 Td [(p)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-430(according)-410(to)-410(the)-411(requiremen)28(ts)-410(made)-411(b)28(y)-410(the)-411(user)-410(through)-410(the)-411(metho)-28(ds)]TJ/F45 10.9091 Tf -63.568 -13.549 Td [(init)]TJ/F15 10.9091 Tf 26.819 0 Td [(and)]TJ/F45 10.9091 Tf 21.486 0 Td [(set)]TJ/F15 10.9091 Tf 17.182 0 Td [(,)-365(and)-358(based)-359(on)-358(the)-358(aggregation)-359(hierarc)28(h)28(y)-359(pro)-27(duced)-359(b)28(y)-358(a)-359(previous)-358(call)-359(to)]TJ/F45 10.9091 Tf -65.487 -13.549 Td [(hierarchy_build)]TJ/F15 10.9091 Tf 89.544 0 Td [(\050see)-333(Sec)-1(tion)]TJ -0 0 1 rg 0 0 1 RG - [-333(6.3)]TJ -0 g 0 G - [(\051.)]TJ/F17 11.9552 Tf -89.544 -33.873 Td [(Argumen)31(ts)]TJ/F45 10.9091 Tf 22.914 -15.794 Td [(a)-3689(type\050psb_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(spmat_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 131.726 0 Td [(.)]TJ -189.645 -13.549 Td [(The)-501(sparse)-501(matrix)-501(structure)-501(con)28(taining)-500(the)-501(lo)-28(cal)-501(part)-501(of)-501(the)-501(matrix)]TJ 0 -13.55 Td [(to)-470(b)-28(e)-469(preconditioned.)-854(Note)-470(that)]TJ/F18 10.9091 Tf 166.818 0 Td [(x)]TJ/F15 10.9091 Tf 11.499 0 Td [(m)28(ust)-470(b)-28(e)-470(c)28(hosen)-470(according)-470(to)-469(the)]TJ -178.317 -13.549 Td [(real/complex,)-534(single/doub)1(le)-494(precision)-494(v)28(ersion)-493(of)-494(MLD2P4)-493(under)-494(use.)]TJ 0 -13.549 Td [(See)-333(the)-334(PSBLAS)-333(User's)-333(Guide)-334(for)-333(details)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(].)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(desc_a)-1064(type\050psb_desc_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 223.514 0 Td [(.)]TJ -177.543 -13.549 Td [(The)-354(comm)28(unication)-354(descriptor)-354(of)]TJ/F45 10.9091 Tf 162.835 0 Td [(a)]TJ/F15 10.9091 Tf 5.727 0 Td [(.)-506(See)-354(the)-354(PSBLAS)-354(User's)-354(Gu)1(ide)-354(for)]TJ -168.562 -13.55 Td [(details)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(].)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(8)]TJ -0 g 0 G - [-333(for)-334(d)1(e)-1(tail)1(s)-1(.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(amold)-1589(class\050psb_)]TJ/F18 10.9091 Tf 103.243 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(_base_sparse_mat\051,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 223.361 0 Td [(.)]TJ -287.007 -13.549 Td [(The)-396(desired)-395(dynamic)-396(t)28(yp)-28(e)-396(for)-395(in)28(ternal)-396(matrix)-396(comp)-27(onen)27(ts;)-426(this)-396(allo)28(ws)]TJ 0 -13.549 Td [(e.g.)-594(running)-383(on)-383(GPUs;)-408(it)-383(needs)-383(not)-383(b)-28(e)-383(the)-383(same)-383(on)-383(all)-384(pr)1(o)-28(cesses)-1(.)-593(See)]TJ 0 -13.55 Td [(the)-333(PSBLAS)-334(User's)-333(Guide)-333(for)-334(d)1(e)-1(tai)1(ls)-334([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(].)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(vmold)-1589(class\050psb_)]TJ/F18 10.9091 Tf 103.243 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(_base_vect_type\051,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 217.634 0 Td [(.)]TJ -281.28 -13.549 Td [(The)-422(desired)-422(dynamic)-422(t)28(yp)-28(e)-422(for)-422(in)28(ternal)-422(v)28(ector)-422(comp)-28(onen)28(ts;)-466(this)-422(allo)27(ws)]TJ 0 -13.549 Td [(e.g.)-444(running)-334(on)-333(GPUs.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(imold)-1589(class\050psb_i_base_vect_type\051,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 326.604 0 Td [(.)]TJ -280.633 -13.55 Td [(The)-387(desired)-387(dynamic)-388(t)28(yp)-27(e)-388(for)-387(in)28(ternal)-387(in)28(teger)-387(v)27(ector)-387(comp)-28(onen)28(ts;)-414(this)]TJ 0 -13.549 Td [(allo)28(ws)-334(e.g.)-444(running)-333(on)-333(GPUs.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -581 0 obj -<< -/Length 5532 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(35)]TJ -0 g 0 G -/F17 11.9552 Tf -401.542 -35.866 Td [(6.5)-1125(Metho)-31(d)-375(build)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 71.636 -20.594 Td [(call)-525(p%build\050a,desc_a,info[,amold,vmold,imold]\051)]TJ/F15 10.9091 Tf -71.636 -25.505 Td [(This)-239(metho)-28(d)-239(b)1(uilds)-239(the)-239(preconditioner)]TJ/F45 10.9091 Tf 182.605 0 Td [(p)]TJ/F15 10.9091 Tf 8.333 0 Td [(according)-239(to)-239(the)-239(r)1(e)-1(qu)1(ireme)-1(n)28(ts)-239(made)-239(b)28(y)-239(th)1(e)-239(user)]TJ -190.938 -13.549 Td [(through)-391(the)-390(metho)-28(ds)]TJ/F45 10.9091 Tf 105.911 0 Td [(init)]TJ/F15 10.9091 Tf 27.172 0 Td [(and)]TJ/F45 10.9091 Tf 21.839 0 Td [(set)]TJ/F15 10.9091 Tf 21.445 0 Td [(\050see)-391(Sections)]TJ -0 0 1 rg 0 0 1 RG - [-391(6.3)]TJ -0 g 0 G - [-390(and)]TJ -0 0 1 rg 0 0 1 RG - [-391(6.4)]TJ -0 g 0 G - [-391(for)-391(m)28(ultilev)28(el)-391(precondi-)]TJ -176.367 -13.549 Td [(tioners\051.)-420(It)-261(is)-261(mostly)-261(pro)28(vided)-260(for)-261(bac)28(kw)27(ard)-260(compatibilit)28(y;)-285(indeed,)-275(it)-261(is)-261(in)28(ternally)-261(imple-)]TJ 0 -13.549 Td [(men)28(ted)-222(b)27(y)-222(in)28(v)28(oking)-222(the)-223(t)28(w)28(o)-222(previous)-222(metho)-28(ds)]TJ/F45 10.9091 Tf 215.607 0 Td [(hierarchy_build)]TJ/F15 10.9091 Tf 88.332 0 Td [(and)]TJ/F45 10.9091 Tf 20 0 Td [(smoothers_build)]TJ/F15 10.9091 Tf 85.908 0 Td [(,)]TJ -409.847 -13.549 Td [(whose)-345(nomenclature)-345(w)28(ould)-345(ho)28(w)27(ev)28(er)-345(b)-27(e)-345(s)-1(omewhat)-345(u)1(nnatural)-345(when)-345(dealing)-345(with)-345(simple)]TJ 0 -13.55 Td [(one-lev)28(el)-334(precondition)1(e)-1(r)1(s)-1(.)]TJ/F17 11.9552 Tf 0 -33.873 Td [(Argumen)31(ts)]TJ/F45 10.9091 Tf 22.914 -15.794 Td [(a)-3689(type\050psb_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(spmat_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 131.726 0 Td [(.)]TJ -189.645 -13.549 Td [(The)-501(sparse)-501(matrix)-501(structure)-501(con)28(taining)-501(th)1(e)-501(lo)-28(cal)-501(part)-501(of)-501(the)-501(matrix)]TJ 0 -13.549 Td [(to)-470(b)-28(e)-469(preconditioned.)-854(Note)-470(that)]TJ/F18 10.9091 Tf 166.818 0 Td [(x)]TJ/F15 10.9091 Tf 11.5 0 Td [(m)28(ust)-470(b)-28(e)-470(c)28(hosen)-470(according)-470(to)-469(the)]TJ -178.318 -13.549 Td [(real/complex,)-534(single/doubl)1(e)-494(precision)-494(v)28(ersion)-493(of)-494(MLD2P4)-493(under)-494(use.)]TJ 0 -13.549 Td [(See)-333(the)-334(PSBLAS)-333(User's)-333(Guide)-334(for)-333(details)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(].)]TJ/F45 10.9091 Tf -45.971 -13.55 Td [(desc_a)-1064(type\050psb_desc_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 223.515 0 Td [(.)]TJ -177.544 -13.549 Td [(The)-354(comm)28(unication)-354(descriptor)-354(of)]TJ/F45 10.9091 Tf 162.836 0 Td [(a)]TJ/F15 10.9091 Tf 5.727 0 Td [(.)-506(See)-354(the)-354(PSBLAS)-354(User's)-353(Guide)-354(for)]TJ -168.563 -13.549 Td [(details)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(].)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(8)]TJ -0 g 0 G - [-333(for)-334(details.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(amold)-1589(class\050psb_)]TJ/F18 10.9091 Tf 103.243 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(_base_sparse_mat\051,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 223.362 0 Td [(.)]TJ -287.008 -13.55 Td [(The)-396(desired)-395(dynamic)-396(t)28(yp)-28(e)-396(for)-395(in)28(ternal)-396(matrix)-396(comp)-27(onen)27(ts;)-426(this)-396(allo)28(ws)]TJ 0 -13.549 Td [(e.g.)-594(running)-383(on)-383(GPUs;)-408(it)-383(needs)-383(not)-383(b)-28(e)-383(the)-383(same)-383(on)-384(al)1(l)-384(pro)-27(cesse)-1(s.)-593(See)]TJ 0 -13.549 Td [(the)-333(PSBLAS)-334(User's)-333(Guide)-333(for)-334(d)1(e)-1(tai)1(ls)-334([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(].)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(vmold)-1589(class\050psb_)]TJ/F18 10.9091 Tf 103.243 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(_base_vect_type\051,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 217.634 0 Td [(.)]TJ -281.28 -13.549 Td [(The)-422(desired)-422(dynamic)-422(t)28(yp)-28(e)-422(for)-422(in)28(ternal)-422(v)28(ector)-422(comp)-28(onen)28(ts;)-466(this)-422(allo)27(ws)]TJ 0 -13.55 Td [(e.g.)-444(running)-334(on)-333(GPUs.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(imold)-1589(class\050psb_i_base_vect_type\051,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 326.604 0 Td [(.)]TJ -280.633 -13.549 Td [(The)-387(desired)-387(dynamic)-388(t)28(yp)-27(e)-388(for)-387(in)28(ternal)-387(in)28(teger)-387(v)27(ector)-387(comp)-28(onen)28(ts;)-414(this)]TJ 0 -13.549 Td [(allo)28(ws)-334(e.g.)-444(running)-333(on)-333(GPUs.)]TJ -51.948 -32.961 Td [(F)83(or)-364(compatibilit)27(y)-364(with)-365(the)-365(previous)-365(v)28(ersions)-365(of)-365(MLD2P4,)-372(this)-365(metho)-28(d)-365(can)-365(b)-27(e)-365(also)]TJ -16.937 -13.549 Td [(in)28(v)28(ok)27(ed)-333(as)-333(follo)28(ws:)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 54.455 -25.504 Td [(call)-525(mld_precbld\050p,what,val,info[,amold,vmold,imold]\051)]TJ/F15 10.9091 Tf -54.455 -25.505 Td [(The)-333(metho)-28(d)-333(can)-334(b)-28(e)-333(used)-333(to)-334(bu)1(ild)-334(m)28(ultilev)28(el)-333(preconditioners)-334(to)-27(o.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -586 0 obj -<< -/Length 8543 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(36)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F17 11.9552 Tf -203.265 -35.866 Td [(6.6)-1125(Metho)-31(d)-375(apply)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 83.09 -20.594 Td [(call)-525(p%apply\050x,y,desc_a,info)-525([,trans,work]\051)]TJ/F15 10.9091 Tf -83.09 -25.505 Td [(This)-407(metho)-28(d)-408(computes)]TJ/F22 10.9091 Tf 115.576 0 Td [(y)]TJ/F15 10.9091 Tf 10.118 0 Td [(=)]TJ/F22 10.9091 Tf 12.862 0 Td [(op)]TJ/F15 10.9091 Tf 10.776 0 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(B)]TJ/F26 7.9701 Tf 8.822 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F15 10.9091 Tf 4.733 -3.959 Td [(\051)]TJ/F22 10.9091 Tf 6.06 0 Td [(x)]TJ/F15 10.9091 Tf 6.235 0 Td [(,)-426(where)]TJ/F22 10.9091 Tf 40.031 0 Td [(B)]TJ/F15 10.9091 Tf 13.266 0 Td [(is)-407(a)-408(previously)-407(built)-408(p)1(rec)-1(on)1(ditioner,)]TJ -239.308 -13.549 Td [(stored)-296(in)28(to)]TJ/F45 10.9091 Tf 54.129 0 Td [(p)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-304(and)]TJ/F22 10.9091 Tf 27.15 0 Td [(op)]TJ/F15 10.9091 Tf 14.008 0 Td [(denotes)-296(the)-296(preconditioner)-297(it)1(s)-1(elf)-296(or)-296(its)-296(transp)-28(ose,)-304(accordin)1(g)-297(to)-296(the)]TJ -101.014 -13.549 Td [(v)56(alue)-325(of)]TJ/F45 10.9091 Tf 40.407 0 Td [(trans)]TJ/F15 10.9091 Tf 28.636 0 Td [(.)-441(Note)-325(that,)-326(when)-324(MLD2P4)-324(is)-324(used)-324(with)-325(a)-324(Krylo)28(v)-324(solv)28(er)-325(f)1(rom)-325(PSBLAS,)]TJ/F45 10.9091 Tf -69.043 -13.549 Td [(p%apply)]TJ/F15 10.9091 Tf 43.976 0 Td [(is)-356(called)-357(with)1(in)-357(the)-356(PSBLAS)-356(metho)-28(d)]TJ/F45 10.9091 Tf 181.711 0 Td [(psb_krylov)]TJ/F15 10.9091 Tf 61.159 0 Td [(and)-356(hence)-356(it)-357(is)-356(completely)]TJ -286.846 -13.549 Td [(transparen)28(t)-333(to)-334(the)-333(user.)]TJ/F17 11.9552 Tf 0 -33.873 Td [(Argumen)31(ts)]TJ/F45 10.9091 Tf 22.914 -15.794 Td [(x)]TJ/F18 10.9091 Tf 45.971 0 Td [(typ)51(e)]TJ/F45 10.9091 Tf 19.777 0 Td [(\050)]TJ/F18 10.9091 Tf 5.727 0 Td [(kind)]TJ -ET -q -1 0 0 1 201.531 554.373 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 204.876 554.174 Td [(p)51(ar)51(ameter)]TJ/F45 10.9091 Tf 48.568 0 Td [(\051,)-525(dimension\050:\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 154.635 0 Td [(.)]TJ -252.794 -13.55 Td [(The)-300(lo)-28(cal)-300(part)-301(of)-300(the)-300(v)28(ector)]TJ/F22 10.9091 Tf 133.655 0 Td [(x)]TJ/F15 10.9091 Tf 6.235 0 Td [(.)-433(Note)-301(that)]TJ/F18 10.9091 Tf 57.038 0 Td [(typ)51(e)]TJ/F15 10.9091 Tf 23.053 0 Td [(and)]TJ/F18 10.9091 Tf 20.851 0 Td [(kind)]TJ -ET -q -1 0 0 1 416.859 540.824 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 420.204 540.624 Td [(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 51.844 0 Td [(m)28(ust)]TJ -316.763 -13.549 Td [(b)-28(e)-263(c)28(hosen)-264(accordi)1(ng)-264(to)-263(the)-263(real/complex,)-277(single/double)-264(pr)1(e)-1(cision)-263(v)28(ersion)]TJ 0 -13.549 Td [(of)-333(MLD2P4)-334(u)1(nder)-334(use.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(y)]TJ/F18 10.9091 Tf 45.971 0 Td [(typ)51(e)]TJ/F45 10.9091 Tf 19.777 0 Td [(\050)]TJ/F18 10.9091 Tf 5.727 0 Td [(kind)]TJ -ET -q -1 0 0 1 201.531 500.176 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 204.876 499.977 Td [(p)51(ar)51(ameter)]TJ/F45 10.9091 Tf 48.568 0 Td [(\051,)-525(dimension\050:\051,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.362 0 Td [(.)]TJ -258.521 -13.549 Td [(The)-304(lo)-28(cal)-304(part)-305(of)-304(the)-304(v)28(ector)]TJ/F22 10.9091 Tf 133.917 0 Td [(y)]TJ/F15 10.9091 Tf 5.74 0 Td [(.)-435(Note)-304(that)]TJ/F18 10.9091 Tf 57.14 0 Td [(typ)51(e)]TJ/F15 10.9091 Tf 23.096 0 Td [(and)]TJ/F18 10.9091 Tf 20.896 0 Td [(kind)]TJ -ET -q -1 0 0 1 416.815 486.627 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 420.161 486.428 Td [(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 51.887 0 Td [(m)28(ust)]TJ -316.763 -13.55 Td [(b)-28(e)-263(c)28(hosen)-264(accordi)1(ng)-264(to)-263(the)-263(real/complex,)-277(single/double)-264(pr)1(e)-1(cision)-263(v)28(ersion)]TJ 0 -13.549 Td [(of)-333(MLD2P4)-334(u)1(nder)-334(use.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(desc_a)-1064(type\050psb_desc_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 223.514 0 Td [(.)]TJ -177.543 -13.549 Td [(The)-319(c)-1(omm)28(unication)-319(descriptor)-320(asso)-28(ciated)-319(to)-320(th)1(e)-320(matrix)-319(to)-320(b)-28(e)-319(precondi-)]TJ 0 -13.549 Td [(tioned.)]TJ/F45 10.9091 Tf -45.971 -13.55 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(8)]TJ -0 g 0 G - [-333(for)-334(d)1(e)-1(tail)1(s)-1(.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(trans)-1589(character\050len=1\051,)-525(optional,)-525(intent\050in\051.)]TJ/F15 10.9091 Tf 45.971 -13.549 Td [(If)]TJ/F45 10.9091 Tf 12.079 0 Td [(trans)]TJ/F15 10.9091 Tf 33.443 0 Td [(=)]TJ/F45 10.9091 Tf 13.292 0 Td [('N','n')]TJ/F15 10.9091 Tf 44.897 0 Td [(then)]TJ/F22 10.9091 Tf 26.019 0 Td [(op)]TJ/F15 10.9091 Tf 10.777 0 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(B)]TJ/F26 7.9701 Tf 8.822 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(\051)-457(=)]TJ/F22 10.9091 Tf 22.689 0 Td [(B)]TJ/F26 7.9701 Tf 8.822 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(;)-494(if)]TJ/F45 10.9091 Tf 19.593 0 Td [(trans)]TJ/F15 10.9091 Tf 33.443 0 Td [(=)]TJ/F45 10.9091 Tf 13.292 0 Td [('T','t')]TJ/F15 10.9091 Tf 44.897 0 Td [(then)]TJ/F22 10.9091 Tf -318.945 -13.549 Td [(op)]TJ/F15 10.9091 Tf 10.776 0 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(B)]TJ/F26 7.9701 Tf 8.822 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(\051)-278(=)]TJ/F22 10.9091 Tf 18.788 0 Td [(B)]TJ/F26 7.9701 Tf 8.822 3.959 Td [(\000)]TJ/F23 7.9701 Tf 6.587 0 Td [(T)]TJ/F15 10.9091 Tf 9.089 -3.959 Td [(\050transp)-28(ose)-228(of)]TJ/F22 10.9091 Tf 63.302 0 Td [(B)]TJ/F26 7.9701 Tf 8.822 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(\051;)-263(if)]TJ/F45 10.9091 Tf 18.99 0 Td [(trans)]TJ/F15 10.9091 Tf 31.12 0 Td [(=)]TJ/F45 10.9091 Tf 10.97 0 Td [('C','c')]TJ/F15 10.9091 Tf 42.575 0 Td [(then)]TJ/F22 10.9091 Tf 23.697 0 Td [(op)]TJ/F15 10.9091 Tf 10.776 0 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(B)]TJ/F26 7.9701 Tf 8.822 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F15 10.9091 Tf 4.733 -3.959 Td [(\051)-278(=)]TJ/F22 10.9091 Tf -324.4 -13.549 Td [(B)]TJ/F26 7.9701 Tf 8.822 3.958 Td [(\000)]TJ/F23 7.9701 Tf 6.586 0 Td [(C)]TJ/F15 10.9091 Tf 10.733 -3.958 Td [(\050conjugate)-333(transp)-28(ose)-333(of)]TJ/F22 10.9091 Tf 115 0 Td [(B)]TJ/F26 7.9701 Tf 8.822 3.958 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.958 Td [(\051.)]TJ/F45 10.9091 Tf -207.253 -13.55 Td [(work)]TJ/F18 10.9091 Tf 45.971 0 Td [(typ)51(e)]TJ/F45 10.9091 Tf 19.777 0 Td [(\050)]TJ/F18 10.9091 Tf 5.727 0 Td [(kind)]TJ -ET -q -1 0 0 1 201.531 324.037 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 204.876 323.837 Td [(p)51(ar)51(ameter)]TJ/F45 10.9091 Tf 48.568 0 Td [(\051,)-525(dimension\050:\051,)-525(optional,)-525(target)]TJ/F15 10.9091 Tf 188.998 0 Td [(.)]TJ -287.157 -13.549 Td [(W)83(orkspace.)-1532(Its)-696(size)-697(shou)1(ld)-696(b)-28(e)-696(at)-696(least)]TJ/F45 10.9091 Tf 219.886 0 Td [(4)-525(*)-525(psb_cd_get_local_)]TJ -219.886 -13.549 Td [(cols\050desc_a\051)]TJ/F15 10.9091 Tf 73.906 0 Td [(\050see)-475(the)-475(PSBLAS)-474(User's)-475(Guide\051.)-869(Note)-475(th)1(at)]TJ/F18 10.9091 Tf 223.719 0 Td [(typ)51(e)]TJ/F15 10.9091 Tf 24.956 0 Td [(and)]TJ/F18 10.9091 Tf -322.581 -13.549 Td [(kind)]TJ -ET -q -1 0 0 1 176.026 283.389 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 179.372 283.19 Td [(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 54.627 0 Td [(m)28(ust)-556(b)-27(e)-556(c)28(hosen)-555(ac)-1(cordi)1(ng)-556(to)-555(the)-556(real/complex,)-611(sin-)]TJ -78.714 -13.549 Td [(gle/double)-333(precision)-334(v)28(ersion)-333(of)-333(MLD2P4)-334(und)1(e)-1(r)-333(use.)]TJ -51.949 -32.961 Td [(F)83(or)-364(c)-1(ompati)1(bilit)27(y)-364(with)-365(the)-365(previous)-365(v)28(ersions)-365(of)-365(MLD2P4,)-372(this)-365(metho)-28(d)-365(can)-365(b)-27(e)-365(also)]TJ -16.936 -13.549 Td [(in)28(v)28(ok)27(ed)-333(as)-333(follo)28(ws:)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 108.863 -25.505 Td [(call)-525(mld_precaply\050p,what,val,info\051)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -592 0 obj -<< -/Length 1284 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(37)]TJ -0 g 0 G -/F17 11.9552 Tf -401.542 -35.866 Td [(6.7)-1125(Metho)-31(d)-375(free)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 151.817 -20.594 Td [(call)-525(p%free\050p,info\051)]TJ/F15 10.9091 Tf -151.817 -25.505 Td [(This)-333(metho)-28(d)-333(deallo)-28(cates)-334(the)-333(preconditioner)-333(data)-333(structure)]TJ/F45 10.9091 Tf 282.728 0 Td [(p)]TJ/F15 10.9091 Tf 5.727 0 Td [(.)]TJ/F17 11.9552 Tf -288.455 -33.873 Td [(Argumen)31(ts)]TJ/F45 10.9091 Tf 22.914 -15.794 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-308(co)-28(de.)-435(If)-308(no)-308(error,)-313(0)-308(is)-308(returned.)-436(See)-308(S)1(e)-1(ction)]TJ -0 0 1 rg 0 0 1 RG - [-307(8)]TJ -0 g 0 G - [-308(for)-308(details.)]TJ -51.948 -32.96 Td [(F)83(or)-364(com)-1(p)1(atibilit)27(y)-364(with)-365(the)-365(previous)-365(v)28(ersions)-365(of)-365(MLD2P4,)-372(this)-365(metho)-28(d)-365(can)-365(b)-27(e)-365(also)]TJ -16.937 -13.55 Td [(in)28(v)28(ok)27(ed)-333(as)-333(follo)28(ws:)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 134.636 -25.504 Td [(call)-525(mld_precfree\050p,info\051)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -600 0 obj -<< -/Length 3993 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(38)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F17 11.9552 Tf -203.265 -35.866 Td [(6.8)-1125(Metho)-31(d)-375(descr)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 131.772 -21.173 Td [(call)-525(p%descr\050info,)-525([iout]\051)]TJ/F15 10.9091 Tf -131.772 -26.697 Td [(This)-349(metho)-28(d)-348(prin)28(ts)-349(a)-349(description)-349(of)-348(the)-349(preconditioner)]TJ/F45 10.9091 Tf 265.591 0 Td [(p)]TJ/F15 10.9091 Tf 9.532 0 Td [(to)-349(the)-349(standar)1(d)-349(output)-349(or)-349(to)]TJ -275.123 -13.549 Td [(a)-355(\014le.)-508(It)-354(m)27(ust)-354(b)-28(e)-355(called)-354(after)]TJ/F45 10.9091 Tf 143.39 0 Td [(hierachy_build)]TJ/F15 10.9091 Tf 84.049 0 Td [(and)]TJ/F45 10.9091 Tf 21.444 0 Td [(smoothers_build)]TJ/F15 10.9091 Tf 85.908 0 Td [(,)-360(or)]TJ/F45 10.9091 Tf 20.552 0 Td [(build)]TJ/F15 10.9091 Tf 28.636 0 Td [(,)-360(ha)28(v)28(e)]TJ -383.979 -13.549 Td [(b)-28(een)-333(called.)]TJ/F17 11.9552 Tf 0 -34.171 Td [(Argumen)31(ts)]TJ/F45 10.9091 Tf 22.914 -16.391 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(8)]TJ -0 g 0 G - [-333(for)-334(d)1(e)-1(tail)1(s)-1(.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(iout)-2114(integer,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 212.06 0 Td [(.)]TJ -166.089 -13.549 Td [(The)-376(id)-376(of)-375(the)-376(\014le)-376(where)-376(the)-376(p)1(rec)-1(on)1(ditioner)-376(description)-376(will)-376(b)-27(e)-376(prin)28(ted;)]TJ 0 -13.549 Td [(the)-333(default)-334(i)1(s)-334(the)-333(standard)-333(output.)]TJ -51.949 -33.259 Td [(F)83(or)-364(c)-1(ompati)1(bilit)27(y)-364(with)-365(the)-365(previous)-365(v)28(ersions)-365(of)-365(MLD2P4,)-372(this)-365(metho)-28(d)-365(can)-365(b)-27(e)-365(also)]TJ -16.936 -13.549 Td [(in)28(v)28(ok)27(ed)-333(as)-333(follo)28(ws:)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 108.863 -27.293 Td [(call)-525(mld_precdescr\050p,info)-525([,iout]\051)]TJ/F17 11.9552 Tf -108.863 -30.916 Td [(6.9)-1125(Auxiliary)-375(Metho)-31(ds)]TJ/F15 10.9091 Tf 0 -21.174 Td [(V)83(arious)-444(functionali)1(tie)-1(s)-444(are)-444(implemen)28(ted)-444(as)-444(additional)-444(metho)-28(ds)-444(of)-444(the)-444(preconditioner)]TJ 0 -13.549 Td [(ob)-55(jec)-1(t.)]TJ/F44 10.9091 Tf 0 -30.517 Td [(6.9.1)-1150(Metho)-32(d:)-511(dump)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 0 -34.723 Td [(call)-525(p%dump\050info[,istart,iend,prefix,head,ac,rp,smoother,solver,global_num]\051)]TJ/F15 10.9091 Tf 0 -26.697 Td [(Dump)-333(on)-334(\014l)1(e)-1(.)]TJ/F17 11.9552 Tf 0 -34.171 Td [(Argumen)31(ts)]TJ/F45 10.9091 Tf 22.914 -16.39 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(8)]TJ -0 g 0 G - [-333(for)-334(d)1(e)-1(tail)1(s)-1(.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(amold)-1589(class\050psb_)]TJ/F18 10.9091 Tf 103.243 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(_base_sparse_mat\051,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 223.361 0 Td [(.)]TJ -287.007 -13.55 Td [(The)-396(desired)-395(dynamic)-396(t)28(yp)-28(e)-396(for)-395(in)28(ternal)-396(matrix)-396(comp)-27(onen)27(ts;)-426(this)-396(allo)28(ws)]TJ 0 -13.549 Td [(e.g.)-594(running)-383(on)-383(GPUs;)-408(it)-383(needs)-383(not)-383(b)-28(e)-383(the)-383(same)-383(on)-383(all)-384(pr)1(o)-28(cesses)-1(.)-593(See)]TJ 0 -13.549 Td [(the)-333(PSBLAS)-334(User's)-333(Guide)-333(for)-334(d)1(e)-1(t)1(ails)-334([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(].)]TJ/F44 10.9091 Tf -68.885 -29.605 Td [(6.9.2)-1150(Metho)-32(d:)-511(clone)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 140.362 -21.174 Td [(call)-525(p%clone\050pout,info\051)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -607 0 obj -<< -/Length 5175 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(39)]TJ -0 g 0 G - -401.542 -35.866 Td [(Create)-333(a)-334(\050deep\051)-333(cop)28(y)-334(of)-333(the)-333(preconditioner)-333(ob)-56(ject.)]TJ/F17 11.9552 Tf 0 -34.596 Td [(Argumen)31(ts)]TJ/F45 10.9091 Tf 22.914 -17.24 Td [(pout)-2114(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 131.726 0 Td [(.)]TJ -189.645 -13.549 Td [(The)-437(cop)27(y)-437(of)-437(the)-438(preconditi)1(oner)-438(data)-437(structure.)-757(Note)-437(that)]TJ/F18 10.9091 Tf 289.635 0 Td [(x)]TJ/F15 10.9091 Tf 11.145 0 Td [(m)28(ust)-438(b)-27(e)]TJ -300.78 -13.549 Td [(c)28(hosen)-292(according)-292(to)-291(the)-292(real/complex,)-300(single/double)-292(precision)-292(v)28(ersion)-291(of)]TJ 0 -13.55 Td [(MLD2P4)-333(under)-333(use)-1(.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(8)]TJ -0 g 0 G - [-333(for)-334(details.)]TJ/F44 10.9091 Tf -68.885 -32.034 Td [(6.9.3)-1150(Metho)-32(d:)-511(sizeof)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 160.408 -22 Td [(sz)-525(=)-1050(p%sizeof\050\051)]TJ/F15 10.9091 Tf -160.408 -28.396 Td [(Return)-333(memory)-334(fo)-27(otprin)28(t)-334(in)-333(b)28(ytes.)]TJ/F44 10.9091 Tf 0 -32.947 Td [(6.9.4)-1150(Metho)-32(d:)-511(allo)-32(cate)]TJ -ET -q -1 0 0 1 226.837 469.376 cm -[]0 d 0 J 0.398 w 0 0 m 3.764 0 l S -Q -BT -/F44 10.9091 Tf 230.6 469.177 Td [(wrk)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf -28.137 -21.999 Td [(call)-525(p%allocate_wrk\050info[,)-525(vmold]\051)]TJ/F15 10.9091 Tf -108.863 -28.397 Td [(Allo)-28(cate)-375(in)28(ternal)-374(w)27(ork)-374(v)27(ectors.)-568(Eac)27(h)-374(application)-375(of)-375(the)-374(preconditioner)-375(uses)-375(a)-375(n)28(um)28(b)-28(er)]TJ 0 -13.549 Td [(of)-439(w)28(ork)-438(v)27(ectors)-438(whic)27(h)-438(are)-439(allo)-27(c)-1(ated)-438(in)28(ternally)-439(as)-438(nece)-1(ssary;)-491(therefore)-438(allo)-28(cation)-439(and)]TJ 0 -13.55 Td [(deallo)-28(cation)-276(of)-276(memory)-276(o)-28(ccurs)-276(m)28(ultiple)-276(times)-277(du)1(ring)-277(th)1(e)-277(execution)-276(of)-276(a)-276(Krylo)28(v)-276(metho)-28(d.)]TJ 0 -13.549 Td [(In)-272(most)-271(cases)-272(this)-272(strat)1(e)-1(gy)-271(is)-272(p)-27(erfectly)-272(acceptable,)-284(but)-271(on)-272(some)-272(platforms,)-284(most)-271(notably)]TJ 0 -13.549 Td [(GPUs,)-318(memory)-315(allo)-28(cation)-314(is)-314(a)-315(slo)28(w)-315(op)-27(eration,)-318(and)-315(the)-314(default)-315(b)-27(eha)27(viour)-314(w)28(ould)-315(lead)-314(to)]TJ 0 -13.549 Td [(a)-361(slo)28(wdo)28(wn.)-527(This)-361(metho)-28(d)-361(allo)28(ws)-361(to)-361(trade)-361(space)-361(for)-361(time)-361(b)28(y)-361(preallo)-27(c)-1(ati)1(ng)-361(the)-361(in)28(ternal)]TJ 0 -13.549 Td [(w)28(orkspace)-373(outside)-372(of)-373(the)-372(in)28(v)28(o)-28(cation)-373(of)-372(a)-373(Krylo)28(v)-372(metho)-28(d.)-562(When)-372(using)-373(GPUs)-372(or)-373(other)]TJ 0 -13.55 Td [(sp)-28(ecialized)-387(devices,)-400(the)]TJ/F45 10.9091 Tf 115.359 0 Td [(vmold)]TJ/F15 10.9091 Tf 32.859 0 Td [(argumen)28(t)-387(is)-387(also)-387(necess)-1(ar)1(y)-388(to)-387(ensure)-387(the)-387(in)28(ternal)-387(w)28(ork)]TJ -148.218 -13.549 Td [(v)28(ectors)-331(are)-332(of)-331(the)-331(appropriate)-331(dynamic)-331(t)28(yp)-28(e)-331(to)-331(exploit)-331(the)-332(accelerator)-331(hardw)28(are;)-332(when)]TJ 0 -13.549 Td [(allo)-28(cation)-409(o)-28(ccurs)-409(in)27(ternal)1(ly)-410(this)-409(is)-410(tak)28(en)-409(care)-410(of)-409(based)-410(on)-409(the)-409(dynamic)-410(t)28(yp)-28(e)-409(of)-410(th)1(e)]TJ/F45 10.9091 Tf 406.724 0 Td [(x)]TJ/F15 10.9091 Tf -406.724 -13.549 Td [(argumen)28(t)-334(to)-333(the)]TJ/F45 10.9091 Tf 80.94 0 Td [(apply)]TJ/F15 10.9091 Tf 32.272 0 Td [(metho)-28(d.)]TJ/F17 11.9552 Tf -113.212 -34.596 Td [(Argumen)31(ts)]TJ/F45 10.9091 Tf 22.914 -17.241 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(8)]TJ -0 g 0 G - [-333(for)-334(details.)]TJ/F45 10.9091 Tf -45.971 -13.549 Td [(vmold)-1589(class\050psb_)]TJ/F18 10.9091 Tf 103.243 0 Td [(x)]TJ/F45 10.9091 Tf 6.374 0 Td [(_base_vect_type\051,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 217.634 0 Td [(.)]TJ -281.28 -13.549 Td [(The)-422(desired)-422(dynamic)-422(t)28(yp)-28(e)-422(for)-422(in)28(ternal)-422(v)28(ector)-422(comp)-28(onen)28(ts;)-466(this)-422(allo)27(ws)]TJ 0 -13.549 Td [(e.g.)-444(running)-334(on)-333(GPUs.)]TJ/F44 10.9091 Tf -68.885 -32.034 Td [(6.9.5)-1150(Metho)-32(d:)-511(free)]TJ -ET -q -1 0 0 1 205.345 145.421 cm -[]0 d 0 J 0.398 w 0 0 m 3.764 0 l S -Q -BT -/F44 10.9091 Tf 209.108 145.222 Td [(wrk)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 30.582 -22 Td [(call)-525(p%free_wrk\050info\051)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -612 0 obj -<< -/Length 658 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(40)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [(Deallo)-28(cate)-333(in)28(ternal)-334(w)28(ork)-333(v)28(ectors.)]TJ/F17 11.9552 Tf 0 -33.873 Td [(Argumen)31(ts)]TJ/F45 10.9091 Tf 22.914 -15.794 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-28(de.)-444(If)-334(no)-333(error,)-333(0)-334(is)-333(returned.)-444(See)-334(Section)]TJ -0 0 1 rg 0 0 1 RG - [-333(8)]TJ -0 g 0 G - [-333(for)-334(d)1(e)-1(tail)1(s)-1(.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -619 0 obj -<< -/Length 7418 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(6)]TJ -0 g 0 G - [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(41)]TJ -0 g 0 G -/F17 14.3462 Tf -401.542 -35.866 Td [(7)-1125(Adding)-375(new)-375(smo)-31(other)-375(and)-375(solv)31(er)-375(ob)-62(j)-1(ects)-374(to)-375(M)-1(LD2P4)]TJ/F15 10.9091 Tf 0 -24.929 Td [(Dev)28(elop)-28(ers)-414(can)-413(add)-414(completely)-413(new)-414(smo)-28(other)-414(an)1(d/or)-414(solv)28(er)-414(classes)-414(deriv)28(ed)-413(from)-414(the)]TJ 0 -13.55 Td [(base)-240(ob)-55(jects)-240(in)-239(the)-240(libr)1(ary)-240(\050see)-240(Remark)-239(2)-240(in)-239(Section)]TJ -0 0 1 rg 0 0 1 RG - [-240(6.2)]TJ -0 g 0 G - [(\051,)-258(without)-239(recompiling)-240(the)-239(library)]TJ 0 -13.549 Td [(itself.)]TJ 16.937 -13.846 Td [(T)83(o)-332(do)-332(so,)-333(it)-332(is)-332(necessary)-333(\014rst)-332(to)-332(select)-333(the)-332(base)-332(t)27(yp)-27(e)-333(to)-332(b)-28(e)-332(extended.)-444(In)-332(our)-333(exp)-27(eri-)]TJ -16.937 -13.549 Td [(ence,)-371(it)-363(is)-363(quite)-363(lik)28(ely)-364(that)-363(the)-363(new)-363(application)-363(needs)-363(only)-363(the)-364(de\014ni)1(tion)-364(of)-363(a)-363(\134solv)28(er")]TJ 0 -13.55 Td [(ob)-56(j)1(e)-1(ct,)-350(whic)28(h)-347(is)-347(almost)-347(alw)28(a)28(ys)-347(acting)-347(only)-347(on)-347(the)-347(lo)-28(cal)-347(part)-347(of)-347(the)-347(di)1(s)-1(tr)1(ibuted)-347(matrix.)]TJ 0 -13.549 Td [(The)-396(parallel)-397(actions)-396(required)-396(to)-397(connect)-396(the)-396(v)55(arious)-396(solv)28(er)-397(ob)-55(jects)-396(are)-397(most)-396(often)-397(al-)]TJ 0 -13.549 Td [(ready)-281(pro)28(vided)-281(b)28(y)-281(the)-280(blo)-28(c)28(k-Jac)-1(ob)1(i)-281(or)-281(the)-281(additiv)28(e)-281(Sc)28(h)28(w)28(arz)-281(smo)-28(others.)-427(T)83(o)-281(de\014ne)-280(a)-281(new)]TJ 0 -13.549 Td [(solv)28(er,)-466(the)-440(dev)28(elop)-28(er)-439(will)-440(then)-439(ha)28(v)27(e)-439(to)-440(de\014ne)-439(its)-440(comp)-28(onen)28(ts)-439(and)-440(metho)-28(ds,)-466(p)-27(erhaps)]TJ 0 -13.549 Td [(taking)-333(one)-334(of)-333(the)-333(prede\014ned)-333(solv)27(ers)-333(as)-333(a)-334(starting)-333(p)-28(oin)28(t,)-333(if)-333(p)-28(ossible.)]TJ 16.937 -13.847 Td [(Once)-329(the)-329(new)-329(smo)-28(other/solv)28(er)-329(class)-329(has)-329(b)-27(een)-329(dev)28(e)-1(l)1(op)-28(ed,)-330(to)-329(use)-329(it)-329(in)-329(th)1(e)-329(con)27(text)-329(of)]TJ -16.937 -13.549 Td [(the)-333(m)27(ultil)1(e)-1(v)28(el)-333(preconditioners)-333(it)-334(is)-333(necessary)-333(to:)]TJ -0 g 0 G -/F25 10.9091 Tf 16.364 -23.705 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(declare)-333(in)-334(the)-333(application)-333(program)-333(a)-334(v)56(ariable)-333(of)-334(the)-333(new)-333(t)27(yp)-27(e;)]TJ -0 g 0 G -/F25 10.9091 Tf -10.909 -23.704 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(pass)-333(that)-334(v)56(ariable)-333(as)-334(the)-333(argumen)28(t)-334(to)-333(the)]TJ/F45 10.9091 Tf 201.455 0 Td [(set)]TJ/F15 10.9091 Tf 20.818 0 Td [(routine)-333(as)-334(in)-333(the)-333(follo)28(wing:)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf -152.819 -28.485 Td [(call)-525(p%set\050smoother,info)-525([,ilev,ilmax,pos]\051)]TJ 5.727 -13.549 Td [(call)-525(p%set\050solver,info)-525([,ilev,ilmax,pos]\051)]TJ -0 g 0 G -/F25 10.9091 Tf -86.09 -28.485 Td [(\017)]TJ -0 g 0 G -/F15 10.9091 Tf 10.909 0 Td [(link)-333(the)-334(co)-27(de)-334(implemen)28(ting)-333(the)-334(v)56(arious)-333(metho)-28(ds)-333(in)27(to)-333(the)-333(application)-333(executable.)]TJ -27.273 -23.705 Td [(The)-442(new)-442(solv)28(er)-442(ob)-55(jec)-1(t)-441(is)-442(then)-442(dynamically)-442(included)-442(in)-442(t)1(he)-442(preconditioner)-442(structure,)]TJ 0 -13.549 Td [(and)-288(acts)-289(as)-289(a)]TJ/F18 10.9091 Tf 64.226 0 Td [(mold)]TJ/F15 10.9091 Tf 27.135 0 Td [(to)-288(whic)27(h)-288(the)-289(precondition)1(e)-1(r)-288(will)-288(c)-1(on)1(form,)-298(ev)28(en)-289(though)-288(the)-288(MLD2P4)]TJ -91.361 -13.549 Td [(library)-333(has)-334(n)1(ot)-334(b)-28(een)-333(mo)-28(di\014ed)-333(to)-333(accoun)28(t)-334(for)-333(this)-333(new)-334(dev)28(elopmen)28(t.)]TJ 16.937 -13.847 Td [(It)-382(is)-382(p)-27(ossible)-382(to)-382(de\014ne)-382(new)-382(v)56(alues)-382(for)-382(the)-381(k)27(eyw)28(ord)]TJ/F45 10.9091 Tf 247.41 0 Td [(WHAT)]TJ/F15 10.9091 Tf 27.074 0 Td [(in)-382(the)]TJ/F45 10.9091 Tf 32.573 0 Td [(set)]TJ/F15 10.9091 Tf 21.347 0 Td [(routine;)-406(if)-382(the)]TJ -345.341 -13.549 Td [(library)-319(co)-28(de)-319(do)-28(es)-319(not)-319(recognize)-320(a)-319(k)28(eyw)28(ord,)-322(it)-319(passes)-320(it)-319(do)28(wn)-319(the)-319(comp)-28(osition)-319(hierarc)28(h)27(y)]TJ 0 -13.549 Td [(\050lev)28(els)-410(con)28(taining)-409(smo)-28(others)-410(con)28(taining)-409(in)-410(turn)-409(solv)28(ers\051,)-429(so)-409(that)-410(it)-409(can)-410(b)-28(e)-409(ev)28(en)27(tual)1(ly)]TJ 0 -13.549 Td [(caugh)28(t)-386(b)28(y)-386(the)-386(new)-386(solv)28(er.)-602(By)-385(the)-386(same)-386(tok)28(en,)-399(an)28(y)-386(k)28(eyw)27(ord)1(/v)55(alue)-386(pair)-385(that)-386(do)-28(es)-386(not)]TJ 0 -13.55 Td [(p)-28(ertain)-393(to)-393(a)-394(giv)28(en)-393(smo)-28(other)-393(should)-394(b)-27(e)-394(passed)-393(do)28(wn)-394(to)-393(the)-393(con)27(tained)-393(solv)28(er,)-408(and)-394(an)28(y)]TJ 0 -13.549 Td [(k)28(eyw)28(ord/v)55(alue)-333(pair)-333(that)-334(do)-27(es)-334(not)-333(p)-28(ertain)-333(to)-333(a)-334(giv)28(en)-333(solv)28(e)-1(r)-333(is)-333(b)28(y)-334(default)-333(ignored.)]TJ 16.937 -13.846 Td [(An)-222(example)-222(is)-223(pro)28(vided)-222(in)-222(the)-222(source)-223(co)-27(de)-223(distribu)1(tion)-223(und)1(e)-1(r)-222(the)-222(folder)]TJ/F45 10.9091 Tf 331.849 0 Td [(tests/newslv)]TJ/F15 10.9091 Tf 68.726 0 Td [(.)]TJ -417.512 -13.549 Td [(In)-353(this)-352(exam)-1(p)1(le)-353(w)28(e)-353(are)-353(implemen)28(ting)-353(a)-353(new)-352(incomplete)-353(factorization)-353(v)56(arian)28(t)-353(\050whic)28(h)-353(is)]TJ 0 -13.55 Td [(simply)-416(the)-417(ILU\0500\051)-416(factorization)-417(under)-416(a)-417(n)1(e)-1(w)-416(name\051.)-694(Because)-416(of)-417(the)-416(sp)-28(eci\014cs)-417(of)-416(this)]TJ 0 -13.549 Td [(case,)-336(it)-336(is)-336(p)-27(oss)-1(ib)1(le)-336(to)-336(reuse)-336(the)-335(basic)-336(structure)-336(of)-335(the)-336(ILU)-336(solv)28(er,)-336(with)-336(its)-335(L/D/U)-336(com-)]TJ 0 -13.549 Td [(p)-28(onen)28(ts)-347(and)-347(the)-347(metho)-28(ds)-347(needed)-347(to)-347(apply)-347(the)-347(solv)28(er;)-354(only)-347(a)-347(few)-347(metho)-28(ds,)-351(suc)28(h)-347(as)-347(the)]TJ 0 -13.549 Td [(description)-333(and)-334(most)-333(imp)-28(ortan)28(tly)-333(the)-333(build,)-334(need)-333(to)-333(b)-28(e)-333(o)27(vv)28(erridden)-333(\050rewritten\051.)]TJ 16.937 -13.847 Td [(The)-333(in)28(te)-1(r)1(face)-1(s)-333(for)-333(the)-333(c)-1(all)1(s)-334(sho)28(wn)-333(ab)-28(o)28(v)27(e)-333(are)-333(de\014ned)-334(u)1(s)-1(in)1(g)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf -6.61 -23.054 Td [(smoother)-534(class\050mld_x_base_smoother_type\051)]TJ/F15 10.9091 Tf 51.64 -13.549 Td [(The)-333(user-de\014ned)-334(new)-333(smo)-28(other)-333(to)-333(b)-28(e)-334(emplo)28(y)28(ed)-333(in)-334(the)-333(preconditioner.)]TJ/F45 10.9091 Tf -51.64 -13.549 Td [(solver)-1584(class\050mld_x_base_solver_type\051)]TJ/F15 10.9091 Tf 51.64 -13.55 Td [(The)-333(user-de\014ned)-334(new)-333(solv)28(er)-334(to)-333(b)-28(e)-333(emplo)28(y)28(ed)-334(in)-333(the)-333(preconditioner.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -623 0 obj -<< -/Length 1848 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(42)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [(The)-374(other)-373(argumen)27(ts)-373(are)-374(de\014ned)-374(in)-373(the)-374(w)28(a)27(y)-373(describ)-28(ed)-374(in)-374(S)1(e)-1(c.)]TJ -0 0 1 rg 0 0 1 RG - [-373(6.2)]TJ -0 g 0 G - [(.)-566(As)-374(an)-373(example,)-384(in)]TJ 0 -13.549 Td [(the)]TJ/F45 10.9091 Tf 19.014 0 Td [(tests/newslv)]TJ/F15 10.9091 Tf 72.589 0 Td [(co)-28(de)-354(w)28(e)-354(de\014ne)-354(a)-354(new)-354(ob)-56(ject)-354(of)-354(t)28(yp)-28(e)]TJ/F45 10.9091 Tf 176.051 0 Td [(mld_d_tlu_solver_type)]TJ/F15 10.9091 Tf 120.272 0 Td [(,)-359(and)]TJ -387.926 -13.549 Td [(w)28(e)-334(pass)-333(it)-333(as)-334(follo)28(ws:)]TJ -0 g 0 G -0 g 0 G -/F45 10.9091 Tf 11.454 -36.065 Td [(!)-525(sparse)-525(matrix)-525(and)-525(preconditioner)]TJ 0 -13.549 Td [(type\050psb_dspmat_type\051)-525(::)-525(a)]TJ 0 -13.549 Td [(type\050mld_dprec_type\051)-1050(::)-525(prec)]TJ 0 -13.549 Td [(type\050mld_d_tlu_solver_type\051)-525(::)-525(tlusv)]TJ -11.454 -27.099 Td [(......)]TJ 11.454 -13.549 Td [(!)]TJ 0 -13.549 Td [(!)-1050(prepare)-525(the)-525(preconditioner:)-525(an)-525(ML)-525(with)-525(defaults,)-525(but)-525(with)-525(TLU)-525(solver)-525(at)]TJ 0 -13.549 Td [(!)-1050(intermediate)-525(levels.)-525(All)-525(other)-525(parameters)-525(are)-525(at)-525(default)-525(values.)]TJ 0 -13.55 Td [(!)]TJ 0 -13.549 Td [(call)-525(prec%init\050'ML',)-3675(info\051)]TJ 0 -13.549 Td [(call)-525(prec%hierarchy_build\050a,desc_a,info\051)]TJ 0 -13.549 Td [(nlv)-525(=)-525(prec%get_nlevs\050\051)]TJ 0 -13.549 Td [(call)-525(prec%set\050tlusv,)-1575(info,ilev=1,ilmax=max\0501,nlv-1\051\051)]TJ 0 -13.55 Td [(call)-525(prec%smoothers_build\050a,desc_a,info\051)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -629 0 obj -<< -/Length 1780 ->> -stream -0 g 0 G -0 0 1 rg 0 0 1 RG -BT -/F42 10.9091 Tf 93.6 740.002 Td [(8)]TJ -0 g 0 G - [-378(Err)22(o)1(r)-378(handling)]TJ/F15 10.9091 Tf 401.542 0 Td [(43)]TJ -0 g 0 G -/F17 14.3462 Tf -401.542 -35.866 Td [(8)-1125(Error)-375(Handling)]TJ/F15 10.9091 Tf 0 -24.352 Td [(The)-352(error)-353(handling)-352(in)-352(MLD2P4)-353(is)-352(based)-352(on)-353(the)-352(PSBLAS)-352(error)-353(handlin)1(g.)-502(Error)-352(condi-)]TJ 0 -13.549 Td [(tions)-235(are)-235(signaled)-235(via)-235(an)-235(in)28(teger)-235(argumen)27(t)]TJ/F45 10.9091 Tf 197.254 0 Td [(info)]TJ/F15 10.9091 Tf 22.908 0 Td [(;)-268(whenev)28(er)-235(an)-235(error)-235(condition)-235(is)-235(detected,)]TJ -220.162 -13.549 Td [(an)-256(error)-255(trace)-256(stac)28(k)-256(is)-256(built)-255(b)28(y)-256(the)-256(library)-255(up)-256(to)-255(the)-256(top-lev)28(el,)-272(u)1(s)-1(er-callabl)1(e)-256(routine.)-419(This)]TJ 0 -13.549 Td [(routine)-415(will)-414(then)-415(decide,)-435(according)-414(to)-415(the)-415(user)-414(preferences,)-435(whether)-415(the)-414(e)-1(r)1(ror)-415(should)]TJ 0 -13.55 Td [(b)-28(e)-319(handled)-319(b)28(y)-319(terminating)-320(the)-319(program)-319(or)-319(b)28(y)-320(r)1(e)-1(tu)1(rning)-320(th)1(e)-320(error)-319(condition)-319(to)-319(the)-319(user)]TJ 0 -13.549 Td [(co)-28(de,)-457(whic)28(h)-432(will)-432(then)-432(tak)28(e)-432(action,)-457(and)-432(whether)-432(an)-432(error)-432(message)-432(should)-432(b)-28(e)-432(prin)28(ted.)]TJ 0 -13.549 Td [(These)-418(option)1(s)-418(ma)28(y)-418(b)-27(e)-418(set)-418(b)28(y)-417(using)-418(th)1(e)-418(PSBLAS)-417(error)-418(handlin)1(g)-418(routines;)-459(for)-418(further)]TJ 0 -13.549 Td [(details)-333(see)-334(the)-333(PSBLAS)-333(User's)-334(Guide)-333([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ -0 g 0 G - [(].)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -634 0 obj -<< -/Length 3978 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(44)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -/F17 14.3462 Tf -203.265 -35.866 Td [(A)-1125(License)]TJ/F15 10.9091 Tf 0 -22.758 Td [(The)-333(MLD2P4)-334(is)-333(freely)-333(distributable)-333(under)-334(the)-333(follo)28(wing)-333(cop)27(yri)1(gh)27(t)-333(terms:)]TJ -0 g 0 G -0 g 0 G -/F45 9.9626 Tf 141.219 -32.877 Td [(MLD2P4)-1050(version)-525(2.1)]TJ -130.759 -11.955 Td [(MultiLevel)-525(Domain)-525(Decomposition)-525(Parallel)-525(Preconditioners)-525(Package)]TJ 57.534 -11.955 Td [(based)-525(on)-525(PSBLAS)-525(\050Parallel)-525(Sparse)-525(BLAS)-525(version)-525(3.5\051)]TJ -57.534 -23.91 Td [(\050C\051)-525(Copyright)-525(2008,)-525(2010,)-525(2012,)-525(2015,)-525(2017)]TJ 0 -23.911 Td [(Salvatore)-525(Filippone)-2100(Cranfield)-525(University,)-525(Cranfield,)-525(UK)]TJ 0 -11.955 Td [(Pasqua)-525(D'Ambra)-4725(IAC-CNR,)-525(Naples,)-525(IT)]TJ 0 -11.955 Td [(Daniela)-525(di)-525(Serafino)-2100(University)-525(of)-525(Campania)-525(L.)-525(Vanvitelli,)-525(Caserta,)-525(IT)]TJ 0 -23.91 Td [(Redistribution)-525(and)-525(use)-525(in)-525(source)-525(and)-525(binary)-525(forms,)-525(with)-525(or)-525(without)]TJ 0 -11.955 Td [(modification,)-525(are)-525(permitted)-525(provided)-525(that)-525(the)-525(following)-525(conditions)]TJ 0 -11.956 Td [(are)-525(met:)]TJ 10.461 -11.955 Td [(1.)-525(Redistributions)-525(of)-525(source)-525(code)-525(must)-525(retain)-525(the)-525(above)-525(copyright)]TJ 15.691 -11.955 Td [(notice,)-525(this)-525(list)-525(of)-525(conditions)-525(and)-525(the)-525(following)-525(disclaimer.)]TJ -15.691 -11.955 Td [(2.)-525(Redistributions)-525(in)-525(binary)-525(form)-525(must)-525(reproduce)-525(the)-525(above)-525(copyright)]TJ 15.691 -11.955 Td [(notice,)-525(this)-525(list)-525(of)-525(conditions,)-525(and)-525(the)-525(following)-525(disclaimer)-525(in)-525(the)]TJ 0 -11.956 Td [(documentation)-525(and/or)-525(other)-525(materials)-525(provided)-525(with)-525(the)-525(distribution.)]TJ -15.691 -11.955 Td [(3.)-525(The)-525(name)-525(of)-525(the)-525(MLD2P4)-525(group)-525(or)-525(the)-525(names)-525(of)-525(its)-525(contributors)-525(may)]TJ 15.691 -11.955 Td [(not)-525(be)-525(used)-525(to)-525(endorse)-525(or)-525(promote)-525(products)-525(derived)-525(from)-525(this)]TJ 0 -11.955 Td [(software)-525(without)-525(specific)-525(written)-525(permission.)]TJ -26.152 -23.91 Td [(THIS)-525(SOFTWARE)-525(IS)-525(PROVIDED)-525(BY)-525(THE)-525(COPYRIGHT)-525(HOLDERS)-525(AND)-525(CONTRIBUTORS)]TJ 0 -11.956 Td [(``AS)-525(IS'')-525(AND)-525(ANY)-525(EXPRESS)-525(OR)-525(IMPLIED)-525(WARRANTIES,)-525(INCLUDING,)-525(BUT)-525(NOT)-525(LIMITED)]TJ 0 -11.955 Td [(TO,)-525(THE)-525(IMPLIED)-525(WARRANTIES)-525(OF)-525(MERCHANTABILITY)-525(AND)-525(FITNESS)-525(FOR)-525(A)-525(PARTICULAR)]TJ 0 -11.955 Td [(PURPOSE)-525(ARE)-525(DISCLAIMED.)-525(IN)-525(NO)-525(EVENT)-525(SHALL)-525(THE)-525(MLD2P4)-525(GROUP)-525(OR)-525(ITS)-525(CONTRIBUTORS)]TJ 0 -11.955 Td [(BE)-525(LIABLE)-525(FOR)-525(ANY)-525(DIRECT,)-525(INDIRECT,)-525(INCIDENTAL,)-525(SPECIAL,)-525(EXEMPLARY,)-525(OR)]TJ 0 -11.955 Td [(CONSEQUENTIAL)-525(DAMAGES)-525(\050INCLUDING,)-525(BUT)-525(NOT)-525(LIMITED)-525(TO,)-525(PROCUREMENT)-525(OF)]TJ 0 -11.955 Td [(SUBSTITUTE)-525(GOODS)-525(OR)-525(SERVICES;)-525(LOSS)-525(OF)-525(USE,)-525(DATA,)-525(OR)-525(PROFITS;)-525(OR)-525(BUSINESS)]TJ 0 -11.956 Td [(INTERRUPTION\051)-525(HOWEVER)-525(CAUSED)-525(AND)-525(ON)-525(ANY)-525(THEORY)-525(OF)-525(LIABILITY,)-525(WHETHER)-525(IN)]TJ 0 -11.955 Td [(CONTRACT,)-525(STRICT)-525(LIABILITY,)-525(OR)-525(TORT)-525(\050INCLUDING)-525(NEGLIGENCE)-525(OR)-525(OTHERWISE\051)]TJ 0 -11.955 Td [(ARISING)-525(IN)-525(ANY)-525(WAY)-525(OUT)-525(OF)-525(THE)-525(USE)-525(OF)-525(THIS)-525(SOFTWARE,)-525(EVEN)-525(IF)-525(ADVISED)-525(OF)-525(THE)]TJ 0 -11.955 Td [(POSSIBILITY)-525(OF)-525(SUCH)-525(DAMAGE.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -638 0 obj -<< -/Length 6503 ->> -stream -0 g 0 G -BT -/F42 10.9091 Tf 93.6 740.002 Td [(References)]TJ/F15 10.9091 Tf 401.542 0 Td [(45)]TJ -0 g 0 G -/F17 14.3462 Tf -401.542 -35.866 Td [(References)]TJ -0 g 0 G -/F15 10.9091 Tf 5.455 -25.347 Td [([1])]TJ -0 g 0 G - [-500(P)83(.)-289(R.)-290(Amesto)28(y)83(,)-298(C.)-290(Ashcraft,)-298(O.)-290(Boiteau,)-298(A.)-289(B)-1(u)1(ttari,)-299(J.)-289(L'Excellen)27(t,)-298(C.)-289(W)83(eisb)-28(ec)28(k)28(er,)]TJ/F18 10.9091 Tf 16.969 -13.549 Td [(Impr)51(oving)-344(multifr)51(ontal)-345(metho)51(ds)-344(by)-345(me)51(ans)-344(of)-345(blo)51(ck)-344(low-r)51(ank)-345(r)51(epr)52(esent)-1(ations)]TJ/F15 10.9091 Tf 355.304 0 Td [(,)-322(SIAM)]TJ -355.304 -13.549 Td [(Journal)-486(on)-487(Scien)28(ti\014c)-487(Computing,)-524(v)27(ol)1(ume)-487(37)-487(\0503\051,)-524(2015,)-525(A1452{A1474.)-487(See)-486(also)]TJ/F45 10.9091 Tf 0 -13.549 Td [(http://mumps.enseeiht.fr)]TJ/F15 10.9091 Tf 137.454 0 Td [(.)]TJ -0 g 0 G - -154.423 -24.564 Td [([2])]TJ -0 g 0 G - [-500(M.)-272(Brezina,)-284(P)83(.)-272(V)84(an)27(\024)473(ek,)]TJ/F18 10.9091 Tf 123.379 0 Td [(A)-301(Black-Box)-302(I)1(ter)51(ative)-302(Solver)-301(Base)51(d)-301(on)-302(a)-301(Two-L)51(evel)-301(Schwarz)]TJ -106.41 -13.549 Td [(Metho)51(d)]TJ/F15 10.9091 Tf 34.594 0 Td [(,)-333(Computing,)-334(63,)-333(1999,)-333(233{263.)]TJ -0 g 0 G - -51.563 -24.564 Td [([3])]TJ -0 g 0 G - [-500(W.)-342(L.)-342(Briggs,)-344(V.)-342(E.)-342(Henson,)-344(S.)-342(F.)-341(Mc)-1(Cor)1(m)-1(ic)28(k,)]TJ/F18 10.9091 Tf 244.734 0 Td [(A)-366(Multigr)1(id)-366(T)77(utorial,)-368(Se)51(c)51(ond)-365(E)-1(di)1(-)]TJ -227.765 -13.549 Td [(tion)]TJ/F15 10.9091 Tf 18.679 0 Td [(,)-333(SIAM,)-334(2000.)]TJ -0 g 0 G - -35.648 -24.564 Td [([4])]TJ -0 g 0 G - [-500(A.)-306(Buttari,)-312(P)84(.)-306(D'Am)27(bra,)-311(D.)-306(di)-306(Sera\014no,)-312(S.)-306(Filipp)-28(one,)]TJ/F18 10.9091 Tf 272.057 0 Td [(Extending)-333(PSBLAS)-333(to)-333(Bui)1(ld)]TJ -255.088 -13.549 Td [(Par)51(al)-51(lel)-359(Schwarz)-360(Pr)51(e)52(c)51(onditioners)]TJ/F15 10.9091 Tf 156.737 0 Td [(,)-335(in)-335(J.)-335(Dongarra,)-336(K.)-335(Madsen,)-335(J.)-335(W)83(asniewski,)-335(edi-)]TJ -156.737 -13.549 Td [(tors,)-305(Pro)-28(ceedings)-297(of)-298(P)83(ARA)-297(04)-298(W)83(orkshop)-297(on)-298(State)-298(of)-297(the)-298(Art)-298(in)-297(Scien)27(ti\014c)-297(Comput-)]TJ 0 -13.549 Td [(ing,)-333(Lecture)-334(Notes)-333(in)-333(Computer)-334(Science,)-333(Springer,)-333(2005,)-333(593{602.)]TJ -0 g 0 G - -16.969 -24.564 Td [([5])]TJ -0 g 0 G - [-500(A.)-380(Buttari,)-392(P)84(.)-381(D')1(Am)27(bra,)-391(D.)-381(di)-380(Sera\014no,)-391(S.)-380(Filipp)-28(one,)]TJ/F18 10.9091 Tf 279.591 0 Td [(2LEV-D2P4:)-546(a)-401(p)51(ackage)-401(of)]TJ -262.622 -13.549 Td [(high-p)51(erformanc)51(e)-423(pr)51(e)51(c)51(onditioners)-424(for)-423(scienti\014c)-424(and)-424(engine)52(ering)-424(applic)51(ations)]TJ/F15 10.9091 Tf 364.505 0 Td [(,)-423(Ap-)]TJ -364.505 -13.549 Td [(plicable)-445(Algebra)-445(in)-445(Engineering,)-473(Comm)28(unications)-445(and)-445(Computing,)-472(18)-445(\0503\051)-445(2007,)]TJ 0 -13.55 Td [(223{239.)]TJ -0 g 0 G - -16.969 -24.563 Td [([6])]TJ -0 g 0 G - [-500(X.)-410(C.)-410(Cai,)-430(M.)-410(Sarkis,)]TJ/F18 10.9091 Tf 126.22 0 Td [(A)-428(R)51(estricte)51(d)-429(A)51(dditive)-428(Schwarz)-429(Pr)51(e)52(c)51(onditioner)-429(for)-428(Gener)51(al)]TJ -109.251 -13.549 Td [(Sp)51(arse)-337(Line)51(ar)-337(Sys)1(t)-1(em)1(s)]TJ/F15 10.9091 Tf 107.029 0 Td [(,)-315(SIAM)-311(Journal)-310(on)-311(Scien)28(ti\014c)-310(C)-1(ompu)1(ting,)-316(21)-310(\0502\051,)-315(1999,)-315(792{)]TJ -107.029 -13.55 Td [(797.)]TJ -0 g 0 G - -16.969 -24.563 Td [([7])]TJ -0 g 0 G - [-500(P)83(.)-366(D'Am)28(bra,)-375(S.)-367(Filipp)-27(one,)-375(D.)-367(di)-366(Sera\014no,)]TJ/F18 10.9091 Tf 220.753 0 Td [(On)-388(the)-389(Development)-388(of)-388(PS)-1(B)1(L)-1(AS-b)52(ase)51(d)]TJ -203.784 -13.549 Td [(Par)51(al)-51(lel)-380(Two-level)-379(Schwarz)-380(Pr)51(e)51(c)51(onditioners)]TJ/F15 10.9091 Tf 206.489 0 Td [(,)-363(Applied)-357(Numerical)-358(Mathematics,)-363(El-)]TJ -206.489 -13.55 Td [(sevier)-333(Science)-1(,)-333(57)-333(\05011-12\051,)-333(2007,)-334(1181-1196.)]TJ -0 g 0 G - -16.969 -24.563 Td [([8])]TJ -0 g 0 G - [-500(P)83(.)-352(D'Am)28(bra,)-357(D.)-352(di)-352(Sera\014no,)-356(S.)-352(Filipp)-28(one,)]TJ/F18 10.9091 Tf 219.527 0 Td [(MLD2P4:)-495(a)-375(Package)-375(of)-375(Par)51(al)-51(lel)-375(Multi-)]TJ -202.558 -13.55 Td [(level)-312(A)26(lgebr)51(aic)-312(Domain)-312(De)51(c)51(omp)51(osition)-312(Pr)51(e)51(c)51(onditioners)-312(in)-312(F)77(ortr)51(an)-312(95)]TJ/F15 10.9091 Tf 324.852 0 Td [(,)-294(A)28(CM)-283(T)83(rans.)]TJ -324.852 -13.549 Td [(Math.)-333(Soft)28(w.,)-334(37\0503\051,)-333(2010,)-333(art.)-334(30.)]TJ -0 g 0 G - -16.969 -24.563 Td [([9])]TJ -0 g 0 G - [-500(T.)-398(A.)-399(Da)28(vis,)]TJ/F18 10.9091 Tf 81.911 0 Td [(A)26(lgorithm)-418(832:)-580(UMF)1(P)76(A)26(CK)-418(-)-417(an)-418(Unsymmetric-p)51(attern)-417(Multifr)51(ontal)]TJ -64.942 -13.55 Td [(Metho)51(d)-307(with)-307(a)-308(Col)1(umn)-308(Pr)51(e)1(-or)51(dering)-307(St)-1(r)52(ate)51(gy)]TJ/F15 10.9091 Tf 211.246 0 Td [(,)-289(A)27(CM)-278(T)83(ran)1(s)-1(action)1(s)-279(on)-278(Mathematical)]TJ -211.246 -13.549 Td [(Soft)28(w)28(are,)-334(30,)-333(2004,)-333(196{199.)-334(\050See)-333(also)]TJ/F45 10.9091 Tf 184.031 0 Td [(http://www.cise.ufl.edu/~davis/)]TJ/F15 10.9091 Tf 177.543 0 Td [(\051)]TJ -0 g 0 G - -383.998 -24.564 Td [([10])]TJ -0 g 0 G - [-500(J.)-381(W.)-381(Demmel,)-393(S.)-381(C.)-381(Eisenstat,)-393(J.)-381(R.)-382(Gil)1(b)-28(ert,)-393(X.)-381(S.)-381(Li,)-393(J.)-381(W.)-381(H.)-382(Li)1(u,)]TJ/F18 10.9091 Tf 364.973 0 Td [(A)-402(sup)51(er)1(n)-1(-)]TJ -342.549 -13.549 Td [(o)51(dal)-452(appr)51(o)51(ach)-452(to)-453(sp)51(ar)1(se)-453(p)51(artial)-452(pivoting)]TJ/F15 10.9091 Tf 192.083 0 Td [(,)-462(SIAM)-436(Journal)-436(on)-436(Matrix)-436(Analysis)-436(and)]TJ -192.083 -13.549 Td [(Applications,)-333(20)-334(\0503\051,)-333(1999,)-333(720{755.)]TJ -0 g 0 G - -22.424 -24.564 Td [([11])]TJ -0 g 0 G - [-500(J.)-443(J.)-444(Dongarra,)-470(J.)-444(Du)-443(Croz,)-471(I.)-444(S)1(.)-444(Du\013,)-471(S.)-443(Hammarling,)]TJ/F18 10.9091 Tf 301.5 0 Td [(A)-459(set)-459(of)-459(L)51(evel)-459(3)-459(Basic)]TJ -279.076 -13.549 Td [(Line)51(ar)-313(A)26(lgebr)51(a)-313(Subpr)51(o)51(gr)51(ams)]TJ/F15 10.9091 Tf 132.739 0 Td [(,)-294(A)27(CM)-284(T)83(ransactions)-285(on)-284(Mathematical)-285(Soft)28(w)27(ar)1(e)-1(,)-294(16)-285(\0501\051)]TJ -132.739 -13.549 Td [(1990,)-333(1{17.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -544 0 obj -<< -/Type /ObjStm -/N 100 -/First 893 -/Length 11666 ->> -stream -539 0 547 132 545 266 549 412 502 466 546 524 552 643 554 757 424 811 551 870 -560 1002 558 1160 555 1306 556 1460 557 1614 562 1761 79 1815 559 1868 569 1987 563 2153 -564 2305 565 2458 566 2612 567 2759 571 2912 83 2966 568 3019 580 3138 578 3320 572 3466 -573 3617 574 3769 575 3923 576 4077 577 4224 582 4378 87 4432 579 4485 585 4604 583 4738 -587 4885 91 4939 584 4992 591 5163 589 5305 588 5451 593 5597 95 5651 590 5704 599 5810 -595 5960 596 6107 597 6254 601 6407 99 6461 103 6514 107 6568 111 6622 598 6676 606 6808 -604 6958 602 7104 603 7251 608 7398 115 7452 119 7506 123 7560 605 7614 611 7746 609 7880 -613 8027 610 8081 618 8187 616 8329 614 8475 620 8627 127 8681 617 8735 622 8867 615 9001 -624 9153 621 9207 628 9300 626 9442 625 9588 630 9742 131 9796 627 9850 633 9956 635 10070 -135 10124 632 10178 637 10284 639 10398 139 10452 300 10506 231 10560 227 10613 347 10665 348 10719 -% 539 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F45 255 0 R /F22 225 0 R /F25 257 0 R /F18 307 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 547 0 obj -<< -/Type /Page -/Contents 548 0 R -/Resources 546 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 550 0 R -/Annots [ 545 0 R ] ->> -% 545 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 549 0 obj -<< -/D [547 0 R /XYZ 92.6 752.957 null] ->> -% 502 0 obj -<< -/D [547 0 R /XYZ 435.906 4328.445 null] ->> -% 546 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F45 255 0 R /F22 225 0 R /F25 257 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 552 0 obj -<< -/Type /Page -/Contents 553 0 R -/Resources 551 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 550 0 R ->> -% 554 0 obj -<< -/D [552 0 R /XYZ 85.4 752.957 null] ->> -% 424 0 obj -<< -/D [552 0 R /XYZ -3930.637 615.536 null] ->> -% 551 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F45 255 0 R /F25 257 0 R /F22 225 0 R /F18 307 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 560 0 obj -<< -/Type /Page -/Contents 561 0 R -/Resources 559 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 550 0 R -/Annots [ 558 0 R 555 0 R 556 0 R 557 0 R ] ->> -% 558 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 555 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [364.686 526.079 377.588 535.102] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 556 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [199.125 485.431 212.027 494.454] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 557 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [402.247 454.268 409.694 467.901] -/A << /S /GoTo /D (section.8) >> ->> -% 562 0 obj -<< -/D [560 0 R /XYZ 92.6 752.957 null] ->> -% 79 0 obj -<< -/D [560 0 R /XYZ 93.6 715.095 null] ->> -% 559 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R /F45 255 0 R /F18 307 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 569 0 obj -<< -/Type /Page -/Contents 570 0 R -/Resources 568 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 550 0 R -/Annots [ 563 0 R 564 0 R 565 0 R 566 0 R 567 0 R ] ->> -% 563 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [235.009 613.666 250.941 626.568] -/A << /S /GoTo /D (subsection.6.3) >> ->> -% 564 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [357.486 512.53 370.387 521.553] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 565 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [191.925 471.882 204.826 480.905] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 566 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [395.046 440.719 402.493 454.352] -/A << /S /GoTo /D (section.8) >> ->> -% 567 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [338.092 390.587 350.993 399.61] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 571 0 obj -<< -/D [569 0 R /XYZ 85.4 752.957 null] ->> -% 83 0 obj -<< -/D [569 0 R /XYZ 86.4 715.095 null] ->> -% 568 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F17 148 0 R /F45 255 0 R /F18 307 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 580 0 obj -<< -/Type /Page -/Contents 581 0 R -/Resources 579 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 550 0 R -/Annots [ 578 0 R 572 0 R 573 0 R 574 0 R 575 0 R 576 0 R 577 0 R ] ->> -% 578 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 572 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [334.588 640.765 350.52 653.666] -/A << /S /GoTo /D (subsection.6.3) >> ->> -% 573 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [374.629 640.765 390.561 653.666] -/A << /S /GoTo /D (subsection.6.4) >> ->> -% 574 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [364.686 485.431 377.588 494.454] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 575 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [199.125 444.784 212.027 453.807] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 576 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [402.247 413.621 409.694 427.254] -/A << /S /GoTo /D (section.8) >> ->> -% 577 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [345.292 363.489 358.194 372.511] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 582 0 obj -<< -/D [580 0 R /XYZ 92.6 752.957 null] ->> -% 87 0 obj -<< -/D [580 0 R /XYZ 93.6 715.095 null] ->> -% 579 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R /F45 255 0 R /F18 307 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 585 0 obj -<< -/Type /Page -/Contents 586 0 R -/Resources 584 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 550 0 R -/Annots [ 583 0 R ] ->> -% 583 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [395.046 386.522 402.493 400.155] -/A << /S /GoTo /D (section.8) >> ->> -% 587 0 obj -<< -/D [585 0 R /XYZ 85.4 752.957 null] ->> -% 91 0 obj -<< -/D [585 0 R /XYZ 86.4 715.095 null] ->> -% 584 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F17 148 0 R /F45 255 0 R /F22 225 0 R /F26 363 0 R /F20 364 0 R /F18 307 0 R /F23 361 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 591 0 obj -<< -/Type /Page -/Contents 592 0 R -/Resources 590 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 594 0 R -/Annots [ 589 0 R 588 0 R ] ->> -% 589 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 588 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [399.894 589.76 407.341 603.393] -/A << /S /GoTo /D (section.8) >> ->> -% 593 0 obj -<< -/D [591 0 R /XYZ 92.6 752.957 null] ->> -% 95 0 obj -<< -/D [591 0 R /XYZ 93.6 715.095 null] ->> -% 590 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 599 0 obj -<< -/Type /Page -/Contents 600 0 R -/Resources 598 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 594 0 R -/Annots [ 595 0 R 596 0 R 597 0 R ] ->> -% 595 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [395.046 559.996 402.493 573.629] -/A << /S /GoTo /D (section.8) >> ->> -% 596 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [395.046 223.562 402.493 237.195] -/A << /S /GoTo /D (section.8) >> ->> -% 597 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [338.092 173.43 350.993 182.453] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 601 0 obj -<< -/D [599 0 R /XYZ 85.4 752.957 null] ->> -% 99 0 obj -<< -/D [599 0 R /XYZ 86.4 715.095 null] ->> -% 103 0 obj -<< -/D [599 0 R /XYZ 86.4 431.215 null] ->> -% 107 0 obj -<< -/D [599 0 R /XYZ 86.4 365.879 null] ->> -% 111 0 obj -<< -/D [599 0 R /XYZ 86.4 153.691 null] ->> -% 598 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F17 148 0 R /F45 255 0 R /F44 205 0 R /F18 307 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 606 0 obj -<< -/Type /Page -/Contents 607 0 R -/Resources 605 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 594 0 R -/Annots [ 604 0 R 602 0 R 603 0 R ] ->> -% 604 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 602 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [402.247 579.493 409.694 593.126] -/A << /S /GoTo /D (section.8) >> ->> -% 603 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [402.247 212.842 409.694 226.475] -/A << /S /GoTo /D (section.8) >> ->> -% 608 0 obj -<< -/D [606 0 R /XYZ 92.6 752.957 null] ->> -% 115 0 obj -<< -/D [606 0 R /XYZ 93.6 561.815 null] ->> -% 119 0 obj -<< -/D [606 0 R /XYZ 93.6 481.328 null] ->> -% 123 0 obj -<< -/D [606 0 R /XYZ 93.6 154.517 null] ->> -% 605 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R /F45 255 0 R /F18 307 0 R /F44 205 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 611 0 obj -<< -/Type /Page -/Contents 612 0 R -/Resources 610 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 594 0 R -/Annots [ 609 0 R ] ->> -% 609 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [395.046 635.859 402.493 649.492] -/A << /S /GoTo /D (section.8) >> ->> -% 613 0 obj -<< -/D [611 0 R /XYZ 85.4 752.957 null] ->> -% 610 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F17 148 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 618 0 obj -<< -/Type /Page -/Contents 619 0 R -/Resources 617 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 594 0 R -/Annots [ 616 0 R 614 0 R ] ->> -% 616 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.6) >> ->> -% 614 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [334.005 661.934 349.937 674.835] -/A << /S /GoTo /D (subsection.6.2) >> ->> -% 620 0 obj -<< -/D [618 0 R /XYZ 92.6 752.957 null] ->> -% 127 0 obj -<< -/D [618 0 R /XYZ 93.6 715.095 null] ->> -% 617 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R /F25 257 0 R /F45 255 0 R /F18 307 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 622 0 obj -<< -/Type /Page -/Contents 623 0 R -/Resources 621 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 594 0 R -/Annots [ 615 0 R ] ->> -% 615 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [387.161 701.019 403.093 712.708] -/A << /S /GoTo /D (subsection.6.2) >> ->> -% 624 0 obj -<< -/D [622 0 R /XYZ 85.4 752.957 null] ->> -% 621 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 628 0 obj -<< -/Type /Page -/Contents 629 0 R -/Resources 627 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 631 0 R -/Annots [ 626 0 R 625 0 R ] ->> -% 626 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.604 739.006 100.627 748.453] -/A << /S /GoTo /D (section.8) >> ->> -% 625 0 obj -<< -/Type /Annot -/Subtype /Link -/Border[0 0 0]/H/I/C[0 1 0] -/Rect [277.347 583.943 290.248 592.966] -/A << /S /GoTo /D (cite.PSBLASGUIDE) >> ->> -% 630 0 obj -<< -/D [628 0 R /XYZ 92.6 752.957 null] ->> -% 131 0 obj -<< -/D [628 0 R /XYZ 93.6 715.095 null] ->> -% 627 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 633 0 obj -<< -/Type /Page -/Contents 634 0 R -/Resources 632 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 631 0 R ->> -% 635 0 obj -<< -/D [633 0 R /XYZ 85.4 752.957 null] ->> -% 135 0 obj -<< -/D [633 0 R /XYZ 86.4 715.095 null] ->> -% 632 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F17 148 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 637 0 obj -<< -/Type /Page -/Contents 638 0 R -/Resources 636 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 631 0 R ->> -% 639 0 obj -<< -/D [637 0 R /XYZ 92.6 752.957 null] ->> -% 139 0 obj -<< -/D [637 0 R /XYZ 93.6 722.069 null] ->> -% 300 0 obj -<< -/D [637 0 R /XYZ 93.6 697.846 null] ->> -% 231 0 obj -<< -/D [637 0 R /XYZ 93.6 630.21 null] ->> -% 227 0 obj -<< -/D [637 0 R /XYZ 93.6 592.4 null] ->> -% 347 0 obj -<< -/D [637 0 R /XYZ 93.6 554.287 null] ->> -% 348 0 obj -<< -/D [637 0 R /XYZ 93.6 489.076 null] ->> - -endstream -endobj -643 0 obj -<< -/Length 6525 ->> -stream -0 g 0 G -BT -/F15 10.9091 Tf 86.4 740.002 Td [(46)]TJ/F42 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Ref)1(erence)-378(Guide)]TJ -0 g 0 G -0 g 0 G -/F15 10.9091 Tf -203.265 -35.866 Td [([12])]TJ -0 g 0 G - [-500(J.)-450(J.)-450(Dongarra,)-479(J.)-450(Du)-450(Croz,)-480(S.)-450(Hammarling,)-479(R.)-450(J.)-450(Hanson,)]TJ/F18 10.9091 Tf 320.772 0 Td [(A)26(n)-466(extende)51(d)-465(set)-465(of)]TJ -298.348 -13.549 Td [(F)26(OR)76(TRAN)-355(Basic)-355(Line)51(ar)-356(A)26(lgebr)51(a)-355(Subpr)51(o)51(gr)51(ams)]TJ/F15 10.9091 Tf 221.802 0 Td [(,)-331(A)28(CM)-331(T)83(ransactions)-331(on)-330(Mathemat-)]TJ -221.802 -13.549 Td [(ical)-333(Soft)28(w)27(are,)-333(14)-333(\0501\051)-334(1988,)-333(1{17.)]TJ -0 g 0 G - -22.424 -24.84 Td [([13])]TJ -0 g 0 G - [-500(S.)-1026(Filip)1(p)-28(one,)-1199(A.)-1026(Buttari,)]TJ/F18 10.9091 Tf 177.354 0 Td [(PSBLAS)-994(3.5.0)-995(User's)-995(Guide.)-994(A)-995(R)52(efer)51(enc)51(e)]TJ -154.93 -13.549 Td [(Guide)-1084(for)-1084(the)-1084(Par)51(al)-51(lel)-1084(Sp)51(ar)1(se)-1084(BLAS)-1084(Libr)51(ar)1(y)]TJ/F15 10.9091 Tf 257.737 0 Td [(,)-1320(2012,)-1320(a)28(v)55(ailable)-1122(from)]TJ/F45 10.9091 Tf -257.737 -13.55 Td [(https://github.com/sfilippone/psblas3/tree/master/docs)]TJ/F15 10.9091 Tf 309.269 0 Td [(.)]TJ -0 g 0 G - -331.693 -24.84 Td [([14])]TJ -0 g 0 G - [-500(S.)-330(Filipp)-28(one,)-330(A.)-330(B)-1(u)1(ttari,)]TJ/F18 10.9091 Tf 143.238 0 Td [(Obje)51(ct-Oriente)51(d)-354(T)76(e)51(chniques)-354(for)-355(Sp)51(arse)-355(Matrix)-355(Com)1(puta-)]TJ -120.814 -13.549 Td [(tions)-424(in)-423(F)77(ortr)51(an)-424(2003)]TJ/F15 10.9091 Tf 104.62 0 Td [(.)-405(A)28(CM)-405(T)83(r)1(ansac)-1(tion)1(s)-405(on)-405(on)-405(Mathematical)-405(Soft)28(w)28(are,)-423(38)-405(\0504\051,)]TJ -104.62 -13.549 Td [(2012,)-333(art.)-334(23.)]TJ -0 g 0 G - -22.424 -24.84 Td [([15])]TJ -0 g 0 G - [-500(S.)-312(Filip)1(p)-28(one,)-316(M.)-312(Cola)-56(j)1(anni,)]TJ/F18 10.9091 Tf 155.667 0 Td [(PSBLAS:)-338(A)-338(Libr)51(ary)-338(for)-337(Par)51(al)-51(lel)-338(Line)51(ar)-338(A)26(lgebr)51(a)-338(Com-)]TJ -133.243 -13.55 Td [(putation)-284(on)-284(Sp)51(arse)-284(Matric)51(es)]TJ/F15 10.9091 Tf 131.984 0 Td [(,)-269(A)28(CM)-253(T)83(ransactions)-253(on)-253(Mathematical)-253(Soft)27(w)28(are,)-269(26)-253(\0504\051,)]TJ -131.984 -13.549 Td [(2000,)-333(527{550.)]TJ -0 g 0 G - -22.424 -24.84 Td [([16])]TJ -0 g 0 G - [-500(S.)-303(Gratton,)-309(P)84(.)-303(Henon,)-309(P)83(.)-303(Jiranek)-303(an)1(d)-303(X.)-303(V)83(asseur,)]TJ/F18 10.9091 Tf 258.865 0 Td [(R)51(e)51(ducing)-330(c)52(omplexity)-330(of)-330(algebr)51(aic)]TJ -236.441 -13.549 Td [(multigrid)-349(b)1(y)-349(aggr)51(e)51(gation)]TJ/F15 10.9091 Tf 114.383 0 Td [(,)-325(Numerical)-324(Lin.)-323(Algebra)-324(with)-323(Applications,)-325(2016,)-326(23:501-)]TJ -114.383 -13.549 Td [(518)]TJ -0 g 0 G - -22.424 -24.841 Td [([17])]TJ -0 g 0 G - [-500(W.)-413(Gropp,)-433(S.)-413(Huss-Lederman,)-433(A.)-413(Lumsdaine,)-433(E)1(.)-413(Lusk,)-433(B.)-413(Nitzb)-28(erg,)-433(W.)-413(Saphir,)]TJ 22.424 -13.549 Td [(M.)-349(Snir,)]TJ/F18 10.9091 Tf 43.142 0 Td [(MPI:)-372(The)-372(Complete)-372(R)51(efer)51(enc)51(e.)-372(V)77(olume)-372(2)-373(-)-372(The)-372(MPI-2)-372(Extensions)]TJ/F15 10.9091 Tf 318.187 0 Td [(,)-353(MIT)]TJ -361.329 -13.549 Td [(Press,)-333(1998.)]TJ -0 g 0 G - -22.424 -24.84 Td [([18])]TJ -0 g 0 G - [-500(C.)-347(L.)-347(La)28(wson,)-351(R.)-347(J.)-347(Hanson,)-350(D.)-347(Kincaid,)-350(F.)-347(T.)-347(Krogh,)]TJ/F18 10.9091 Tf 287.094 0 Td [(Basic)-370(Line)51(ar)-371(A)26(lgebr)51(a)-370(Sub-)]TJ -264.67 -13.549 Td [(pr)51(o)51(gr)51(ams)-395(for)-396(F)26(OR)77(TRAN)-396(usage)]TJ/F15 10.9091 Tf 149.357 0 Td [(,)-385(A)28(CM)-374(T)83(ransactions)-374(on)-375(Mathematical)-374(Soft)28(w)28(are,)-385(5)]TJ -149.357 -13.55 Td [(\0503\051,)-333(1979,)-334(308{323.)]TJ -0 g 0 G - -22.424 -24.84 Td [([19])]TJ -0 g 0 G - [-500(X.)-408(S.)-408(Li,)-427(J.)-408(W)1(.)-408(De)-1(mmel,)]TJ/F18 10.9091 Tf 147.871 0 Td [(Sup)51(erLU)]TJ -ET -q -1 0 0 1 276.516 340.765 cm -[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S -Q -BT -/F18 10.9091 Tf 279.861 340.566 Td [(DIST:)-426(A)-427(Sc)51(alable)-426(Distribute)51(d-memory)-426(Sp)51(arse)]TJ -171.037 -13.549 Td [(Dir)51(e)51(ct)-342(Solver)-343(for)-342(Unsymmetric)-342(Line)51(ar)-343(Systems)]TJ/F15 10.9091 Tf 222.383 0 Td [(,)-320(A)28(CM)-317(T)83(ran)1(s)-1(actions)-316(on)-317(Mathemat-)]TJ -222.383 -13.549 Td [(ical)-333(Soft)28(w)27(are,)-333(29)-333(\0502\051,)-334(2003,)-333(110{140.)]TJ -0 g 0 G - -22.424 -24.84 Td [([20])]TJ -0 g 0 G - [-500(Y.)-466(Nota)27(y)84(,)-500(P)83(.)-466(S.)-467(V)83(assilevski,)]TJ/F18 10.9091 Tf 163.479 0 Td [(R)51(e)51(cursive)-480(Krylov-b)51(ase)51(d)-480(multigrid)-480(cycles)]TJ/F15 10.9091 Tf 191.67 0 Td [(,)-500(Numerical)]TJ -332.725 -13.55 Td [(Linear)-333(Algebra)-334(with)-333(Applications,)-333(15)-333(\0505\051,)-334(2008,)-333(473{487.)]TJ -0 g 0 G - -22.424 -24.84 Td [([21])]TJ -0 g 0 G - [-500(Y.)-333(Saad,)]TJ/F18 10.9091 Tf 66.97 0 Td [(Iter)51(ative)-358(metho)52(ds)-358(for)-358(sp)51(arse)-358(l)1(ine)51(ar)-358(systems)]TJ/F15 10.9091 Tf 202.98 0 Td [(,)-333(2nd)-334(editi)1(on,)-334(SIAM,)-333(2003.)]TJ -0 g 0 G - -269.95 -24.84 Td [([22])]TJ -0 g 0 G - [-500(B.)-505(Smith,)-549(P)84(.)-506(Bjorstad,)-548(W.)-506(Gropp,)]TJ/F18 10.9091 Tf 200.295 0 Td [(Domain)-516(De)51(c)51(omp)51(osition:)-776(Par)51(al)-51(lel)-516(Multilevel)]TJ -177.871 -13.549 Td [(Metho)51(ds)-432(for)-432(El)-51(liptic)-433(Partial)-432(Di\013er)51(ential)-432(Equations)]TJ/F15 10.9091 Tf 244.309 0 Td [(,)-434(Cam)27(bridge)-414(Univ)28(ersit)28(y)-415(Pr)1(e)-1(ss,)]TJ -244.309 -13.549 Td [(1996.)]TJ -0 g 0 G - -22.424 -24.841 Td [([23])]TJ -0 g 0 G - [-500(M.)-317(Snir,)-321(S.)-317(Otto,)-321(S.)-317(Huss-Lederman,)-321(D.)-317(W)83(alk)28(er,)-321(J.)-317(Dongarra,)]TJ/F18 10.9091 Tf 317.503 0 Td [(MPI:)-343(The)-343(Complete)]TJ -295.079 -13.549 Td [(R)51(efer)51(enc)51(e.)-357(V)76(olume)-357(1)-358(-)-358(The)-358(MPI)-357(Cor)51(e)]TJ/F15 10.9091 Tf 179.356 0 Td [(,)-333(second)-334(edition,)-333(MIT)-333(Press,)-334(1998.)]TJ -0 g 0 G - -201.78 -24.84 Td [([24])]TJ -0 g 0 G - [-500(K.)-303(St)-27()527(ub)-27(en,)]TJ/F18 10.9091 Tf 77.278 0 Td [(A)26(n)-330(Intr)51(o)51(duction)-329(to)-330(A)25(l)1(gebr)51(aic)-330(Multigrid)]TJ/F15 10.9091 Tf 183.285 0 Td [(,)-309(in)-302(A.)-303(Sc)28(h)-28()528(uller,)-309(U.)-303(T)84(rotten)27(b)-27(erg,)]TJ -238.139 -13.549 Td [(C.)-333(Oosterlee,)-334(Multigrid,)-333(Academic)-333(Press,)-334(2001.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -647 0 obj -<< -/Length 1191 ->> -stream -0 g 0 G -BT -/F42 10.9091 Tf 93.6 740.002 Td [(References)]TJ/F15 10.9091 Tf 401.542 0 Td [(47)]TJ -0 g 0 G -0 g 0 G - -401.542 -35.866 Td [([25])]TJ -0 g 0 G - [-500(R.)-408(S.)-408(T)83(uminaro,)-427(C.)-408(T)84(ong,)]TJ/F18 10.9091 Tf 152.549 0 Td [(Par)51(al)-51(lel)-426(Smo)51(othe)51(d)-427(A)51(ggr)51(e)52(gation)-427(Multigrid:)-597(A)51(ggr)51(e)51(gation)]TJ -130.125 -13.549 Td [(Str)51(ate)51(gies)-369(on)-370(Massively)-369(Par)51(al)-51(lel)-370(Machines)]TJ/F15 10.9091 Tf 200.326 0 Td [(,)-349(in)-346(J.)-347(Don)1(nelley)83(,)-349(editor,)-350(Pro)-27(ce)-1(edi)1(ngs)-347(of)]TJ -200.326 -13.549 Td [(Sup)-28(erComputing)-333(2000,)-333(Dallas,)-334(2000.)]TJ -0 g 0 G - -22.424 -22.516 Td [([26])]TJ -0 g 0 G - [-500(P)83(.)-293(V)83(an)28(\024)473(e)-1(k)1(,)-302(J.)-293(Mandel,)-301(M.)-293(Brezina,)]TJ/F18 10.9091 Tf 183.276 0 Td [(A)26(lgebr)51(aic)-321(Multigrid)-321(by)-321(Smo)51(othe)51(d)-320(A)51(ggr)51(e)51(gation)-321(for)]TJ -160.852 -13.549 Td [(Se)51(c)51(ond)-358(and)-357(F)76(ourth)-357(Or)51(der)-358(El)-51(liptic)-358(Pr)51(oblems)]TJ/F15 10.9091 Tf 205.92 0 Td [(,)-333(Computing,)-334(56)-333(\0503\051)-333(1996,)-333(179{196.)]TJ -0 g 0 G -0 g 0 G -ET - -endstream -endobj -666 0 obj -<< -/Length1 2154 -/Length2 17514 -/Length3 0 -/Length 19668 ->> -stream -%!PS-AdobeFont-1.0: CMBX10 003.002 -%%Title: CMBX10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMBX10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMBX10 known{/CMBX10 findfont dup/UniqueID known{dup -/UniqueID get 5000768 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /WOELMG+CMBX10 def -/FontBBox {-56 -250 1164 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMBX10.) readonly def -/FullName (CMBX10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Bold) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 70 /F put -dup 71 /G put -dup 72 /H put -dup 73 /I put -dup 75 /K put -dup 76 /L put -dup 77 /M put -dup 78 /N put -dup 79 /O put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 85 /U put -dup 97 /a put -dup 98 /b put -dup 99 /c put -dup 58 /colon put -dup 100 /d put -dup 101 /e put -dup 56 /eight put -dup 102 /f put -dup 12 /fi put -dup 53 /five put -dup 52 /four put -dup 103 /g put -dup 104 /h put -dup 105 /i put -dup 106 /j put -dup 107 /k put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 57 /nine put -dup 111 /o put -dup 49 /one put -dup 112 /p put -dup 46 /period put -dup 114 /r put -dup 115 /s put -dup 55 /seven put -dup 54 /six put -dup 116 /t put -dup 51 /three put -dup 50 /two put -dup 117 /u put -dup 118 /v put -dup 119 /w put -dup 122 /z put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ=Ó%ċW˜)-{Ùr½uú•)Żœ‚ßröA•ÉÂÜE(ġ@Úŭ{ëı´‡ş“Qğû|ü_‘RÑċğ -ĜĈϤëA³Ċ -T@ĉ|ŭq|VkıżJ% qu8P˘ĝwÄGx³ĊŞÛ̆ÖċQĉŻ6K üŞÒ-UŒ\§Ô%ĦbĠ"t-*xÔġöÓŸÏ˙J‘+ -}ì3{Zà2ŽùĠzŬĴT2sÀ$ZġÌÑ&{Bè–J×{¨ĤŒß=מ7‰ÈڄĒĠKV"~Pr„İ-=›€Lż$ÀŸwc›rlVcÏN &'³{…%¨Gf“#ɨ_iùŭ#S’Xd+½ÁÀìîUż*|’:1çÎmö=â~6üù/ĞaÑGL•fŜ#ÚNOÒÍSĦ}ERÉs´¤{[Ċ˙Ħ.Ĥ÷-jj‡|Ĥtm\Ŝ:Ä x8PÎûbP´è“ïíŭżhÉ[µ°ġƒ_9ˆt2ŝ3“ĥ7ñ„,I2BíН8ÈJ˜ß0ĠmsUWQúdXì!ÑĊ?ÓŭíŞ?ÛQîì4íeR‹H ]ӊ.™p_Í?œä8îž:oé:·Uu¤D“Z[m™^/ÈaµÓÜĉÖ4—µlô4ȒĠċtL<~&Wš…ĴwLa9gPÁqháQ€šÎ ÀjvÑ)…ï]sħqR"ŭŻÇ…#üeîÀ·•ùŭZKPH‘rF›<÷EJ˘²ûš;àÑ.N~ëİ€VÓ°qLJ+_ÑjÓ´â -tŝYvKÙ˘½e\u™LQqŽ"О£tì–Éw;*Ñċˆl5 ż FF BWäú1…S!ŝĊ¤2*µìÔÍ`Œ8:XşòlUи„I˘ô?[wĞâÌc &Zç`§ÑİŸŜ° sdHeFĤ—'¸*sĉè ҁTd9ÔBaऋ‚…Ú[ŽÌa‘$–g²1ğüf\è•0é 7íaRÏ^(šüLj#Ë!mwŜ2ğ#ğnËrá$|‹˙ÑTíL”“]{ĞX§`˙ú4Ċ.G•wĥĴäÛ|Pĝ2BêgÜ´wóbkÀF°ž NĴ§fj;Žd?#l"+6ìĞÂgĉ{ùġ*ùŜîí—Ñ ,SQä2Ĥğ˘ûĴ&'¨n­\`²]Q‹„ƒ:èâŬıÂ6ln0b9†m]ĵñ,ë/Ú¨\Y$6[+UEŠ#Ĉ¸ŒMĦOì( ϲ.DüáLŻâŞ\ġ*á@ĝz3'§Ĥ&•6Ĥ„2—ÜŠż%+(•ôšk€`²Dßŝ/²È•k(ɒŽk˜pŻt`ö^éBú‡âĠħ\H~êY_öİ˒´ŝûc%À~(!Ú -Jv×s}˜Ç9qÖwĉà{ 6†ÎsΓM„™ ĝ&Q-p‚ç'‰&Š™M&²7´ı–tZßû\r|5•M§¸5"³‚*ŻżìÚê<°ŒÎ•DŽŒ³,ğLófj+”‘ìʽżËöëŸÉ"x0Â÷h#Ğßu[@Ú}áèÙ"փ -ÉdI‘E* , jżĉ]ĉĊv.Átxıİ ï’kEÁYl˘ŻĤ}d‡.-eJ ç³ÇġC•Ĥ=İKµD jnŻI"yX‡ ÜDĥ|ĝ&ĵĦˆġk>èiĵÂÙìx°ŒëbıuÂ?Ĥ†Ñħ’È ,™ïVıszÀ•üċAc ğ GÓ ˘Ĉßà7HŸ ğ`Ďĵ'Äĥ)r -şâĥҎ³ŸGÉÖŻ˘Z~›Cç— -‹U. E‹Cğá3Ÿ}Öhen–ħâE‘Ĵ!ùCü[xÌÍxnÂCq#µ#Tiş.ôiĝW×/ñiċ*ƒ?K`ÚɞĦÄÙŭ˙}ég;Îż‘²Ĵ“@¤½Œ>ÖHŻ€ĴÁëûùïİÛmn9Ì1™ú-‡÷ċ ûİ[’ĴíĊ çtj7 3ĊMŬyâzĤ„ĉ,á?Z·@ĉúRPBi>óäëïìÛvˆVFĠ\Ahkħo˜ĥàœ8™ïï*żĈ‰NIQv§94zğ˙‰4×÷m n8)Dêßb]Çٞ˙<ïÍU(gċġĜùŜ(¤`O2—‹ıŭ¤Ûzb30 Ëġ-TV°{ĵŻ ĝ_H^‡[elBÇâ⠗Žü4ŒNñ… äÀúˆı>>ż=eŸ§3Q“-š'0yÑßíİŸŽ#ġJW 0ßŬˆ7\û…t5Ü3”=ŽÎĵĜş¨ÂÖ|[Ršáħ>5I„ޝr·ġ xhhy!kVËSÈ7‡I ĝThÈaT“ġŬoëɁ÷„Ž( WdsUIĝ=ï]úәM|Óš‘dJĝ\YŞRĞGy€·4d(ßN¸{"lù\Š ]kÈ8V -™ĝïAï==Ïĝrġ Vä^ö*ċmxġ(e÷Ĵò=\ĈÊ°!ùŝ Bĥžb8€ıÑX ֙Mİ°½´Œ­Ĝ§âi -pŽà˜‹)Çrïİ  ~äŬ1óš Â׏š<;d,Ż^Ó6ċf,PÀpΨ|kĵR8ş7µô>i ˆˆĥħe ^ż„³œNÒ˘@ğ°hè`Ż[BF‡Ŝ,L%ÔmUœĵè´Be€ĵ*$°noxá3K ġÂóV$[˘[ÁŒŭ…˜fU;4ŝ‹²žQjıó’ú„³‘Šgğ‡g—ßoŜÜ !%UÀĵh‰İğÜ(ԝ 2ġèıן³żħƒ˘§, á´à™½O[ˆ’Î_\?ŽWtË<ȅ/;ı µ"ĉR­mŬŸ›)öİ›EŽ\rÈW1 ÁÓђo”y։Ù)B̊\@ÚgéŒÏJ?m Eqqٔ„ô84^ÖÑÊâżÑDŸĥaü97 ¤¸À{­É§›ĞZ!´_`-rÚlُ*ïğq‚›žäÙşĜŠĦt LCgÒ -:nbJ ˆúLşÄq”Çrçj5^Ä9ŞNRV³Jç­7eàòn²%ìáÏ°YĈ•uÈtÖ–Ûˆ4Ĉ¸‹F΋ėŠv’Q‡ÉjŸŝ’ú6%žc€#¤Ç~µ —ŠËOĉ e҉‘‡'aÙS1šòÏe‡ ĉÂF u s^i"éê…y´w,”µƒ~ C’~âRĈ’`ĵ,ŭj"ƒ+ÙÈĴKk Q5‰œÊIƒŞjËüE†ñbT)"†³>µwéŬvû³á|$.4ê“*@Ós?Û -iĝˆÏp´bĊâ\r 9AĞàZ<ùv+ŞÊŻLCäğ•Î+¨Û8–ùy‹.xCÒÙĈŸ&‚żU¨•}Ù\IċˆrÊúÊJg Àá:ĉÛD?İÊ ’(›òÁ.–ì5XR `/Ûú½¨{9`8à‹âÄÚFD&L‚Ì|_Ġŝ.ÉĴ ’vaêàSċ—;7U%Ìk;L BB`îtk¤} EÂċµ€\ˆHR ĈÍ"F™êíX°‡|ÜyÏïu~ċQhĞkżv4VÓ¤ éKWşÎ8ñ¨”Â3ŽûĠYü^Ĝ‘-íNÙ(}˜} Ġ“.ó‘WiĞa¤Ò„=wƒ§?Ğ~̜Z4Ĵ îîµïNÍ>x;ŜÉ -§~ˆœc/ HèÏĞ+ŽÌ%Bméĥ-7 žSš2ïŭ†*ñĊE”Çoq;żˆĠğÏ/ĉŽş6ê[¨ LÖîo¸Á·T òÜİĦF‰”²>=ĵñĜ8ĥŠ$žŸdċ‹�Ñoĝ”tu[´ÓQÍÌûEUÇ!ĊË\ŜswE˙óĝĴŻÙì6şĞW׍ †Q8 í³< %xl&§ -Öô­î~Bhâ=àF´˘ß"2\ı],äÓħ@re(¨lFç*ĊŠY7üٍÚĜ`¤ ħpS?%¸i|ˋùt|[÷b<ù7M=ùœÒ7sÉnµ‚ĥÑŞw24ŜׅÀd/bîD~[)Żùg4§Ħ3èŭŬG&/pNƒÂ%•Ù;­ĵt“ĉ —:Œpèê êùÂ}wMš/{ ÏĴ€£0.bİ—j!ZŽ@<‹¤ĉ ‚öŝzyÖlÔ)˙ŭ"² ÛġKĦσÀŬUmoҙîÙ2¤c—})€çz“à:<ħ÷ïġۄFù  oÂĊƒݞäèGLyÊTÚ7ò˙Ĥ;ßż··$äñ^Π>,Yœ.Fûܔ¤šŸ%”Gşj,&îU&ÎSĴŞ0ꙌИS­Íg\¸ÂûŠ™ëŬÑ+h8.‡!ɧ´?‘˙4}+ĊÌÉôĦ˜ïdCÌÖĦ;öëGÄ°£€¤ĈĊZ#A´’ĦݳïÒeqEı>żRLŞ ‚ŝ€KĜ@$|ÙDW­™‹Óô/PN³^•3*0KġäéÄŭÜĈ·)}ÓJéMg"Ò$5ú8ñ_gĞCs2Cµ7,KŸĠž?ÎğÎÏ) ĉ•ˆ4Ŝ úÜ1#ÂoşĞ–ı·IXcP÷Ĝ~‰·1 £éaò‚ä^Ċ4ŭÉ6Ӕ)jOĤÚa Äa ^oyŭ^ ĞÒ&9ߗ‰ġçÇĞ%˘ż<mLLN9÷y‰ë³Á†ì a×)ÏUü)D.?ÍÖÖ9ĵŻf4Rö2ŞïŽÑXııÌ w#_RzZÌu)qáà{ úöġ3hSìߛçPàDÊĊ’x)8ÓìÄ“%֗ÂċQ]<ÔoÄÌf‹~Öf›=qœ½·JÄĞĴD!ZÛĠKDÉÒcÁ÷ê(ċ<˘Xǐ.èHéı 3HˆÇ…İJġÂP7ĝ’•#ˏR+¸cUáĞTTá(ž)ĥüEK^dÛ%´À"òŝS‹.KĊŞŸ&|7q‡wĠGŭĜ›úž$àV‰ÑNĦĜŝlmÒ6q2\I†à—ŒşÜÍżì¤"ˆ@a3)Ä -  N7èJ7³Ôá17İċÖK´z*E;ßùÊÍ`o%sÉR?&%yÁˆŞXW—MVÙ°}CİÍùÍ˝gżèİf&,È\ĜÖïóà<\/Äì€Û´X˘­?6’oÏîáG_ŝŜ€ üÖm“öħğìNl!(Óٝ–ïRûÔDĠĵž]-‡÷äPóf)'ìvü4ŠÏĞÁEJVÎ[9żm;ˆìrr!eìÍì;´x^ÒîƒÜNƒ˜Ì™éĴ‘j7WĤê#›³Ò’Ó”×ʳÉÇşBVG(àiä[äI§WA<@¸è›=°6ö?ŻégŒ$ TÊGİëĦ0NsL5ġÙÎé‘LóuŠ-Ž6Ög_vú -LĉoEŻ¸Ĉ˘~I)´K!3XñÎw½ LQ÷ċ{÷Á˜tÎe”.öcĈ\-§AŸA˜Á'3MÉ|Ŭ²Ŭe¤İpôħs^8K1˜ûy*g/”ïĨÚ7ĴêS 9İ÷Í ÜrÍf!ƒ:£×wànÚ;ı• é@AúK š?gŽÂN‘q†ê—4²8)ďTÍ ĊcÀŬ¨˜RSıÏKÊÍ:ëk4£óÜS–}Ù;3<–Ûêʵ<ê— SU^΋opô´˙f"5@A‹ ˘ĉñbqê]öWÖ*VOM­tÚÖ,Sg__]µ 0…Šê-GÊXĠĝz³è+G|’Ħf_’r]EG‘ÛßaqۜŽg§m Ġ]µMn£˙—v(°D²/´ôÚLbĞé‹×dâïÙR­;ÛG›??aJVTáŝy^èÛ­˙·g£m~àš`²Z2Œèáˆ|‹{äAJc—QRĝ¤ qnd(Ŝۜy™ò·öoDÍ`TŞJCÜóH‡zRaÜôÇÓPü²ŭ£×”×ê‰ÊxĈœC@ğŝŒ“MpÎ<[0Ï?¨ŭeÇ;ZTêô+…İR[˘kĝgĊϧ˙ƒÑ”a…ż"Şq^ħbÖ°ßÙÈ *üŝìr÷ìÙñ|::·VNBOÁUzÉÜHbaGŻDHŻí$6$4tLĵµŻJbµ -ĵIîNIC֜qµa.K™,Ĉ­ >€C’y -l•7'žmf“ &´oÊ1Ċáİ:…ĉiŝ҅İċu² mÁŬeNπŸ™@1; BBûìî}Z(ĦÔP3À>f‰ä`ŞômwûyĜĴ²àż]“}L0qoáJ×íÇ ™ôÙïà4äŬVCBBİLçûxÍ1s_İĴ(\2ÊZäZ.ÓÜ -G?÷ŬâêeŒ´uĥĥ8é 3àp–ü8Dq,“Ĉ&ĝŬ[3M ôásÄtÖ/ÏŞÁ¸T ;çî’ûĥC;”]DDħu0Ŭ£ Ġ¤Qü[=z€ŝÊPĦ*KCUq’k ”ƒ#Ï?çkı° )M ñíûGR°ÇWI "RY7§WŝğÜÒÓêÖĈ°ë‰ï™0+@γĠTŬNTÇ?ôŒ¤ÛîağJĞxy~ı8Èupµ˘| ş?5ï°˙$[)sŭNd<#ŽŻàéUĞMÔ(8 ™bEżQëHċt.Âf6çìÖĦUÌĜ ǟ*ċĦxϟOiא`·r/\coωS:Ì#D÷=@KöAċ2Ÿ·Ĥäžé ­gLHmOÙ˜ĞŞ b9P ¸ûoÂÇ•Ñ -•ÉڄOiÛĈI¨Ä8žRUS¨y2ê+n!““%ôŜò‹_Ǐ›&áXŬˆ*zjżAç3”?§‚U•*}bœ€èĜ.ËyŜ=-^ ­KécƒŒÎ5ƒfJïàĊžÚĦGûQ"zZ°Âïž -6ßá>·Żu‹r+l³‘‡ĈW>ĞÎŝntq˘/˖ĉÊ. hÚşÌ² ÜG C˘ -À@?……‚§TW\â3'ĵ1xZNKžŬ‰;Ĉ—Ôn¨!A\Ÿŭòŭ2Àrĵ/–LÛŞÇ*™óQĜ$s2ꂇӊü;hJŸyİ}E í-ġM=ş>A9Jsĥ—•·3BĈÌÀK˙=h­³-[c´´<ŬŸù HÔ^tš|žŬş f?DÑŻ2˙V{D# ˙Œĥ×'ƒ£Ñ26ö:ûG GRĴÌğ\*ŭA•_S´…é¤F¨äËE8ş¸J–ÂÙĵT·Ĝµ›ż y_]äœ[wŠòœú„†ıC|îÔ$+[ĴÛħ`€”q{/ğé(àWBÎzg™û¤˙V‹½ù“Éž÷Á -ÙµH{ϗŜëGşFϔó$ÔËrĊ£â÷šTƒíx-h)ö'RÈTTFÑĞ—ċ*¨Hú_‰5ĵ£…$ĞŠ Äü]5“e腈îçĉ˙¤6= Fáʄ3ÈÎôl.ígèòZ´xH€ûĴ1 BĜğsM- W߀ċùŜ;‹–Y׀žmš%œÈ…c]÷{)D`?G˙bY²VÍö(ó9^{ï‘Ézۆ›ġĴÓ -†Ş“ŽĉÚËìŻżïŽ…C§W!Û´h΍ŠïXì0>b¸N¨ü벗“ÔıŻ#”š(‚¸ĉé'ÊÚıüóŬŸìH™ !èÌ]2Dx‡òÚħf€€Ô/ıXŝbg”y/ˆxA6\ş c4ŜŻµÊ,­Ĥ› 4+şÎ˙†E%@˅~Gñ<|t¨¤ËÈJĵŜ3QáftIĦW#DúX“”üŸL“ÀÍ žŒM˙ ÷“ím!0QÑĴ–žN£ Ôr= ż(ÈHŜ5_ŝµÁî×Îtç~”C%_Ÿ½ÜD‚Ż=,£N˙:}E˙w #ù!ġ½Ŝïѧ ›Ÿ,xıß@Ğßâż@Öżĝ£-‚ùIG‡;œ‘Í!EÛÚMI‘œlûF4ÓkÌ˘1µS‹Ì9cŭryž”PFœ= ĝ‡÷ò=û6I•nıpԍ́׀GèP~ĝ֎‘o9[ıÈìT+ -^@Î"_7Dž9 -ĉóy‘Öû½Xa{Oލ¸Á–-xGĉ#„ô½UêO´J`{ONŜĵY÷íMşf·íé2˙Ú$3h‘Òäş.ŞSĤĵêK·Œ†4Z!ŽB,X}ï„ŭ&ÓyB`żfoKJ5ôÂ*Ó–óˆċˌ<f™2jA\ütċ¨‡“f-s6ĤÊb‰9ı |³ħ:Ê#׍ -ğdŽÏ"{•#XY%  r)p;³…lä_²hœ‹ -L;RĴ%–)z‘7{Ĵ`\ıµvô |ŬçoÚ}Q¸˜˜o£ĉAP+ħiїÇešğèAn ĥ°6\oiŞ0˘6X5gï~;ÑÂÙ½)zQ_âˆD3o‹Á´óŬµM€êÓ4}N8Ó>Fšl#óm ŒâFGÏvá5ŭM4`+5û"ÛôŠ/qHb|-ô q„´EH?Z#Ż‰çoĊ!T>˙ĥÉ>ħgàˆ—ÑNĦÌG‚ìĜEÚ:-\2ħÜ΋0U´èXìÙh n›3Żĝï95ˆñ}ڎ‡0&óDŜ;¸eÁ½ĠıêSö›EÒlxS‰y–zš'ı?ĝb™ Ík·Í BdDŭG)S‹İ9¨+ŭ´GŒi–ċ&żƒ”}h⤽.Jˆ4ƒ¸Ċ¨ !Ó'ÂÇĊTZ&éĊ²ç•¤¤üÌÉ8셛´”F‡\2^Î Â—vż'úŜĠcŻ),0ì•s'œ‘“Œtoû/›ħ…›žµLĝ+.ϵväÉot~îĜ<°“,·ü}ĊÂĵĴ -#çHI¤jŭ0àu´Y—äVQ<§ûžÍVéj³ÛC¨Ç !áş -‘²ëÉ\'~âÙ`-t½D£w÷üŸµ8ŜħxxP–#K›^ç5°ô›†QV—ù¸ħZĉ—'Tá)LZsü%oa³êŽXŻ£){èÙ']ġmĦ.˜íĠ™ö*u–Z+Ĵ‰ŭPĦù´RĤwDáIPââµU'É€èĉñc’ÌD2Ës9ħRÈĜ7aJHâA1¤idû0ÑĈJ/P `ĉÛĥu‹óWI•V•>Ä,O„cÓ]ï$rtè<•‚^}`,ÒqÇşDSÀU—ËW;şÈ•Ií>ë?€e`[î îwú$­ŞŸšħ[\4 Ùm9‘܆ĊtšçVŜ3+ŭÒIĤŒè”Ċôtk NÙÇ|²‰BQÍáQŜl<..š³ŝ¨Oü;v„@û72ħˆ˜žN:‹‰1Ér_¨hwFM!Yu?UQċáˆ*ĦLöAÍìÖ`<ۑœ˘ˆœ ­Ú+Öİe/²§ÁyÄİX hQÏ҄°ĜĴdŭÇVl(U‚M àD™vjwSÏÏ32[S¤‘U3ÌPzB- -mÊÁĉÜÉ’özšYġLy(0ÒsċÍ>ŝfnûj×M/´^è Eˆ›Ŭġ…*‘‘ĵĴ` ƒƒxr|tLŒÙBCÍM_Ö ÂË%7´°>Epġê^qJ‰Kà_ġr÷Ÿá\´4N6ƒáóÎüğߑ“äÏ@G™İw`îgÔŭı/¸ĦcHÖ%3,[m$rGԞ6"1i - ‚ÌkŜ7'}w7İ£½Ù ÁpfàŒšíGI§èo~M>Gı°ˆŬ%lŻEäŒJlë„Q×̒òù`fk@Ia^Cƒ5­Hpİɚ}3B-8م—ùĴŠ+/É5šÛm>˜kôĊDNoÀy7Ğ•ÎXŬQ:íDĵçàñEe)ƒ›4—kıħa;ǘ":AÖ$¤6~ßÏs@OC8ëÌËf]÷iĤl˜ Ğ|˜'ìĥ—‡ÉßëŠcĜ˙M ‹âçè2Ó!;Š0Ĵ,ö蕞 C'ŭĢĊ"ä2Ġ(ĤKĥw+7@OeÖ´lĊÑIY~Ĥ Ħ'¸È‘\5˙–ÉBŽtem†w„”eŬölJĠĞà$’9drzÁ˘—l¨²ĥ Ld;ñı ‰qê ş}¤t°ïÎġÓŭ‹ş·_IÙDBŝˆcá´.6’šÌ~ '˙†$Vè1&ĜâĞTM;8  <2ä™,i $!xb,ŭTaóȗö%òú§BÜóĴY›?[unĤ`M’~h/=$ó÷¸0 (’zŠ´ {ŭe•=!ŭÏÈ,-½tg( -Š2>Z €ż7Iİé)Ï£;Ï˙ŒfĴ™ŻìWA'·ùÎ7ùR·ÓÉáÔÚË˵á7ô˘³ú·Á`‘ò“É•0 1çôb_“œ‚BÌŞÄƒ´;Rè$ó°•VÀË+=5=„†lH°ôÂ$¨e°=më.úĴXqíż”aĉÙP,ìé;Ħ2ÒÜLPó"ċb@ĈùŬĝĦuĊşLĜŜ=7GêŒI2Yı†ċü” Ĉ½iîsD­aĥ~qğ“=* {oŠ.Îġ$ê~éJïòàj“{*ğ³t÷5ñê#;è¸pÉrk7ħµÛÓħ£ıÙ+Ŭßĥ„Ċt˜UVScí˘ĵ™öÂíĉd*În+ĵ0/÷e“ÂÚäŻİ‚VîŠËzZfċİİ͊ÓȲŬx’Á…ŒĞĈZÇÀʐcw%`kx\-ÁÚĵN-b û¨T³ŝñ¤²ó‡]ÍŜ àËoŭħëÁ//Ĉ€p~/™ı’{×r˜GóB` Íw -œ˙ Ŭ6VPéE Ĥa&ĊúĴb_—ìSÚX|…ġaŽ?IÎĞ6ĊUnݎµ˙>î6ğ?rk„‹âNVVÜN38ğš& OÀIı;Êk‡ÄéáÑx7ÑßĴ,uœñ£ t¨ËèWˆ_Dô>Lùß3V˜˜d|{˘ÒPĴ<3@qKPÊ)cżé0 -dxW!xÖ@DP2îê›ġ>ŭe"tXĴ…˘™‡kĤBĥ<2Â]Hhô ĉ*¤ù -ob`"vıwFlß2`Ĵ?&ûŜvúŞÀuħa˘Ŭ(íĦKˆ RoŒ P ²ßÖĉ§Qŭ -Ĥq -FD‰F¸Ó/ŻvT Â,‡5›8Dŭ5”Żè<`QĞ6ó)ŠĜ`AŸ~ÍĠì¨pÔ*Ì:†…ĠÄ·’ĴgIzñtání7uĈĜïy‚JL”)äUԖ]ÍÙeşµ›Ü¤#6ĵµ• -Ħ3ŝÎR×8p ŻÎĈğ][ÖuŸôÙ`„û‡Ù•‰ÛÓ‚Ú -߃98î?ÎÜ/qÚDD8šÎĴŜbĝqU@ĊrJìSLĠUwŬéñt`ñ󸎗µğœŭû<ˆEŸüp Vĉ~ Ħ~cӇ2ÔW ٙkí…N!I„3§IÈ˘C¤á1¨Ñ ĝ]ç$½ġ7€jۚbDžĵyM꽌ŭœR áĞ˙mŬ‘ëİËÀüà}Ȍ³"üܽĝùŸK˙Ğżĝèƒ&)úĈâ°¨ĴŸ Y$…ŬÛġíd}d!nĜïíáħ˙ŜŜdÛ~¸jÔ%M}-Ƚŝŭ -‹¤ d›óRĴHôÄ-uÖaó4˘¤V5¤q^àş ›œê}³ıŭájWê1ßĵŸYp¸Ó.ä–l²½÷ -Z-O…v.CgŸ‡Ç‰…áĠÍğ¸‡_×İÚ2ûš_HJŞAEbL`~àĠ,äßùB*ωîĜ§‡#ċnYú;€öŻğĥ%Ç(³HJ'úBɊOQ*n “XYÊ쇙XW½;U`‡×F9¨ -85Ù½š°0bƒë(°²^D -ŽÙ—Òa(6TKÔÈqìÒ&[ñÒ|Áq rĵVT”U£Ó˙ġÈoù­KGÒġ0?à0ŝŜwh˘ÄX>›òLJ¸,vóÑ’k…é×Úîú¤¤âžÙ@éĜž ê°ÊK¤Ün˙ |Îvsµ(à ˆ]7Ĥ½H!ğٜРóo;šmAo’W^ğQLÄh)Y¤ħô~S!ŝ–—TòlR)ğ/Ÿxož‰ú -SZUíĜjwïchQ ³ĦÍZ]Ž8òŞ–Ò&™\zĠ4ŻµN˙ÀX£¨H W\ıäc°éš.bô :lúŞèĊ0)Îrߛ⠯`·ŸŞmŬÁuİiyñ1ŝ+Èq8HêQ­gĤ“âoÎÂÛÛcƒßđuÂéöI#YWĤRġTŜû=ġAE<Ö0ĵLlƒÇFàRİzSVqƒ=ċ(ù -ħ[éV—Ÿ*İSƒ- Ni&zzċd­o'Ŝ>  …wÁ7 Ÿ(Ŭâ ñûǔ†]e3/ò@AÈ·Hڏ;UŬQƒ}Ó `eJ—XHÎç_K½Aġ -ÀÍBż^lW( W@NeıwÉäÑpX{ÀY>:Yıü T`¸”“Iha³^†íá|­K|Ëj…İ8•›‰–C@}<¸àğW§†QܔaʋöĊYIöŒgrÍĥŽJ…`+£Ä£Œ6pM{Ġ%Ġp ³U›Ħ;ÄĈçƒ"ÛŜöàz˘Œúvw- }†:‰qkm!Ç˙1i­¸kŬ•'Kœ·MÌJr@˜C­ÜqX`ĵâd ħ›Š‡8]˘?7Áò’²ÔUwö}ˆmĈ?£`w˙¸Q[ċs8k܏ ûËàîçĤíä[ï@ôŜùÔ.Ô˙…>$žÚzhCZž 8 -ğG‚˜ÜŻB#£ÀSÓ3€ġğfû~×ïâÌ!S1W„CĊ/[şöš4uH"9›„³ù"Î ÍúĴïLé1C -òŸa8l˙ù…Žż}E,Wö¤šn9ɤ½×ë’ì·ñC_ħî™E ġ„ŝH’"r›ïċMŞoh“eÀŞ…‚Pc´éA'lĝĜ);SX͉<‘ÌmÖ£°6ĜŸŒeXb-g'?³½†R96g§ñDÍĵÏĈ È\ê$™ĊÍħòÍ ‰ßcú()IP¤Kk´íž`j£îü?ÈÛÔ`Ş™ ·€Œ$ŒÍT#Aó§S†QdN%·>ĝĤ’§ôĉ*³˙†@ V™M9ÑÒŬ’x„ÌòÖĥOÜÄp-<3½ñV™@–^Ñ(')`”ÎpYêĜž1šˆÊ™hƒXÍGÓĈho;ÜhË÷ž/lâxżê£t%HMżÍ†nĈÏ[ .`y îöœP(á•RóĜ\û’*+;'3Ĝ”b²‡)Û³•ZÁÌÈĵİĉc˜Ÿ‘kJsúŻŬżşÖÑÒúšÓ@û.÷B#Ïe`Ği¨×öŬ|S(Û ĝĞĵÊsĜ­KWšÄôıüD9ÌËk=ĜèÏ°€ıX4 L ²êRà•…÷^î8}÷|‚ĴZ íJg„Ċ”üs”3v@F6W !ž>?‰²ÖAó:Ż3Û­ġdقï|ŠE͛Ómj…;ôêWzÓm‚ΣC*rÏH]­“B·uF]ÖĴšžÌĥ]: ߌ_ñB˙¤ożù;šïÖí¸7ĉc‡î°p›ÔĴÚXò]÷Ä4Cux"˜1 ¤,6f ğ6m€xá£Q˙SàŞïŬMCe›ScjŸcĀr:İ,ĥivK`f‹lĊÀv?ıSq#—ĞB”1âîÇĦÖĠ+iÂR%P³ [#^vĴİÙG,Ğ\h1ñ QÂ9ĞÌà2CÍyB^^Z.ĊkÙ]°~•ŜB[ë³/+f™°– ħ^:¸€B ĞáD´|/ĉÍĜSepĞRÁ,3ô0‹ÈŒİŜÌLí×Â\€ĜşñžĜ?Cä1àK] Ùú)„ŽCĴĠJ^™˳Ġ–ôËĉ÷Ëĝ›ZšĴeĴÌĊäqwapMúà…éN¸ëĠ÷h|œ–ï‰%1–›ĦöÈ lwŞ}XÒĊuN–—"š§8… ëV}mŠ†= $k‡½Ò›öc ôˆQ,ú€˙JqĈw}äô o3k\ñşšŒ2QĦz›–‚“†ħJB[dŸTĜò¤0ŝG#9ZEWÜÄÉÁĦdg_Ek ıQΌ­ĦĞb„œÂ;•çäJ1š ÏÑBMvŬe˘ÎXvUS%ԁmD ß{ŝ‚…Cî@\‘NûÌĤF˜-O„xo›,zû”LÖ4•¨ma/`ôĴĤ{ĵ™ùPŻlm­‰>&PòɊÑΌ#"äGwp/S,˜<ĝ"jŻ7½ĊI§K‚. Aêï SDí“j€/úB~³³˙néȖÉċ -…ÁĉšŠŸeë:]˘dŭ— Ó¤¸ċ Ĉ™Ò™dyÎxÏΞgVƒ”ŭ˘ °?Í:ó"ÚA ĝtúœ¤×TğûÌ G´Ġ6Ôî|t œĤá{ŞŠì48ZG˙ŭĜVB÷ÜÈĵYEŞ™WŜ~‡“D™öHná F§vħ„ĝA•Gß/á{Á)šdÂfև:·°~S{KxÉDoÜ┋ÓŭwWğËy \FFÚä÷9:&ôd/éŽ0 ˙f:ağä#ôßvİ’w~ġ”cŸG†Úĥeˆkàĉ]c&‚d³Iĉƒ·c6ñŞJĞpÊ°-^şzûĉR§ÍC=¤á_Óş9T²ˆÍ23|œ.$è;ĉ{šŜb|ĥ‡‡>tBägÇ&ħ÷iÁöĊǀ -ôÜZ2û[7·0‰Ib“†]Tïm•ûSŭMl…ŻğSô#èùà£ŭ@ċŽžıjïÍRîħ²—zÍ´~ìÔÜ.żÄ˜gñĈ3$ŸQĴ4Œ°ğÂ^MM½ßÛÑW1€/ëħy0ˆĉŠC3á`xUëàž˙EB˙šçğÄZ9{3Ċ í$PŜñšêµİĝá ̊‰ŞÎŒ;&LĜg µĦ–K°ĴڏO6…È tìs…Ĵšoç¸F½î?AĊŠş\€ŭo -9XġĉpgCùà^û`ğ&3!Ċ,ĥ7ÎÀ×ÊfSJ Zc×?€gœJ°¨$06GŒ2G´^½› -‡A)Ğí6¸‘½+5ĜŜXÖzÖc4ʅŻtÚÍÊĴ´3è”ïaħ•Á–ċêÒäÑBı`xkóIA|ßzQŠxwB[Í>hé>< bc é˙ _ĝżŭısj0M9 µÌQD]7İ‘‘vĝsÍŬ$ğs5½!‘„yI•iç…òĠœ.üA7òĦù]Ëe ŭ@Eœw.‡éĊŬ<ócÒ!Ìî 8h³xàoóóÊËVË žà‘"lıù𣴠Aôìġ—’Q"Jùpm‡e×l<9&9p~‘NŻ&ñPĝ%,:¤÷Úħf€€Ô/#6‰_9ÎĜù¸rĊœ 'yÏ5eÍCÀ§DìÈÉctçúâ\Lä —ŝ÷˙î3ĵÁcê iÒĠë!½ĦaN€>Ğ{"°Á"ß2àÄÄO­÷ ?ÛóvG5.ĵ‰˜Ú@'t({,2@Ô6ĝ -ŒÄsĤ%5CšŒ€ZwI/pö`¤Ż”Ŝ°‰óx°ša>ŒI;µŒH&ħ[ì'ȓ]ŽK˙‡sĉLùz+0ΠVq œµ^,bġ˜êʁħÀÑíóĉ`ÁŸûÖ1Ú˙rÖGs=Bü‡ĜĴËÁ&"0ŠÌp_ËÛîÒûá9½gĵÂ^Œ$<Âġ7­ï+>rdπn–“X4/b´ïÁ2¨oîK²bîJ›ò·€9 CÏP[ Öòıù0B!ÉOYßœ$p˘WÖôšĈ°·Żw-Ïğê Ği´²JÒpäV# ċ7 0?l´¸§é½š§·Ë³Ï[ż2<ê³-_˛0;Ê|œ1Ê ĥŝ}ĥùìĵÔé_LM22żqNżR°+݁Ï£¨‚ED]Ö=€Ĝˉ>ž\ÔĦçeö;•w6鰉pƒ:ĜéğŜƒgáċÜu1²vğU §sbĥE„[ĦO–ĵvħDëĈ‘gµĤe65gŝÊM¤´Âhŝ6›Y!í²ĝó ì$u#½´Ž¨ ”¨WĜfŸ•´Ž–½êşŭàÒGêżìSlYf”ö.£]C~q1ċ)Íü?ˆx nSôô™V_şËœ'Ñú+ĦKJOƒ~A|ŜżÜcÑXîtô¸&rĵÒĉœÒDBËTZË0+6fo¨b"wŜ_ ^Ā9•·uħ[yû°÷ F -‘êßÖ9XW -4ğn8żn­ÂFçġ¤ğĞ$°ĥs2 ĵ3@$8 báÈ%· Ú[³èMFœnVĥëĴò11¨ïûT´u!XÍéŽġĥ@ÒÛP§!"IJŜG Ûşny~4‚ècÔĉgüa¤¸N9ŠşË;ÂÛŭeêpğĤjM5Fê·RGĥÒÔçŝ'ú{¤.}ìJšáËĤAêÄ×Ĉ‘ÈD›Ĥ2iŽ[}ËèšM37ŭë2°WOžE­ÑLÍÒ÷'ò‰Z‰Á°JTQMÚµgyäĴÉZé'?c^vUˆ]Èê{2Üë´.·ÑjóSba ‚< M7ħ°µ NĴJǛ”&4Íëŭ}·w+W²éEx;")p@ĦÚ\ËÈNê~ZjóˆEtWğE]QF†Ô)ĵA!ğÌÑñ`ey­€ĥ -5zıéEg·ċŝ÷²Ù½…†ÉvèŞUEXÍŬ‘ħċV„2lGĞÂ;ôïÇÇù—ÌĉнêéĈÑLˆmxĜµ.š°g„`Ï[aĵiUaċĈìVâD,ú“\ğîrg:ÁÈŝ AS´ìŞPz’ĴaCˆĉváûqİĦm…úvIFw…*šÛ>`)Z -¸Vµë^–àç_áÜ8’*Òì#@|—9Êm-ĠžnëĴEXPKâr:ĦÎ bâ9Èäô„˘JAú4}n@WVGäÍUӜ§9¸Òoħ~+]‰šħèYİbiB(>#q/h W¨tyH .ĉÔ9ÔÚEvñ`ıÛJ#J?n ^ÍИ+ĴÈ|\_Ef·6ß˙o³àDüŜîWŸFm(˘;„<°11áħŝh‰ŝ*?Ż)ŝ†ka˙Cc\ÇӀé™;guħXdôòó"2°œÂ1ÁÇ|Y%ï}ùê™u܅ˆQßŝħĝŬ×÷á8¤{ùKï”6MßZĴâżg*İÙ4"£3ÄĉÖ5‚1 yM§³vµ]o³áÛâ'ĠĤTĤ²vĠ;°œş&¸¨â½DÔ֛• ¨ -aÈVëRT>MñSŞĵ›L‰żĊA]„ĠfaŻ4—yU4ú†|-BİFÚĥĈ6á‰ÜyAĊEüsâ6oŽi ;X?]ÈY¤Ž*ĠĴ)‰Q3ôÀXäAvŠëàœ"nˆˆs’|À^†^­!îĉ'ġ’Bë×áĤ£9 úÙ§÷ ÈúüÈSÄ÷MDυsK`ÒԕRD„’ê(˙~Jâ#€ À@Ż"·Nş•S³ É~PÒc3ĵ¸ 1ĦA×zĊDéü’Ö`bĠY‘˘ó£ĉòGô8™[…\,IĈµ^ÍOż`˙`ˆ9”vifİĈšÌĝÈdğ ’yp—V÷R#FúÙXD&ßÛĈ)Áŝη/lÁp(’udĤ w½„oA”iûĥxçƒú3ĠLpAÖ}œÚ=ŸòĉZÀó Ĥ·)+x J€’n5‹‹ĉâ²&}>hÙÒ° éž²Óħ%oK)£²np#hĵ+l^pÄĝÄ?@ôü\şżQü“½€IìÄ,:ĤÉ ^îŜ눃0Ħ ĦZ<´ù*zg C*DĤߋQ­EÊ^K2 Š²[£!DÀ°êzPîµc(Mĵ}-úH”Íaw~ÍÎùĉÍeEËħüİvu£‡Pĝ,o+‹˙O¸%ˆää!tsœzGTĊ#ç3p[—ÓïYA£öĠt§Ïœ^`ë@(ZÜP•Sô’fË‘Ż}d¸“yJéëĴr8KIYxzƒ„Żží Š–™kóúMöÎĊ“t§7Ġtydĥj0ž^jN@6Á[­È¸aC“CUEP˙›€‚Ĥ&ñ!ñŻjĥÊ`ĉuôÊġ l2Ÿ­˜·mB#„Àœŭ[Yd°WİRŭ$$tğÓîÑɗ|Û2,p3ċĝÚ­ay³ûÂ8µÏü&úż\Ê'<d£úĉĵ3ŭtkFàvqzŸiHAkĝ$Ò6Ĵ;v{M!†ê˘B£á{vàV0Bl˜ -µ0 ¤=ú!€·|Â<=r{dÚEˆJĵ*–Ù4Ô&…Ue}À >OáÍ bóBÁnPş–ŻÂ隘!dn -ĵŬ j|s…oˆòÌ4Š˘ ċ‰‰’ŬEÂ9–ŝ:žZ½·ŝÛĈ.á* }ÜJš~?_y -¤­;­rŭnLŠ0ċŽiZzu“Ĥé‚™É=u'~ŽĝIƒAî PFAjè@éŝġ$–û ıÎö„ž×üuú†—3ÄÊx £àċqµX -endstream -endobj -668 0 obj -<< -/Length1 2180 -/Length2 15410 -/Length3 0 -/Length 17590 ->> -stream -%!PS-AdobeFont-1.0: CMBX12 003.002 -%%Title: CMBX12 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMBX12. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMBX12 known{/CMBX12 findfont dup/UniqueID known{dup -/UniqueID get 5000769 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /XCHSJH+CMBX12 def -/FontBBox {-53 -251 1139 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMBX12.) readonly def -/FullName (CMBX12) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Bold) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 70 /F put -dup 71 /G put -dup 72 /H put -dup 73 /I put -dup 76 /L put -dup 77 /M put -dup 79 /O put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 85 /U put -dup 97 /a put -dup 98 /b put -dup 99 /c put -dup 100 /d put -dup 101 /e put -dup 56 /eight put -dup 102 /f put -dup 12 /fi put -dup 53 /five put -dup 52 /four put -dup 103 /g put -dup 104 /h put -dup 45 /hyphen put -dup 105 /i put -dup 106 /j put -dup 107 /k put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 57 /nine put -dup 111 /o put -dup 49 /one put -dup 112 /p put -dup 46 /period put -dup 113 /q put -dup 39 /quoteright put -dup 114 /r put -dup 115 /s put -dup 55 /seven put -dup 54 /six put -dup 116 /t put -dup 51 /three put -dup 50 /two put -dup 117 /u put -dup 118 /v put -dup 119 /w put -dup 120 /x put -dup 121 /y put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ=Ó%ċW˜)-{Ùr½uú•)Żœ‚ßröA•ÉÂÜE(ġ@Úŭ{ëı´‡ş“Qğû|ü_‘RÑċğ -ĜĈϤëA³Ċ -T@ĉ|ŭq|VkıżJ% qu8P˘ĝwÄGx³ĊŞÛ̆ÖċQĉŻ6K üŞÒ-UŒ\§Ô%ĦbĠ"t-*xÔġöÓŸÏ˙J‘+ -}ì3{Zà2ŽùĠzŬĴT2sÀ$ZġÌÑ&{Bè–J×{¨ĤJ†‹Ĥf^Ö·>½aq4ħ!żÙ<ŞËÏáËé_CŞцcQâ%BÉélSŸ ³7§Òŭ1_£ -sQçŭz‹­Ôœrƒ?ĈktíP2‡™’l„ġ(?è‡è–×6Ĝ˘ĈĊ9~Ò'´’˙@‘Ĝ2bĦt[Á{ax í7ĝñ}ÏÏGnž[ôTYí>TÉ#aÊ1h!Ÿ;`ížWÈĈ˙k>ݍÑKjÌħßJżz˙Nžëcƒ?Ú^<ĉù@ à×qTċu„ĜdŞ[eюšj:JÁnËKûŠ#2S˘°[”ëĊBb?ÌĴM‚o„²7Ż¨aa¤–‰˘'¸‡gô§÷P:δÑİ҈ édŻBd’|ÑIŞî…H^wˆMĞÏe#DDï1Ğ3W“£À‰.ÌóżJ.6×Ô<˜TMÉì"µ>„r(ĴN‚Çž– âƒ#›>·ZjÁöh˘Éµ+˜UŝwŻ˙ñ -ü´$äâ\áWN.C(VÒ\ïNĉĉ ½Â¸3ÔA?òl_sÁİM†P·÷Ş ŽyfSy¨áÖżbàÍ`9upŽĈöPâȐ°NurÖ)L=uhݎĠ‚ÒÈDÎÙĦşÁPԋ^§}·¸ÀÀÔ -ä-¨ÎzU*ÍÛ3Ĵç~öHwƒzċQ:ĠÉğÖáÍ.”ÑcxşŞ£v—Ş(š‚PêŻ}F¤İö­>Ĝĉ˜•ĥ˜ċ4“ĵ8zeU+Jíùk <>,H~^ĞÈU>Ż~Ŝ~)9–GŸ-_„+Ïԇ—2ĝĵmšiĉùΝ1rħ•İìôĊ>ZĞîÌŜ?ώÍ8âPZmè#meDPôњ¨ˆ6ş‘”ù9Ĥv=hEÀ_X(Ĉy†Nĝ˜(9§çd5Ö<˘ŜX4Şğ5! XC›°EJöŽĞ·\ĜÔ]XĦş–´›üÙl*¸ÔÌ:Yµ->pÉ7ö•¸Lşû´ÇĜZžÇC~³ÇlġùġĴŠğd™1¤Í:/ú g!,Ç -½Ü}ĦQÎ+93V{ •QlÖëGµĥâ 7!;yq+áĉĞñ ÒJ´•Aë ĉv÷j/rĠڜƒZP)4°fÖ+OpX_ˆt~ 5–[RZ$Òı¤˜=#e@K*WĵE‰Żt_É-J½”Ç bΣ‡£óZdİh‡–²‹Ä>xNíİ˘ŜpsĤıGL€ÙOh>óŸÓoôÓë ¨ÀÚJ;J+\m -ÎJû6ÊÂkŽÖm9"N `DÒÁ[½ èh6w{Ac<=Ŝv}›ÌPCßÒ*Š|sAחìfKĈ+ô­1!­§“Snù¤Ċ~#_*†]žµ\i!ùJÍiœÊq˘mJ K³ f½ ˆy*Sù}ö‰iGV6wa·á$m²†v<zZQ^LĠç0NêRqšö!Û*7ÉuLOĵÎ=bÍ~îü_ŬJ ŭC‚I?<5ñ T zs§´í}uL`–MĜ€Ş"7žKÓ î÷çğòä†Ŭ8yO ‹{òò¤| v`)Â.D†3ĦÙĉ•K$•£è ™ĵ ,3²š–ÒŬsDğàÓR˙‰“ÂT ĥ€ÌcħĞ2쑃%üyD\M´S9HĜQĵĠrfôG§^ü\55‡•#Ùv[…YÏ´)çKäS^´~nı™­MXû,8&£7a Ĉd$ŝ—Ŭ• ^t/WĜyÏżżÄ§óĴ4¸QK{)Ù=ͅWDĵd>ğoeêÚZ›pٕi„-e@P’L˙b|Ĵö#p"6żKLPXËßzbĤŸZ†cÒ÷}˙í)%LĜKfO2Ŭâà (NÔ´UŻ-´e˙½rŸŒòu RĞıyŒTkl>ş'à²HíÓ Ŝ9т-”)ùżûuħ -Àu+l´dġä4µé¸zİcLs‡“ĝTJ[:ĴvÎü…ĉŒ?W‰Nĝ‹M*ş °NiïîLfófFÔ/§? £Ì”oÎÌ_aÍ! Ü âBêt]ġz‚\½›ĴŜ”R/™r4¤ëèëMú¨–Ġ›×FwÈïe5'Ž]ò´ZÀPÍpÈŽ××ĥĤrŻ?ÈPa„ÉÎL“'-Ċ -ÏcŞ‹Ü÷3G}Tç'šÚĦnÀ#È^>Ò Ö' -›¸€Ŝ€ÜFĝwMOTŻDsJ˜ËQş´úÁƒ{ û½TŜ·ô2V‘NsßҎûò%BƒÚhŒòÛ$×,áó>Ÿĉ‡óoéK—Ú"HÏŻÔ  ¸Ğ2ÎB¨UÍ7'Jħ(ĥïğǛÑò­c1PIŬá÷.l QÔjÉF%jŸ¨P´ -1îğzb2ÉħW€ŜM+mK·„ıĈÇf,"Ü/3~£ÄŻ;ûö–7˘/7Á­=Ëo-çR%€Šĉàn–JBĥ@nĉ˙6A0éÂhÀRF9°ŸTÖ {(˘&˜$߅:Ëôhż÷˙ġM˙jÀ稟 Ĝì%FV„˙ڈGâÈv·‚?`S:àë:JepRĈÌĥÉĝâ9›ĞŒ ËŬy?šO_Éĵ4—ü:â•ħbEç V]„1ĥÒVùb,ƒ"‡KoF0dbaşì˙̟Ŝf4G^ÌĴk’({çÍ:Ü -™µŝŜ]-eJ·Ĝb•ËcĠ?ħŸüÌhÉ÷s+΢ŠúĈ_µs›žĈS²è,at¨yiħñÑÌrŝı%´òF3ügŸŜ‹&˘M}ĜÛ¨È3ŸDkÈh`\Ÿrud>ßñ;÷iıA_î‰ -oF_љckġN›Ô‹ĝn`˘úv×Ġ)2š•Û™’ä$#í 6ùÑ{ŝïüĞçâĥ\FvġUìW ż€lî -%x[g´Ôí…j6~C ÔÜ"’’^klC²ïyşÜ%ŝ)%nĥWĠFœO/M™y­ÉÔç~óZq½íİÚiI˘…$ĤŸCËT›*xƒŞĊ]ûŞç–)ôiŸt4Z›–VÔ]mċ‰VӑÚOû“€ġĵ)giŝı -ò%-JUĈ [f°TX7Ô/.…c‡‹Uˆ,÷h7ï8M˘4Ïê zè9:̳ájŝmrvġ›PôŽ# >’ b€xòğ_÷ğĤËL¸ÄŸ yІޓƒ°ôÏ5ÑR@/{fëQCñ}ĞdÊÀÈ×ö~Ĝr³é!Ż4ğŭŸÑġğŒfP£o·í€żMÓ+^',˜î6_/ÛW{hĜÍÉïÉ/‰ÑšêÌjç³S}ÒŝíJ‡z Ñs†ŠĠĥäŠáÖj ¨Ŝ³~z›L{qA\RÒh$)‹:zNSJLŬyj^žÄ”Ç’µĈ)ÒT~KZAúP0‚JP~(>~9â&ŜvÁâ^˙"ƒ)½‡X5ç=hN҂aNĜ²İ%1âÖv1Ügv?ç€46³7Hö‘ë!ŝóµNôŭÁj˘âO4¨½ÙbŬ˙ċ¤ıtĦFòyòĉ³ċġñ&ï{ówQ[+ZŠJ’˘q¸ -+ıá@ ïmn,ßjMnEfI m ¨RGŻU­´YŻ8šĝN…¨£˙KŠ:]ĤB!ŞĊN?€JŠïç'×A.ökÀ{ĥüç­ác£†À+/lB Ñ~z…÷-ĉ  NœWWcğr酉Œ?ÂV,d€\$;ĤĴtTRÀ%M8ÁDì¸LŸsY{‰D´#4 ĝƒD{aİ\j;·$ndʟ'ÍÍKE –'p“ċ aÓöÜ_C1ÖdüÊüaEEÜ4"żĤ<[êÉĴ}7€7%Ĝş™ç€k/2Iĥk‰'­§wb<ÌB•ö|Ç;Y①żlÀF{ĜŞ,öœĉ9 -',>ƒlë£Zqq@°`‰C‹°î,6Ú|òUè²[2Çİ{ĝ¸Ìċĉ{ô_³ŠÛW{lĵ[À(ġ˜ÜEĴ…œ&´K!.0té)ĴfġĠÔó7•ŽlÑnšMwċX<œ |É żĝĦ¸Ŝw2#ğÊ:|Ëĵ6ŜĦ×4Hù°Ôkrñ~I„EŽmôÔñšv­‰Żb,Â[šxŞ‚áÈY…@·˜àrL·À'ú3Ë:`A7C~X+_ĉ˜R#GäAVÄt]ŠDŜd ´! Ö0€â*ußÛzôbä°‚˜°ëĞrYÑíĤ²NŠ°Ÿĥ%óÑgòÈUX&h͈6ĜOçóúàÔWÎ2ħ^ÚĝzGŻíü iN ÒÎĞŭŭyf½_S˙"Ù>û.g`öB6Gç -ŭÈëB•üÈdXġŽıXE}ħœí……ĉeWğ_èŸllQİ6ŭio¨„’F<³3ԙüZŝŬâN%ŜQ^wÎŬƒ‹{›&E­Œ:˘k= ‰éñšB¨ħ·I|• -Ÿ~ĠڛŻfKİikx îzÁmµ¸ Ó3úÙ³~mík -R£-·rğHħës–Ú‰ÚüZ§ċĴŞ.]ŝÁ]˘Mmëјrxĵñâħ÷ùÁ„{%ìu_†p²Ġ[ -µĵ5£~`3ë1>pßíaë­jûdoTÎÇê™&Ĝ]àżJ[Èŝ°Ŭ[è€@Çż&#F8i ^9›ĥ<“Œ„wÑe+Ħ-§l·½BĦdœ›vï>äBݐ2pá["ójÔáÛ FâS’Ío¨‡ÍaÒŭŠ9Ħú"1·Ġܟ›`I£C†"9<”AOöJxtPӞ#÷’lËy~É].Mż6xĜŸîĤĤ4{J…ÑâĝŸwG>·²xG@,¤ĥ…‚ty -àô½šŜďĝuóoĝŭñ1Hĥ–Š?$YMì;²oáiëûŸaŸ=ۓe•%§Ïù¤H-Ġ+XH² °ÈĠ -"Î'$w‚ŻÂçfħüÓSż"o3"fĊ• -?ìŻJ΂.™·~‚eŽÍ/@CíowK*ĝŝóĜÂÒVeMÛUÎÊô&~7ŒÜÑ;ŝV™–Ġè^İšİ"&%~ÇŜ·$ÀŜñ‹ï6Żĵ½v™%ò? ½Ëö"1öèß(ʲ¨v#òZŬ)HÙûË˙Ŭ2AݵòÓ{ô*5a4h+`K ĊüPġġċY"fÂgÊEş|·%SV>@9 iĠgÖĵµ‹f¸²××KĞxç§ôÒX\tż‚„²8³ß5?EK‹ê´~\‹ *â~Ġì:ĥQúöž&Rìˆħ½†ŬmFú{72ĥepU5ÎB–’<#$ċÏÓİÍ!Ö£'äÇ -öN°Ô'6meí“+2ˆ¤Éwà•nĥ £xÎöVż46NQIu–œ ˙+ÂËž2qğZë—aÖòĉ¤O3Ż) WœşİԐĥ.¸Gdçô·Ŭ_ĉ*-ĦZÖi0Tb™JĴİ›CZöfJÇÄszê³û½Ĥ—]‡d)}…ĝFê´ĉ¨3İ1ş9–ÊHìîγ ù9–{Ó½n ŸĤí¨›Ót€ËŞê"ޤ‰¸zèĝ`ÈĊfXi ó¨o5U?Ġ÷ƒEtĵġÒ_¤í4ñiñ=E=Ê·ÏD\"›T„)P˙,ÓHWP -+Ëù™B ˘¤vġ ˘}ŠnhÊhU:ÁċTÎÀ¨uj÷Ż{×ÀışŝqGI·hŽ‹j[$•¸„Û™Q0€żË!{˘FrvQm(LħÚĵsgżÈ ·È‚g–eiü@’µŻ}†XĴä­<²ÄÍRŠiq[pĜŸĴ\QX†úl¤j K··rKĝávö^8­gáĤ7{2v_ĥϘB¤”à1¨Ž3³üî7ƒŠ&ĉsf5ĥu떏W6ĥŸ4­U‚?6Í},œ†oëÒŬàp&>ŞešêüGYnL–ä+hòûŭ2ê î—Ò÷­X=­‚bWž}Â>RĴĥ^˜ıÜÖÂ*T-˙œ}Ş,†'ÀW{ûLñ_ä'‹ŭ³—b4!À´Ì‰§%y2Ñ—\d•`xkÏ7FhêĈ[ Î@‰[‰ ’0£½ŭû³{‹ïVĜQċ ›P!cänĠ@ħívĞÍ[?¤9à tñ1$ÂCRB2j­ëNRħ§„Ä×êÊ{ÇıDCJv²Ĵ@âĉVĤÙÏB+÷z•˙!Şy£Żŭ(×3,ıCşŻ‹éŜµÒ‘w[ ԝz:F>ÏekÇ´ëbókŭañß½{]9dz ysĊWX…2GìŸŬ|„:–ûn1Lë r"àèÚ?nFÄf?E=‚Q³iô]x™ƒb;²:–††Ó µĉÓ\à=Ž Ȏoµ:ĝĠĤ1TR╠lŬeĵI.˘6›1Â+Ì­6›?‚§&ö £ÖŝaĊâVPTÊ[£•Î*]ÈlöĠC}úQ…{Î#çÖÊTC†Ò ]_6¤i(ëççÑ˙cEиÙFb„ö,Š^ ¤ى$)Vİ^MĴĊÄÏڂ…÷Ê˘._Ĉ„‰nœ†!nĞ"—1vFì6!ώr]€'z_‰áC8*üÚ ÔŬݧĴSşó“f|ùüšá— òâX"T”Öz¤¨Ô<um Tˆ7Nu‡žéoİĥ ÔÚç†ânâá!s˘XÑÛEô(u‘ŸQ>&ıŜl>ĝ…#NċINtÓV-,ŒPv>̞}­û_ş!§ŭÀ÷ÚkÜ˙íƒÙvçKdı’µ?²*g”š QpĴ›’ÂöPİ–ÂÊp@ˆ@´:·;ƒâQaâfӘĦF>š…ÀÉdîQQġİ5§ù°5zNf€¸Q$pŜvâ§C6…eûZ‘œ×•ÔvSħlzP>™kğsĝxĉà€ĦÇYkÙğʙÓáIA1™ċ$z4éԈ·´šŭŠĝĝC"˘ê²ê˜îè?ÇkY'4)`vBz°TnĈ쁕>hŻ0-³ş_x6pIfOÑ=q@˘û’Òğ-nÖíÏȑï2íµ€q9C×z,>ùi½˙§@¨¨­€tŞ Ä€ŬÈĠħ†Òsħ!<3Ĝ&Lş¤'!sҜ4Ş*pĊ̃Pµ"'çE{ınĜL8Ż2İĵìҝǞx3}P/½?úôGišˆ)… £žeŜ'ÊġƒdöRñĥ ™ƒAÒ¨ŬĉXZ+RĤ• - âĤo­tQ)6í]UëŬ¸ò:ƒ† Ü)k\œî=ñ˜Ğ€~ Fˆô%Ĝ3àֈğíÀğƒ$œô'3³/€Cójô:Ĉra€Tà |Ca,´‹ëï·˜Ż¸j¸³|şŭ["-ı.Ž0WlE¤i3˙¤iÍrĊn+>ndêâ„`úwĤ,Y"D%E¤‚‡ŒnF’ûÊdŸm' ~KipdäĜşüJ 3 ˜3·?Ĝ7µ\/†žµ N• ZÚÌ@<ѳѐ·Œ!ٗ+³)ZI1 0àĠœĤ”!Ġf@âĦÙqÉdD+E)H5áV ›íìs2ĦÄġŞ° e=Ig\œŝ‰˙ ñôPOzHT;­¸Úë Ê8Ğêġ>ċap"PĤşäŽŠ‡=:}è{<À‹ŒĝDŸìÏ<$È-y…Ŝ4˘ĈÓC0ÌdÄHW΃f=PS - hËÇĊĞÔlxo‹êıÉpqˆ: ĉ°üĥ<Ì^M—Ŝ².ê8Û^P]ÚËYcšpŝȳÔÔ€ĵçcŭ(}) ̍ &IVÎckxÀÓÛz‚§yŝNÒ šh ÷FġÄġV°ƒlHöĴ×ĠŠ(Ĉuy$(‰/„sŝ‡9ÒÔ|C‰>À2…AüŽëzşN´˘ò!(Â3è–Şòq@ÖèıÒxsŽ,Ż -‰„ŭĦ/!-NşÊFÜ8{LN,˘÷‘UġëżòtsÜöBNŭ{aq#]2ŸĈÚ5şĦĝ§†a°#E!>b”–ö޳Öŭì:† -µ’QÑëRR¨zóÒ,aWcòRáœ9FRöK>İ RóŝÎV/½ê“ÂŞo=Y–ĝÁ§,]ÑìúßCv:‹¨V ¤> ì|´À뙤]^˜g>ž‰[‘Q”­EచȎ+<ü<Ù͋ĉz|,°ËÒ-½àpMC÷öy˜œÒ§^r‘íİm˙…Fw%Ù -̉·ĜÇäÌJ﷘”:qJ˘P‹ÌÔöî1%1mŜûù)h -.:zL,aÛ)[XвrPĝâÏtı.îöñdGÔo"[í!¨&ì Ĵù9şİL;ħĝ>%™óžpiUñáDɆf½š\R-ÙŞàŠûĈĝ8Üë„ÏĊĤ?ò|'>—Šü?aZ,JÜÓ#ċ3(™o.doċí…tĤÒäD£ƒ[HÈĵ֒ïú„†=…­Hl$Ĵ>}ËĴ9Fİ–ögĤV1Ħ ˌëK°JîÎŻù„uÍĴ pöËV?§ĝ\ë>Ù!ħçÈNĠKŞĵ\Yj Nh†e ™O4[2 i2Ûp‚Ñ2 İE|äJPÔy'³ôè,Xú’żèıw š`Éŝ…Y˙ß{šž"QŒ‡f#î”6Ĝ!zÊÓûĤ)ħ3¸Aç̘r™9–bm‘ò¸p-ö eFOôŽâڊŭ‡wıŬm‰>Lú¤/ŝ÷”H²gAɲ2l–Èĵâ6ñÎĞôšżş†^›ŽqËYÍà0-H‡ÁGkǃï›Cê“5ĵ?Nw[^=ëiŠÂBäĥÖYÔĊÓiègìiR˘ Ĝ!Ú)ÜèƒîĊPLœÌġ<ħò´9~€ßRpµšíÏ ]Ĵ9í .|)Ûy)†düÛÖú ÔïO•€żßsâï!o{*ÉW;}€nĝË·˘ LMRíÇŬüë"ⲉ²ñÓĞÒL´Ÿ€WUê ’VËë…}4‘šœa²ĈœşO|”hÈÑKtdU$À mêĦ:{84;íğ–™~·L¸Ô÷Ó0 „ù–Ċ|B²`M4“çyÈg‰˘Ż:­ÌXÎ̈́ĵı„Š…¸MzíĊAPá„bÏêjK?Ÿ¸À’”ó”‹2Dcßvg3Îӌ|s“>ġ8™,Ŭ/" -b{,ÙÏûâO`X¸úR8µ­îñ5¨ħUQ`2u›j#@~MržNµ8sԗ<ù ·”cŞù„n¸Tùh§ŭóR ]³Şû²>ô9œ>¸;ğâu³#U-*‚ZhŭÍ û£"Jlì ĞîëŽ(PĴ²1ċf9£Mž‰`Ĉm. ÷C§(ÌiÎû•Òu6Ïr›<ÓïĞ'Ç9vÉïGé":Ž\È0?GµŬn“pċŠŻÀMea˙*û('­='Íû·tù!(ŝJCÀE²"4ş@&ş6-ŠĥĴ(ğ$Q ŝy°‚)Üb=OĜ /4Ó²5…µeU{'*ŭĥ éb<5AšËyz>ÀµĤċv46œK)DˆpjË=âŻüJ@ -qAò´(Ŝ²_FM½öO=uÎ]ş‚óRĥ"Óħ­Ë{ĴÓŝJ£u?,şñì(/ş_Ê\+ÇŭJĊ˙•ĵ_òò^OXµ€”Ż-ìcTĊŒĤ™.¨ċ+àS€tzìBÉĤ<Ҥܤ]|ƒ;ĈRċdÊ&+ -ËŭÇċóġz‘ÖÁ|e­r#ż;‚ŠXÙJÔ^RÜßÊĝó3{ÀĈ0UÚp¨AéíDžLİ[É*ŠĦ-†ƒíŸQïÔÁƒ‚›ña³Ĥî^ÄN§~•³Ò%p†Cw Ù´+ş‡?½íĈÈëċ]ÔsnŬ5`v>³wv-.ş´ĝaˆ#Ĥó÷wq8+”TRż r$hŜ_l²‹!áVDµŝµ×Ĥ>ÓÉŭ›¤şÒĜ?ŭpô“şD^RA&­·ŭ~ħÎ=pâ—.BOXıY3Wç Ñ6š)iÄ&o *ÏTHm}ğrRäú6ĵ§MhĊ/ġˆ”ìB˘gıµÂG·–‚â!3İ…ĞL£ÔGÁœĈ‡myçžÎñ䀤%‰˙̐|p³e³qHhJ<ÛöÇĠLf_ŝy"Ä'WîĊ>bçzŠìr³;}Q0ODìÀ*êÓÏv‰,ĉf d4ízì—mĉ}SÓÏ ­ßîÁìAéz›—RK%RĤv.Aùgí4xçöä^,ĉYvX‹£àk_2QHDÄUİ´Ş‘̆†ë˘Zow%]íäjêœÍ!ġZvÄT5¤#:]Ö¨G^m>/”f•Lu˜ĉh0ĞġŸ‡‘§6Ĵħ*ĉTŠsŽĞto'/,ÊE\Ÿ‚ŞĤÜŜ#¸í"ĜùD›vˆ~0XµĜ·Ĵ‡U½ż)ŻXġµ^˘Ÿ“§WD:ôħ¨ësıÎИċ ”lyĠËyXÊY, Ö÷gE8—¸}Y{ZŬ>^‡QF_q&˙Ï8Ž÷ì|Ĝ —>§ÛÚ¸sï€`rYÒÁc­°ĠyŭlÓğ×öb˙ż’eÓ×e7”ħĵ@AvÌ2+4ÑÎc%rĉs;›ú U'‘êvˆDĤ£†:_{絝•Î% W¸A[ÖöiY\!„êŝdÍ -Zé3‡qišìì8֊td9(Qĥ—œÂ -˜——C %¸ Î6× bĉ aT÷xE´ëksxû~ˆ0ÙŬ‘.n‚CŒGŝ áżAĵq‡ÒìwÜ4á!ŬiˆĴBç…Ev˙6´H…˘=,)êÜĞòıЎ—oLöZÙäáϞ¸Q‘˜· X³˘ÌSİ69™³‹bbżƒżypşw˜¤ŽWaÙ -{@×-6ĉ6-SŭXÏ"ëò>"pÌ8oĥ½ÏZ,à×V›Ġ¤Bċ›1&ċ4Ĝ)ğj³Ïü$äP<Ħí/Lo<pÌ{ˆ×šbIlÊ#ĥĜ>áULÙÄÂ\MD‰Ĝ×áËEŸİsšè!Ö'½Á$.[rENÂ-ĜĊd?=Ÿ@ŸŽNsì€×ÊÁqGFÚK³3Ċ¨b´ĦÖ´^úĊ•Œ˙L&ĜĈj` ž£Ĉ³½?Ê”Ä -È֑Ï\WRĊ)cÎJ³K)`S{ò&żìÍ[–yGnâ{ĠÁŝ˙8/§˘(1&ÚŻNA>cSĈr ›áe)ŜôĜc Ñ}œû—żŞ•—½Ñîĝ‹žä|İ7ġ}ĴRŞ€srمǤ´dÇŬN+;ħNtDŭèıFT`Y×Ôeçùä÷ÇĤ6ġ­•Faq‚-\‘%a~ġPޏS²ÌMµ1“€Z0g=8-="Í+W%~së1ˆfTp­żíŒ’;+ÇÙBX„Â?׀ñ,à~… ç¨%áŽâhœ’í€ħo!]B{SƒÜ²èM‹‡! ÂżyJóñÁQşGüĦ;şŝğ'‹8Ä˙ïÇkf%½/fuĦ à”LŠşl²ä£`k ¤CË_–vÇq·‚£”Ê·O`äñ 4ĉSPé!§ŬC„„QĠü m ¸ZŸsÍîÄ*ĉ(}§ ŝÛ·÷½w´Á8QĈv0앨úDÛt‡Üçíßy$ó@£áj÷wi3sÏg,Šù³'RŠÚ£I÷,÷Rħ˜#cĥßpwVKEêŜ:á‘ĜŸÈġjI”÷û}Ió˘VĞÉ…]DÔŝö ´ÜêIĉêqû^uU~ù,żìoVûFż›EX£.p³zCAğİLĈ·#‘ĉ‘, [ğ?˙v ż/½žzmêęM'S"ŝ³½ `Ċ͚CĥÍİ°^ŻžíKËA™ŝ‰1J̓Ħ×2?›gR­? †Ĵ²|ĝ"Ġħòá1ÌrĝA/RïvÌLĠ -Óŭ†nxz VÚ!jż§ëäQ;%<—T‰İ'À§Ícùlm´ǨΧôÔŻĦ -'˘P•†×ĞjJKk_^°Ŝ á¤Êäŝ!ԑñhnĞ 4;@ĝAëñÁ:8Ŝşnì1^Ò6\ĤÔ=ç%ñ§AĤOA:*&‹Y|n(ïÊntö–Ñ[ÁJ= ´ï‡AZ~éúW­ŒŒ PDvˆ%ñŽz„ó:2Iš‘|cíŭG(=ÏşœÛ‚VvÂb˘À½aÉÚ¤ĥoíëZé&ÎM§ıq˜&î&Ó(–Ê ĠÏŠÚ —Y\0‡˘"sJM\˘AĄñ—ëU^ÊħÔ·@âËĦĊKRÁŞá’¤çZKœ‡ˆ#ġ÷˙ŠC*ŸÊ+pghż°\ÇĊd ÇÛ-J ìCB˜óĝÌŻˆ˘â"HğÁxŸShY³HŜ$6óàwvڐg7—Èx³âqN_˙ƒÛÍĝ+Ŭn,À³`s(ußµIj­#!6÷ûi&y­£ÊAŜÄĉ³ŬÉ´öé†˙G"§R+b ¨áéì)6"h gÀ°³ŽÁµUsŒÎͳ_ġ}àwqxâĞğŻ\´UêêMɃĈˆ3ÔoÎŞ´­0Ĵ’œ >'—­kÊŬĵ*ŝ“".T1³\ˆ·ċÇÏZMĝÔïÉ˙â/44öĊNŽpHGë(`nüQóŽf_›t1?hîMŸ˙ȆŞĴ1[(ŞfÚ}ĜFT›µœLaxcz³viàmaµœi™‡+²Ç”qôıĥ„ ìhs]àŜĴè(ċÏšD²ĝןJö™W1ı$ö„ĈUÏËMġħhO|Ëà,Êp•üÀЭݸàÙN\Úß<ôó‚¨>AŬߚQj^¤£/& ½:şšgu-ç3œĴ`{Ï÷äĤe>‰İ}Ñnßë:ĝ²%Iי™{ċ_ÌIġ#şÚÍožëä”m°m;ž -ìŸáé’½; ŒÎSßfL˘ìhÚqO “zJĆNŠ²aûĵ¨£x½8^fĤIš+ÛE<™%ĥ*”_żp'ŝÚŭÛ(3Yĝ“ĥ™R7½3ş™~(ħ‚fXĉ§HŸƒéĠœ7ĠĈ’§†çŞĝÈĉ°g­—ûNËwiŒƒ—Ĥèŭ6ÀÚéĜäPHb% ĈL‹xĥ£D@Ħ‘?îjŞpĞŭŭŒ[çÁĴ:İ•s•J¸U£nÊ:br -gL(HÎ h‰U˘QŒŭğŭ6Â0Y”3"ï\d7Ğeˆëô1‹ğ½ŸŻ/=ô—ïíƒOÏê‚D2@vyšêŭŝ/­ŻpXF=ëT¤bf¤µ2yÀ“ (04iÈ}ÙlHsî7MOˆšaÒî?rˆdşz/€Ħñr’)&ÍDu9tĥœÀgxĦ5Ÿrı ŝ°èniüû„¤ËgqĞ­h޽ žÖÍïó¤ÊXÍà .|‘ˆ! 9ïĵcw™ċċ ɛb°úRìk†ƒŭîˆD×]ğìÖ<ˆÁv7ċġǏ •ƒ0Kyñ—7ŻZ9Ŭ9[6äÔW[˘|ÏGvÏL›K÷ì۝*/‡÷p_7›–Ug^ßÂZŜ| ôĠíĵÑ>ş -÷ğ¤k<§h‡Ë“לĜ~ŒNüç0ÑÛUĈĠyÚŬ-OlEĈpTŒd]ċ32ßĝ4š…˘JJ ½ íÙ!aûˆÀ#,’Şû”Q‘˘÷cÉ\çÀş - ŭŜ½6?Ŭᑕµ1üMşúħdÄèí—‘ñd×RL‚2A³P~ħ:kOıñƒ–ÏŜGWß)ÑInZÈ:ôŜ×KĠKöÜmSĝÁħĦX@wyË Ż_ŝ.ĉ6Ĥ›Ù—żî,ŸŬo†§?ÇWZóĤ áJVŝìàŒ1‹üÂÌĜú¨£mBkı33(„“ħžb[&J÷D'}TŞ0oÎÏL}-žï{Ĥuûş ˘—+ÍĜ°ŬqÙ`Nf½P°ú´†+IĊñô£IÀ$°ŽïKœ"Ŝç”\aüÍVÎs4(+pZdxv‘jŻiÏċs*úo’²Ï--‰wя˙iAÑâ¸ëPV -qéɞ6é¤Àtx3U+i‹dsùeÍtqMĥB—q=[P½YâDàĤgş~f>,ş:è Œ½/òm•p'•¨Ĵ Hbà7Aä—1Š‰íħéĞq[e[ɛP`D♈×azı‚²ÖM4û—0˜œbN|ÚMÀ ÏßY<ĉQJÊG½É$MxġșÜÏ/ÁÛżĠö,ävô—{Bèêĝ“öEÏ'ĵÓĠV+aú~ N"ÓK-óğĵz§şkIB3[]E[Š5–wÚv­“ƒ|?î1EĴ`˙´ˆ| g!&6ĴġàÁ]#ÔÔ&_MÀ½ÚòPw.t ŭ­ÄıËچúS“ÑVHïŞé'„†’ş' ícĜ…é?‹Tpüt9K”2ëôĜY  |Ğo‹›ûèËĠQÓëġó%İpe2kÉİFfSĥfô‰‘S/ÇrާŞ$ÉÄÜĴŬ˘wóGÈ3·Ĝñ ™˜%ÜMXú6 Ñş˘Ĉ€ĠĴÓCÛ·!$ëÚ q;İ';˘ -óUléX&_H7˘“òÀK(C~ĥ@hĞTT ÒEIG xħ˘6²Ù$a„mÙD͑6MÔzÌháÉŜ¤ÂbĥĴ7‡—ĦÓ[Èĵ"äà÷ٔRO¨ıkQpD߂X†›żžYÜP†KL:&Z’ IZ ĊĞH\£’´ùžE½cĈŠ9Šg­/ʵ,Ižkž™Èî3‹Ìı’·1Ë܃ÇzZĉV£baŜw )!vŻ 1ôrœu|[·ĝZ9żZ}´+,$xÔRĵKŜƒHœ7ö§²jR—…[UçâÏ -endstream -endobj -670 0 obj -<< -/Length1 2067 -/Length2 14426 -/Length3 0 -/Length 16493 ->> -stream -%!PS-AdobeFont-1.0: CMCSC10 003.002 -%%Title: CMCSC10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMCSC10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMCSC10 known{/CMCSC10 findfont dup/UniqueID known{dup -/UniqueID get 5087402 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /EYIYGL+CMCSC10 def -/FontBBox {14 -250 1077 750 }readonly def -/PaintType 0 def -/FontInfo 10 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMCSC10.) readonly def -/FullName (CMCSC10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -/ascent 750 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 71 /G put -dup 73 /I put -dup 76 /L put -dup 77 /M put -dup 79 /O put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 85 /U put -dup 97 /a put -dup 98 /b put -dup 99 /c put -dup 100 /d put -dup 101 /e put -dup 56 /eight put -dup 102 /f put -dup 53 /five put -dup 52 /four put -dup 103 /g put -dup 104 /h put -dup 105 /i put -dup 107 /k put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 111 /o put -dup 49 /one put -dup 112 /p put -dup 40 /parenleft put -dup 39 /quoteright put -dup 114 /r put -dup 115 /s put -dup 54 /six put -dup 116 /t put -dup 51 /three put -dup 50 /two put -dup 117 /u put -dup 118 /v put -dup 119 /w put -dup 121 /y put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ<ï˜ĝX2-Τ^tĊEÒ_á’SœÚKŞFÙÄ1F^jżNBqĝžŜ×ó{ä³´y4ö-FègbÖ˙öԓ{÷"Ö¸ĦW–B:§rĊP‹À ?dgĊS%|'²Ĝ“w&¨F7J…ĵNÀ°¨œL9VìâRtıbÈTċ5ô'ŸâmƒŒ\‰—Nš"K<ù -’wŻàÇÊÈÜÄÁ‹Jv‚ċ$†tE;ÈD4ŻVܢüŸ§vëš{bG@ëdĊŞ,ċ|e( *VßVÈû:\Ä?)…E™í¤ôeߘʴ‘aÒ.†zĞbQ¸’Ŝ*%–EJÊçh…FZ€ççyš,¸ġŸÙĴ‹dw8¨ċw:GIà Ħ„z:X4(Ê·Ù‹nĥAï˘N;H0hA²oé˘i.a)÷8êMaÈßç4Ä@-ßĤóóé~)Ázavŭ”³¤¨ÛjFá·Fwö]:˙LE_”Éĉ;ÇĦĉÍݐµc<(ŸVzÜ5ĵ„?Êú™<{STdïÍĝ#׍ZaĴİk²öŒžÂáÀü„cŻìZƒïJĴÔ<Œs‹´Éóò<"Zd„{OĠ/öñËŠm‚v‹;§dA˜˜hE_ŭmĴz*Ż&%f£šƒ.DrkŒél÷l°´:“ÈFXPÍLğÚWż5é%1šJ|ÎÁÇ~"‘)İş&9!H,Ñ蠙]„ÉF˜z²QĞE?ċVñĦ,Ì_?•3{ĝ·<ÊhÛ!5ŭ™.ô@+Çc3J˜×ĈîÂé!àßßŜòH˜Í•w‰ñiüÀî_ Ï,ĝTaĞğ‹‚hݏ3Üà€ċŻ4*ŝ´ ïÓş(f4Ż÷8šžzÜpyM”띔ôuu°–z„ˆhY\Èäf~ù•WġċQgS"GjGïĈĞ(Üî|OhpŭLg6Ì}cŬÜoˆ˜áŸ†nD2ĉİe¸i4A‰#7†Y‘ôjċ³8ùġ‹G8ñ~ŝ›Gñ¸ğÂş4>jĉ1ıĥ­4âS/cYtŒ›Ü1Ÿœd˘÷b,0 jġ4À§ÔïڕÑĉĜ†ŜCyÉ-‡%ĜX£WN²2wQÛRŝyCOE„bMv_‹c[d™xt˘­ï #†;œżĵ †Ğ8Ê@ϋ¤˜×ÈE Şŭċ·z"T´]ptX_+ċkäK’‘—żè+¤‰sŸÛ’ŬWǖÏŬIŻMñWXıRıè§ĵž*;R ta‚¨ÌÍÓéW`4bàúäßÑü_ŝÔżPğĝ/`µÈ|ìèô÷v—ü˙4¸e4UVhĦ8R'|ÖÄeù‡$EŒ&ì)% H2ôúN]èpGÖşó°·m}ï#Â÷ĈôĜ{ˆtĦ$‘ µ˙zĜĦ…=™[|ôâ;żÚ!Ψaç-Dâœ3Ù VzûŜĵèڈ‡L4Ĝ½~Ŝĝĉ—¤(›LˆĠ(:¤k"HP£wŞ5WvX ³!I×66×Ğw/òÒlgj a+œ„U:Â4_ħöECì‡˙À‘;V|ǤùdŞşjBĠ–ÖğdK[ż=f ¤'Yu§ŜWÑö,`6L -£P:'Ş°jMÀ]ŭŻ?gzàÓj– §ŸÒğùĉ—MàŸí/NQÇâ)d>|tUUnXaIuyt—Ĉ|Q·ßû?]!H&kO­pÌlò(@NÔNgt3€Ÿ[<Ñıû† ÄßdòI>³°Ñr%ÊàTñŭŝëô!ɋ$fè‹ü³İ2qŽ…uûÈwĈÄĝŻĵ³uÁRŠ*ÓÜe6`ġŠ* ùˆÇN„mB²Ğyf­v.óu+îÙ"û£| ?.XÍ"Ħl'êËžĠ~]ä/rÔĝ†]]/p˜ `´ûÜp`ËJ+"}ġ•÷µ*֗§ĉHŽ4% û Vbáàž$Ŭwùĵ–ĤփRĠ -ġC´ĥ–rUhĞU<ôáÂ[µĤižÇçI0@Ŝ mŠ*8ĴƒżË_fü/ñ3MċÑ -*LĞc6˜Ä½}nĠ²$S•‚ŒE‘UöKÌ _Úoц"Òâ -_Ġ˙!›XAġ—cÇŞ—†ġœŬ‰9q8͂k†“ôEöúŒBÎ,JèclQ ĦĴŬU„Ş•cşsCĞ­Eĵ:)iAH ñRp‰$_ŸC-G™qµBûíÏaBì/"Û)G âbߌ.˙ >¸'‚9-ŭá΋ŭÚ7×Ξ¤á”‰_Ÿ0='@ñe^ĉÎŜn×dž„ŜKˆŠ‹óħMN˜<èŝ._‡żPeŻSşżĠM3ġıĈĥo°9ßZÚ12CO+;½ççÀĞ‘éAÚĜf•™_@b„}TÈbÖ'§ŭÏü‡N‡>ì,Qôè°ġ -w_ÊÑÌÇ3láİS)]>ÑĦŞĞµ?ğÒk, /Êèˆ;ŠÙ´u”[Ô /£öF‹ĞĜXJŸÈ4ŜrË+Âüök {Êb%Ŝ ­_êCŭĜ!wn÷Ĝ†"^ŝ+7ħmxG2Qo“Ŭ -:!ŠŻSfġJfŻYvĵ‚™a(ˆ"…¤`\Âﷆ³I,Š3„×SĜó×U¤Â|TċÎż˘ÊkèSÁYëjbƒžG>żÉa^ÄpÓb´éÉË8= ŝn†g‰ż&¸ZĞDİ ĝêħ y~iÍOĨGŜ àHqÜv•1࣎€K"&ü]¤ñsÓ͎g‘é4ıM¤EĦÎŭoċÖáÂä8ßAX]Dħŝä2bĞÓİúéùAĵü$ĵĴL[ÁKö/ğc  Ż+À˜Ñw -zĠÏÓ׍Ċ§!ÌÔ‡ŞİĜiú]žÎ"^Œö!)٘Ĝ°Ĵ2­Eso“‡G´íÍrùĦÏ6ß>$_Í´2/£ö@]Ĥ h“ Û疁lgˆ0ĠboSŭÂQÔâH²>—HHIÍ0X/i!Ú`†ƒ_P„œL1슒ġO>e$+)Ċ_ĵWŸzѓğVü,ÎzdÍÉcǘUN3RZ˘Sx@4šÎQ#ĵÈs{½÷àÛ•°ö,Ĝ>ÂdÓKasO w‰`żİ5ŝ{e ´uĉ!Óo4ç}ĉqĵ‚²hJ_ž9¸0Y²pvfte9-ha0íyÛ ÒÙ9Ĵ˘-€•£ï\,Ӈ@Hò.چN&,gb³:N‹A,ô¤BQxÈ!§ïtŸœşŽ˘>ż"ŞZÓ Ëó*ûŒÒ›#uħìĉé—·p˜Îu‡ĵNBk.À8ŝµˆ=NÉDİ˘Î9g›oU•×­g…maĊoÁ ŝCnŽçŻgeµÄÉ!ĴkŭÒl‡ÂHt·§.ĉ³Gt½J+…²6$CġÁNa@q"ċFNÜÔ\˜ígŞ“–úŬ´ù÷‡Ĉ/i@r/‡’ßİìb´ˆ²ÌÜ?Ĉŭˆ§UÑXÒn뽏, -@ÉTžM’Rw½–sŸeh׸°¸k>À"Iù›ÛHä.™˘Ħáä^Iĝ+ƒHħgSÏ‚Ġ}ĊîŜ…ĜÈx­Y“‹+­ë[vEÄyÎÙD)%l½ ì÷䑤Š^CIŬ+ĉĴ˙¸ñ~d½/{ÒŜŜU ‰]W†ë1QÏPœ(C çĝ"çQÌ5¨nĊóÄÓ×´ŞÑLm°`£&aĉĜĤj ɛ‡\ç§ċ›ŭ}¤üĥ´èçiíxƒsúıU;bT­²‹ Nĝĉ‘5ٖ‡ô+Êİ{“>M|€ócġFññİ+B­|çÁ—’Sĥ%ÚdóúoÀé 5ì*"’Ħs×vıĴmíNi5q -mo’ÛŜϝjv–´ù‚Ŝ˙"|ÄLí!ƒ   –çà7ĞZ2Äĉ‰ĥRT’éVíU";%÷?q‹ġÓċ -éd”ċ´áà?÷cç·äqIŽĉBNËE€l•CŒ<–6n·n0Éú†É TJÁĊĨF,}€ĴċTAqÄÙËŭAòĠŻŜ³Qä5‰G6c]BĜ÷™zĤBĥžb9°5ñ•r÷µ\²Ħ>/ûşLŞÍPû›²ùBŭ%ĥÒSĞÍUŝh|é^(ÒàdJ˘/:Û@ùiÎşùNÔ[6G/;À2×Ġ2ËVH4ëgĜŠŬcÂ>(uÙR$eŸ“‡Şä:š€ûġ­3ƒĥv}œû)‹/öp‚ĵÏkѤrŠ‰½<‹ Ä…ÌÈĉ"kLĴsÌâ[ú‡ĠI£ĥÛ@†Żyeë‰ü´¤;’ı­Şt °’.ËÑ .²ÏeR’é3H•5žIô‚Bçŝċ]E.Lާaí˘ -Ğá ÚüŜäï=ħ=€’ĈĜĠa+Är]{u&9[×ôİżË< ô‚6[ÙĠ87 Ĵ‹M…”ö2=\ñâĞÍfƒŬ€7\ëŜ„ì ÊŻëpş—w8SĊñtAR_ ¤óİ2 -YQq‚ú§³JµÚÏŞ@´8B$›…`ħA|ȋ)Ħ ‘ ÇG:TË]S{…Fĝħ -Öxħê6@§†yêĈĦd{µĤ "ë·Ĵ*üVğa˘í{Á÷ĵĞšTÄ&Yè·1ÄUA,RŸ†ùŭê'TXcZvœ ç Üx˘û5 -{˘a#˜ÒB2ŽOLĝš>67pUÁ2#;;\‰ê=⸑µW¸/bĤ€ĵ&ş<}Ğ€ ò.Ŭ'D–Q^0v÷^ċí)0Ĝ“²IßlâÚħ3ጟB"âşxèĠżĥ‰bÉZQÎħÏŬYŽ7\ıû™Ê­…NFûĦĞżš–PÈë{u‡…ğ{g‘w .Éo`†fúp›€ċ>x“ٝ˘•$jöÓV!„—ıQ %ìÎÁ…,`Ŝ=´ÛqÑ£ŭÈÇ<ż(ùĈ1>÷lß ž\Šĵaŝ("´`8ôXh çĝÎlv}Cá´Ë{Ĵ‘ĵĝ ĵΞPaûZèŠŞ)|<ŒÏ–Á/Iŝ°{6íA—ÔkëmjÒÏ×CQR:!Y ˘¤ 3|ŝ14µXÑÀàĉİ÷`ÁĠ4‚‰ĉÒûĠ óx`û"ÓËTšŬ˜&K,LQ Ñ„÷E!uÌz†˘+07Y žçĊKRİöµ· mz#UdÄXía`/[#€‘ìT,ZHhZ•žMŽ[OxYŽ{Bfĝé·œ“CvܳTdYlô £ĠÒ3‹'Ǥ+ïggCiÍ[lvÖİŝŜ;;úò1lŞzs<÷Y-İfêŭŽ2E‘׍ȣµX›oŝñùX?ÀoÀ­†ĵGÈġó>˘ò5~ƒ5÷­"z“ù)÷Ôq¨ŒPЉÁO·XLèl; =…n˜wIÒd—ö‚œû¨âĴ‡£Ŭ@”Â^ÜÑQö³jN¤G É\”|g\§]#ò·QĈg“J]ĥô]ìÒöGñ6ĤµOú.=Ÿġ瑋%ÑïßÒ 6Í5לIpÇËnü'$:Ŝbm¨Á½Ӊìê‡İw~ :Ĥ–Ĉĥדd#ó~lFt‰<ğĊ˘à÷ĊԘ÷}ĊÑwwı_­i•*h„ĝĈ˘”c)ñİ\*ÇÁ™G™ŝü0ñ@_Ñ~\³Â1Ï;k0Ö;f(d* • ›rĴvŬşnA„c–Œód S2Ĥ´nż”¸-š¨0U@$BLi- W˙Ÿ§ܖÖħ•ß§¤cĦşÁ1_يxĥmŻĴÌĤ¸(Żk£Š&‘ĠrêH€p-"µ‘ŞÎŽÁb2mĜF˜“àt~4p3Vžvi ú(f÷\$:&|ÇYûÌzoÀƒ00YAŽò.ÊGA9°k+ÔYF›o>·şċ]¤l-œĤ˘~ ¤Ġ_â8ĉ—³Cü÷ƒ½ôÒÎ5İÇ"KċUDÜȧĝìÔ£—Dv6WV -·ŞÂ— µÂvžğġyÓù…9ú~ŒġĜıRn†AÒ>˙xË^‘Ĉğ:‡ mW@›÷"˜(ĠïvıĜÉ1°)g~·#K 7khú%w½jĤ9ġÀrDÑíħ–e^ -O˘àuı˙ˆËç šÈĠ€ù½y9ñr‰Àô#Kġŝ;A8 (”Ħ‡½J#ıÛÍÌuÔ~[”Ħ˜§€Ċ˙‹R2Q*÷`ŝ]ŽCW%’WiĜ˘ŝ!IUú¨‘ÇÁŽó4…[ÔÄA—™Ħ§Î‰ĵştlÊ4sP÷ƒĵ•ĥk!Àfê‹­ħANê‚ÍFG¨-Úo™†âó履Ì8NŬ!›vŞPDŻ=€ş{Œ´ƒX&âváM¸ĵù*áük}µöŭċšÁ–…éŞAhùLQ,:Vtƒâ­%ġ&‘ûtOsħ™AW`ÏíK"‹İPš ^€‹e¤&Bħô?b -ˆL3\A|z´‘™|ÏĊRĦg[ŝim/“É°àĊš£îşÏZĦfŞêqx§Ùın;ÒìÖ½w)× şFşE Y˙Nï[:·ĴGÍn•#†ŭ„ÖŞZĤ8"SvbiÈ/•Ò§ġPK³ĥtùo$âġ¨2Ĉ%m3ĥ’ƒyכàôIƒ°‹Ü}b†Ç!†şbÉs§ċJ¤]Ïs'í–T½Ĥ”j'›Ħßx•÷mXpŝ<S “ĞĊĉ"ş$@ĥĠ9müË|ĦÛá:ÉĤY_•1ŝɓ/Á÷,Dğ(gJ‹ûëµ…0ĝ]+Ŭ¤ÑÁÜ&˙L˙´Ç( zÍâM2‹`)ÛÈŜë”Ĥĥîúo÷…„ĵeĈF˜ gZÚé^$Ôğê@ŝcĵ ‰ÏâŭĜŠt\:@Yû_ŝ~ˆïl/Ä9ûŽ§=&ín„Ŝ$ÈĤîBzƒQ…2#9ÏàzOéàĤKփGkòG>njöÈ~Sôb^Œ˜Öi$3€^n“ŞUÁÚ-öT=kEĠ§Àŭ!‚A *x:E£ë1R•H+`0,oĝÓĤÀ£ - -0XĞñgžçñ Ž×„èL¨:ôuÁˆcWRœ¨Nj6{EQ ?ê4ÏxjŬDĞÍ£|´ĠyÜĠGÍ&7., Šp…ċt­ĦsC[ s >kW°œÖ#E7$}Ċ‚t,0­éûF ‰Ä‡ûïÍU›ŽŜq‘Ù êöS½ß8)Û"à1ŭBhĉANlĊ|ŝħ²ÙĞĜ wyAżĥ1 vwUIlR¸úüÀwÁ\ álÎü†üy‚Ic6ĝŻ.äË0ħB—Ùïô”Ĵ2SÈQ BŸ*&PĊ˙*œÓ>› -'Mˆd%˙\C‚‰ÇĜf²ä}=ÌJ£{n²:iBÀߜŬG]ĉ%AÓK5ĤQԍòp%ûjÏHîe -à!xWèım!iñˆuY£š?Ġ(.Ĝ}ܐŬ T…j&•DŜŬŭx“¤aò.­hCt%C ɘŽġxŒRd9Q&{ -LéLĝgĥú6‚ëÔëµ5bšÈŬòġ†È3'Trħ2Î)[U×ŜeàÔ/ŜCúJĈ-‰œkޞ²° sV²#Ùz› ¸—_k·( œˆ=VLĠŭ§ƒ‹EûR`uÛÍ?ĜÈÜ%‘V”µ]‚ 0ĞF˘·)ÖǃuKɐ=3C´ÂhÌ’èšĥák¨5"%Èż {~ác•µµQħaµĈ¸ĈzBŽ‰KkB6SEµñĊ8+^5ĠY„ƒ˙ÜûÇÍÓ)ĉÎÚp;kXHħókr|ä‰o™mÇ_Œŭ쏸²62ŠêÒŞ ôîŽ!ÑĠ&—G‡Ħ@ñZ½’‹³˙×EK'š·2‚ĦğSs.éaƒŬ*·“‹QîŒS­ċ9癚9uĉżÜZÁó…œ0£”WÒĉ·ċ§âWŽĤt;e>3b1b‡˜À0êÉĤ1Û|fÈ òx û~hV&ä‘|z½’@AhôÄÊ'HĠò5lȚ†-f<ˆ¤ ëï.ú˙:'ïáÈ'a„_R\ßXdY˜Ö!äCk9)˘úqħ:™çkuyu™ñ–Àɒœ§šBÄwh"j˜ómŠlÒM’§›‡J!71eñ°W]t\`İĈÀ3ˆ(ıíÁğ>Ż(dVÀ`óĴŝİ#bD˜ ˘ĉ“ż6Qùó@ħüċŬĠj™GܔŜş˘3ŝDUSkħ/Şš@ …?ŬîdVVY„†{;Ùzħp_d ÜákİĞèĥüŝÈ ANğ>e+˘qRİ: Ó1Ŭ -§Î s@†Mqs ŝ×dŠ˜ğÌò3·—Ġ@·D:_5€H'û丁ĞŬnÉÁíÒ eDE!ğB÷]OŠ…Em‡ĉBbŒ˜ *,j“€K‹ÙNUGŽĜĊ47ò!ÁFoµ$à^ğPċv£D­ -™<cR`ħ* ÜL‚Ş„ĵ8Ï—XµÔ‚Qš-Oċaì•, aÄĵd_ŜËĤJj½ġc~òY Ĝı*§×ÉzËgûÓϐNó#BWöá97!Gc˙İó´KùĊ—\>9?^ %Ê j„Ôײf}HŝIkí7ĜĤy˜&Ç@˜ëgQ§ëUbô V˘RıH˜A%û~ĈÍ:H²jzè$˘´€Jq<ÂSïŭ„NÓ¸ï{#ÊÚÈ<€–Ġĥ9†7üŬjÑžƒvópbĵ΋Üj#ŬϤ"$Z·Êİœ3ï-€^Ĝˆ-ßÖe=†+¸“b\³~ĝÀtÜÈ˘vž×BƒÇŻ 9xi SŬ -ANE‰ÎiqÜñĥ·H6f°¸#9kô{BC3˜Ŭhŭ£ Bġ“à^*RÎŝ÷粳ȁçU‚fegnÔìÊ˘‘“fĜâe*ùƒdq}Â?ŽĤ³TZX2ıŠoIٖlšÓJ ²j1i’! - …Z^Rĝ(pġ–f ²ĥ”j4@ɀ|bˆ¤Lı‰CŬDŽ#Uşl4çvŬêDҐO°ejtÍG•ĞŜ'ċŠa'è–Áöñm"FNga˘ġÈıZoúĠXĜ‘˘Ĉ ²„ÓĊħ@y·ûh•âŸñ˙e7>´5—+¨ ;SbóVpKġ5Ò}T×e‡ÁĈħ#ŒFö’ÊFž7"ÑÇWʔċ?˘˜Ħ^ =žSDñ·%×j#U½*‰`ò{[âwGÁ–]]²éĉU<Ê˙y#“(8p9@Vş3òµ[,aùÎe`„gÀq†EáDßCé|ÁfUċÀ†ÔîĴš|ÀҕlİǙ -z£ö$ k$`+¸iĠ¨\ċтUĴx?‰ËĤÖh<^Œğŭz›RêÏaâ5Êô·=(ĜH ƒÍg-V˙ĊĵV (v`Ñ9Müˆ83HŬs ö§î¨ü@Ñ;NÈMFÇʃèûvfĞ6\%H1z,àĈKš“ĉ´VböXŒşËè~„<‡‚,ÙhS3ÒİmŭVĠÇâ˙1*Ħİŭ0Ú6²ó_PÔ „]˜Íŭ6ɲחih\Üĵ‚ĝ sOŒñ˘žh }ŬNúA˘°ÇANg9ĉżJW ˆÒÙt -ġp‚#M2ÚHIKƒ_+()SôlĜg)Žzu?Úq¸)…;`ż"Zv0>ı}ÀJä{Û9/hµ1oU"Ħnîŭ'àÌóıqN$ġ§y>uùZĥêç³qeM -Ô'˜Ë@x:qMÑX)ŭżĊ>Ġ´(ĝLo˘ĝ›Şĵ€Ŝ×ÇšÚUmuWħżŭn˘ âíÛO×N‚äcPû4ŸğÀĦ†·v§F&‹£gqIàרÍt‹i{cÇE…uœ\./QnÄĴFš';T§[#OÁ)‡Jŝw›ÈE:Ĝ_qè*$çbfœŻÚ0ZĊ˜ŻÖĥ²g´1tew¨Œû ŞTŬ¤ZÇ?2[ÄU†S0ĵ3wkÀ&ħ2ÙäuĉXnĠÍôĊ|ëaêŬ2Ξg·qĵçú<9WÚu‡¤ĉšèh;ö ĤgâáÒb^/˘XıŽŬ¨÷jújÖDäTĴT½”ŠFÒIê›ğ6&ÌÂڌ tÊŻù!ĵäHÁÍ+†]@³Ó’œ<ùZE )Œ0JÜ 'Bù;ƒêĥwà§сr†wJ}ßD//=JßĤĝ]ĥğ -­<äĥz §ŻBÚİÇq„ƒĤŸUàv]÷†Q|ġħ‚Òä{ıż¤-~…JeIŸ*˘ĴRġ˜‘›1A̅’gĊm½şuŞ"ó1 -AsÖ}P†Â>^Gıàċ˜?PŝSë/f€ŭdaÑi;ċöFï™wi§|ÂÍáWìˆ^ ÏĊ>üZlÄCž --u›u{­ħVħ)Î 8„4…@q;)²,\]OÙ ĠÏ<èáĴGo ŝ˘ç{¨BX^*Û0ÇĦli÷ŭ¨$l¤äÓĜìâ ôb¨"²š%Ġfá ֋ÏN}˙~§îLû1m:Ĝà<%ŬġÛğ{|8lMÖU•NĞ2ó HXû ƒ½BÜ5Ù[ĦĴĉĵ‡vÉ{ü²ZùŽOÙ¤é³Zà@'­lĴV§âµîzħšWĜêa"½sş#žù +;†“ĝŻÀ²_óóÍqŭĥÉ.rñĥoäJ&™·™sÈ­ÍÇş.n#!}°ƒĉ§„`r'l‡61žD‚RJ.&ċPu„/ƒu“8Úż­ey×FÍ#$B!òF2-E\`>Á„ÑŞxC£äùşÑĊw.ŝ6O?kıwV˜Ĥ{tŝE,ĞŒĦËıÔĈ†cT†£gÇ@5·J2%fĥûsÁr]Ŝû˘2ÌĵĦâDßç2‹£·LÓ2`)Ä&˘g×´tô )Ğ‹A~-`J -⿢o {6!€'3Ġ‘ù,ʕċ#ï;FwşáÊ -Òę9#Ž eĵ7X›_$s4pˆ|˘ëÊ÷ğ_zĴG”ÍRlžfd†)(¸Á7ԇNփ`(½à-5[$:V Ĥ1˘sCi† -'Œ#öqDÙWÛ.&žÎh̖Sĝ=çşĉ…´|âô?ĵš³.•ûLI0v6f÷גȘĞĝHÒËâny\.X+Í‹ïÚö#X~2‰ÂÉ=g—ÒĊġXU°P”—·Ŝ”ÂÈöğĈÈX¸ĝŽCŸp€³ı’ï¸ġÛöw²>äGB>Ú@·1>gü‰„Ù[fl‹è#Ĥ~° fšüz1îyïôëäĠ•ÛeÏÏf^c-öştzLÀûuŬ„í Û³qWpÚ÷bÀkĈ/Ï8SNJAĈĉ'5[{a§Hö&Á­úMü4˘Dŭ0Qf¸OÛeĈ"bżħ÷Sċ3Ö`{´àĦ§˘D§‹ŻG^—;´Dˆ|)Ĵ;Ç\­ŝ²ÇeÒÈûğ˜÷Ó3 óñ–ÜèÈHt×Ä5pV³IZOX°êVŠ’ÀĉĊ\‚aÀĉ—™ á›|’BÚöÜ77˜Îf İùż€=@Ôjà9))SÓş6iXĈ֞'=7ċfávĉ–˘\N -c·JoHŭY4BdŻĉ'{s‰³•ŞFBĞÀĵvŻ/T~‘ù˙} × Ú ïĤôÌÛ×/½òDڞ5ìŬu—ĠCùü‰#·9- –‰‹_š}QuÀŠŽ£ Ž‡]PĉN™M’_AŜ&.Is;-(‹Šß 2Ĝ$Hğ-%W\×@ŻNï?Ux½„6ßùîy2@òÌKÇ÷ĉżêäû‰Š&´‰ÌċáÂ/HżÁMkŒ‰’ñQ8j¤ n–Z nâp¨ĜyġGŒ÷†À\¸HZá։6˘-*(}‹…hëŬ-KràSjĝŬ4O;˜:à†ĉR Ûi_Żĵ5cPlw{‚ŠWŬ“Ċfkp˘!˜c=µĦé²iċÉò-:²šôÏ"_‰ÛÈf^6L%Çûi3›ċ½ßħ{ĵğ/ùeä•[­ÎX~NŻ×˘Ħ셗˙Cß½ùuÙ'¤/ċ„ŝRëY<_ü§VR û&_‰d>N|TĉúM0ž^Q qĞùLfüŒÏèGD´|ÖÉЌq>"˜ :’tפíĞĵ0èñ{ˆüöŬĜ‚ÑCiá×ċ|אÛÓ+9oZ”Jıˆ\[ĈûİT|qİ:Ĝ÷É)Mù!Ŝ[i‡sñżàí¨{Œ$o‰ VV "˜a)—}ßjÉĵ.(ÏjèHé%kĊāošP|.÷Ğô|˙V|À²#ñ˜-ڈdÉ7²ÍܟˆÁNùtM?û,97@[Ñ8'üĈŬ„´Òù‡¸%ġp…GV–l†ftim)Ş=‘ÖŒĉqxĈ5˙‰ÉÖħE‡SŠ]…éö§NÁjMġ¤ĈZמah#ç Lı TE¨=Ħ™ž(všÔgw -a*7z{?ߎ -1–öŬ.€¤ïvŻ`‰NlĦH‡M£™hĠ&İ -&ÓÉ÷ddÔğŒkĞ*ZüF·!(ş’TâUIW3K§’&jŜñ9ŝ‘aôÇLNı{³ïĞ$Żŭ ‰íÒÓŭiDĤ/î(#?ÙŻu!ä6ĉÙ&û@ĦÊÉħs¤şŭµ}O&½Ï´¤GġqE4Žhz‘i‚O!ÈZ"XÁBŭ!ezM;*şp‹_q+vqÜt”ĵÊúE‘he]6ÇÙ:6Úe;Èv,ûĤÀí;Áߖl™ï ->ż[­S+˙{+[ĉŸü­•Ĵ[@ißF\à/:›{r´‚|Ñ43Hëiċ%f“³éħ>F€Ú”ĈZaÂe‘ò /¨ËGR"£F$û‰ı€‡‡Ó‡ÖûŸLüFnŝUŠ„&ŸÛWió3ŒpħٝO52o&dGPċŝ”ë쐤‰ ³ŽĈ·ÒÂlh+1[¨rĠb-“<|™+·eù>hbÁqnŜ–DOċwŜħá¸CòQÄÍyr7H.ÖۃŸ|ħ‰W)xêԗŞĦ‡·ô˘İç”Ù&ÙµNí2‡m­'mâ (ƒİL^?µۍÛÑì>uŞeŒ"ga˘bAféڃ4Ìzbzħ7SXİ)$úE &*\ŽùŞ’äìoŒP”Ż£k”Z ämï)Ÿ÷pĴĠt°tÏ°)œ“$(rÑ5÷ÌèÒ&SŬŭ¨ˆ˙8Jy]__$J)î/À%‘†Ġ^ğßwL·u¨ÍĵZ{ġèÑ ‚ÍdögPçĤïcPxO™‡FN³żÖµš%–Cž³êr³ĝé˙HÊèYùµ×ÛĦÂà°öz.Ŝ:-YĦ+R+ĵˆWXÙĥ}Ž$š¸|ƒĜ)ꍅÀž"ġ{í üFHŒ/ĊĊÄMêĦîvġŻ=îsV6}%ĝá²Âğu߇ŭ.äx@Ï·ìġ!ħb?ĥ€ĉ³Â]âè˜LLÇŻ½ fòR|FúTC`ċñĤ8­Ç^#‚#4:“›ÌŽÄI—ĵŠ0fpqŽ^i Ž ·lÙ³ċëñ`àÏÉqU9Á½Ü›&?ŜkChMbÔ§T*–4ÑN…ÛŽf~£qĥŜRĵ“n{Òżû›Zi;*cœĉ—eáahn*ڜ)ĝ¤Ux|ëŠS½‡$Ízç"ĝú -ĥ@ív4&›û›5=Żż&?˜ıËi ʨ=:ŝIKL:†ı´Òf—W|uv÷ÒY6"sn-0ü.Z=iĠe„0ŠK_èĤ&~ĞFL÷ϤВë×Âċ‚ŠÑϨ¨ûnÄQSLRş#H0 =^Ù=gÛÔàM@ó˜RFÜX´}ĝJú€qċúíÄ/ú" -k_Mag”ĥ‹ıEà°[×ò’=’9Ž™×B˜x†_v8M­żı“àĤ…ó?Uĥ% ²nH߄=LÛĉMÒşUÂèó)M5İoM —7ġž‹÷ĞDvĴ*Wm¤)k*ŝşñp ‰ŭŝÒi;Dûs½İlµÈí@„ċ›v,S/É,t+½´‡`Jƒ`ÓŞô(“?dÚt4Ĵe jxż]%À'Ħsö7Ĵ^Œœ)"ù2²g¸Œ|ħ ߄äâYo)ù%$şk$Ì"¨€ÛħlV<—‡I½f£ĥß×kmëR½ô5-l§|*ròr‚Ŭ;pzçħÍPl;àb9YÙ ìËdsuçFϙAY‡´¤Ĉ@Jwĉá$ĥ Ž5:·ĊŜ#I°Xlż–IìLŒ^Ŝà‚yK$}-tóÑ#¤ónG†_ı3·‰íĤ›Ž .6ÛTœ¤nAq~…ñL‘üçlsïëwI¸0gw‡¨×ĜBŞ ?“ĝpVcìÊRF6ı*ĞQäŝrdRİ ÀÉÛU ĠáÎż—0âïĠĤû„ĝP.y$6'qz3£¨%Az(O*·€áúµĜ“uí-ô³ÚmÌ-ŭÁí@’ħdD"–Ϟ}È<*ĠròE:Üv?Ó63—dĦeVrm4˘µ—4­: -›Ĉ2qDh -ÖÀóµ* Ñ 2ĥ$P)·]ŸYĴ0lE…vž3qK™Ù‰=bĠM—ÁµÛÔ/ -LĤSQ”½éQ8ċĈi‡Ä …xĥ׳„Ä ‚M¸‡‰yıa˙ĊíâġL!A@…Ĵ,2?]Ùkħܐ$z˘½nÚĞ _vÑ%êżƒ€[è9ï<îž0cóÇB$ĉ…$÷’T– à~b]R !3ƒpTtħózҏOZFTàYŻ–Ât=ĥĠdĜ!z‘‹ĤP?ëkä×ÔÀ7bĊ:Ȇ£UĊÛíÚCĊÉJ o~&^Ü-<°í½áío$ı9eċÓN˙4Aybr;öĉJ/üU% Ğö&XMŭirĤµö†œWûĝz­ŜŻ šP!r#ۓ™ĝ¸úħ-o˜EÜK2Ïè~ĜĈAıġ‚ZÑŜ7İ•+Ĥu1™Ċ)8âwor*êŞAŜ‡úİŬĥqî6Ûc†]L}b’ƒ½+Ÿx9‡ N9Ĵ§Ŝî–î–{‡ÇğzËÔĤĝĵaò*^)rd½ y|U ċ¨³Ò`ĉżŸlG1“HVÙ× `Ĝä3Sî7ĈJ7Ŝë‡4œċ*8/ · œ †PF+öĊvƒÖûĊì€öË܏/è聞•ġ œ ¨UóÉU=Âu½3ċu”Tĵ´˘ù0P:úQĈ³yŭ§4‰9{ - ­teĜÇŻù‰!°sÈħ³,ír¸ĝmr'ġÖz­/YİTˆu’žDZx] ’ÈšÔm…OÀwDíĊ|¸&³"ÒÜCò¤ ͟ŠC9˘µClvm ßC°şßŽ oOÓKqö;4ŞŜ‹íğ":&‰=úTN 5VŬ„`ħŸñŸ ÷ÜÏ9ÀÒ‹o˘ñÁI­Ġ RŞĉ½i4Q–­+W£Z£;[‘@N²ĝ -Ê;àVrH=j“<‘öûĞĜĴÂÖÓ2°|Ĵ­[€ŭĎ*Ŝ!4hh6¤2^8'd×·/µžBQz@‰+çG6½„ta‚4—rL Á£ŬcÛMĊ˜Ż¤òŭè·ñK½báÍĵ‡•^+ĴI#ë#lĝâż3î\T§ïÀHšϝ-ĥ ÜyAm}ƒ“˙YpecW„FCÛ9qœ|Ż^úGù:³ÔĜ9$´µù*Ù# -ŭ”Ió€‚ö³ÀĦŞÇ!˜Oô>ĥât˙X÷ÉE?Pİ S1­w#9™Ŝ’Ħ.Ž÷JB{J -ŽCpÙÔ#żmRuWVf}š/ÀfsgšB9ˆÜĊ°ñˆħQa!Xĵ|n`Ĵûpû´"ġ•ÎI¸!Îô„Ä\9œêDĈÓÓìœĥCÑÄ9ĥ‹Ñû31 -endstream -endobj -672 0 obj -<< -/Length1 1539 -/Length2 6948 -/Length3 0 -/Length 8487 ->> -stream -%!PS-AdobeFont-1.0: CMEX10 003.002 -%%Title: CMEX10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMEX10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMEX10 known{/CMEX10 findfont dup/UniqueID known{dup -/UniqueID get 5092766 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /YJJMFD+CMEX10 def -/FontBBox {-24 -2960 1454 772 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMEX10.) readonly def -/FullName (CMEX10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 26 /braceleftbigg put -dup 27 /bracerightbigg put -dup 0 /parenleftbig put -dup 1 /parenrightbig put -dup 113 /radicalBig put -dup 88 /summationdisplay put -dup 80 /summationtext put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ=Ó%ċW˜)-{Ùr½uú•)Żœ‚ßröA•ÉÂÜE(ġ@Úŭ{ëı´‡ş“Qğû|ü_‘RÑċğ -ĜĈϤëA³Ċ -T@ĉ|ŭq|VkıżJ% qu8P˘ĝwÄGx³ĊŞÛ̆ÖċQĉŻ6K üŞÒ-UŒ\§Ô%ĦbĠ"t-*xÔġöÓŸÏ˙J‘+ -}ì3{Zà2ŽùĠzŬĴT2sÀ$ZġÌÑ&{Bè–J×{¨Ŝ£Ô!Žfp˙G?[öTtkuœ'5O P 1òÍ[.BÉB•ìBo0”Í ÌVoG;£òwŸëġĴCMdK†&\YT{#vĴ mÉ ĵE57şG~ßĦ +‚3[Ċ…š7Œ3Ċ:&uNĦ]Bä Je ¤ÎŝvûÂ(âˆ7JIFO/kZ)CĤk“zĞ™*7XuvwšÄ Œ§Ù†ĝg&֋ĴUüî+D­WAĊàßÔ³íäÇĠPx;£%]r@¤à˙ŽŸĦG•à€íċ~fúJ4„ë8Ĝù{v”FMô˘ĝĝâ·"›~Ĵç’êwšvĴâÇԇŝ1µëŝÄëI mJXk kŽĠéĊ51DžˆŜĈ[ËWopl^(íï;Òw‚á\FÖôËIz÷H…İ°y$—˘$r ´Ù./ħxjÍ83›ġÛîá>ƒz>ĉ½9÷Nќv-Úòv£à)üTT£D*ğIL}Ÿĥq°â¨Ûbx×>÷öu}½&é:Îë=l]Ġì™Ño:··´‡ê¤E“‹­iÛ§í[A^–Ïŭö ˆÇ[—/ċERÍ;ÈñRé;”"Ĉ6(ĊݳK?C!Í>;gh)Ġ Gaıï 9nQİŬÀ<‚@ĉ†(<Úˆ›|+†)}ĠPĈˇ2&İħd–qmcüß#Ih²ĥèċFöeIû-ˆS³žÙ „näçÌ|{cˆfyv40ûÂë]vO‡?ñŬ‹ZωÊN#Iî'\9ÜwÉû…Ppóŝş`ê½i­ì(ä2ËNzf˘òŻŒAĵʑ[?‘ùÊ˙}—Ó7NÛ)Ċ-tġ)¤^ĞEI(^ܒM[ß Ò½¸ëTf¨[ëżËzŬé{ Ü rCÖ2żYócâCĊ¤ÇĊĴ­ùfċŭùvËn­TîgTBgÙ^fş„O¤WĴ …3KŬgç³iuèĜ“e>öùNı…×•ĝĴĤ÷q¨1ĜS.ËÖ˘+ĵ0ȉ<á÷§]ĥÌvžÖmZ÷î É ›Żû=½WVhY&Rŝ{­!2ÛÜĵè'ëNr6Éħb k¤_ƒÚİÑé°ŝŸÀİÍáë'À@ˆ1Ĉá3µ{MKŬ€_öû_ÙÄGaŬTżAbʊÍ0Z¨B{ä¤Ħ dÖċ½2Jö–ä>û 7RÓ‰ÎKĴ7Œá˜×ÑĜÁT;È°èì­+[4Bó*•żq4~;7 ³D 5…W?S÷ğ&×3•¨ÑŜñ[LċíùĞö^'{ŒüP)VÌ´~ĦB,›10Z]TûĠC2e;=@Ó7ŜnúŻ6 -|ŸġĠÜ,E µú‚+Êğ%Żó_B Îş7() †û…xK6™”üqÂQŭlŬ: ĤÉ`qíÔyïiŸó_O£7éâMK!ż5°(sêf<ÊE0ğHwŜZë>g´§ÄÍHQ1N‹9!ċ;8 @Úߙ:€ÏĴ&ê-(Dƒ00·¨fkC[Ÿ–ÜxŒŬ'=x†ÁWHòİ i~ -s§ŠŭĴw‡ù£³O¤½€Vꈅi›ÔJ†LàÓú%’•{ĠyŬ˜Fü": -Ĝ1[Üŝï[ nÖs…ežá]-Dċ.–ò˜œct&_–CĊ$žI]DĜ˜ĈĞŞ'˘„‘ÎïöDG‡SÄQ$ҀpŞĠ„ż6<˙çĝ°~"DéżgĠž1àoÔ/+8óá>ÜY½‚Xœ+Ïê°­ö҅‰Á:fĞXMÁÜìĦ‚(§~t~xŒÄèôc¨+Ş`Hc‘äv"œ+!ĉgŽl;%kèÎı #‚Œšvì" ‚¸%ÛMİÂA’6ֆN{…È%ş•]Dû²`;ĉ>Iëĵ³ĉ£Ĉċgĥ!œĦCSièĜ˜ofÇgŠlu:o3 y–UŬ˘×\aŸÁ;ì'“à‰fĞ@ᛙvĜâĴŠŝZŭŻj NB²]ƒ.y¸iġW3û 5{ˆŒÈ$";é×Yü]Ў` !i1ñ{ü²ħZ„°n|óĴ„VS,vŻ6ÜĊâ.Çam$|%Ù>ÑÒâí)TCżç–Ôk"£‘3o²@*RU×,ŽÖ6ˆä<#4Â4`ŒxDĈÄo:EÖtÛ{M„6#:‡—†š]wçŜžġ›CAޞ•'j]Ħ=ûûK4ˆôîEA=¤ħÎ:ËMOÔaĈÒ+VXÉ[Ĥb,ŬmaÙ*ıŠ’Í69—ZŠ°]ʤğĵˆƒ|Ż`ÊÏ?‹tvñFè˘wĜÎr2)Ĉ‰Ö/ä-Ovħ5ĊÁ@yİ‹‚9 ]ş#˙×ÑÈùóx~†{ï! Ë£zÉ{TĊD]7ş˙ëÉdáì{“ù­ÒWtòƒMp† iځ(Ħ÷+\, pZ]8·ż˘ı­wcl_EìĜüÀ¸Î€G#ù×ÔÓħÁÂĥꭚ=]Y7*œŽÖrƒQŝ !WQÜӄrĊġŞögàdM9ÀÓn*ğP² ´ŽœàŠbß3„ĞéBşxe ö@1RhOjĝ……ù\÷˜ÍBycw˜zĈÊj eµµÓÓH×?Ċé´ •U•~péÌE‚èäĤ.ĴkÇI“àc4g<ÖéğäÛBêşùZë\żBĞ…5h‚rĥ†E£ „d^ĊwŞÂŠÙiµ·m ˘;ġ2 "?Ċê -]`_ħİZ 8P\éÎôw˜œ)ƒ9%9 ó›d„S6ÔX?}†Œ+žLÉY¨JÏ^y@1ùÊè ë(h{U²üe²mĞí,F/d䘊Ô"H7?Âj œV}‚ö–2 -ĉl -O´lb(FY8ÍGúßħí4°.Ċ eS²]¨<ħ²’b@{ÌɤA.Sˆ Éf>ŒoÀöL£ĈĦ6—/Ŭ翔ĊOHeAᤇÇôÎ#:jîċ -´7 À6µYäÀ^Rvr´é?´NĝÖVÒIÑÙz1µĤx^PAéÎĠ˙ß~ĴĉĝžKut’S˙‘`ZƒàGR`T•g3ìHÁ4á×'ÑeKR `ŞÜk+·ĞŜáŜj|áı7ÜoàğHNPq‰Jg4Òíéà£{ù"ŒçNñŬJïÚĜ.éñóôàGo[öyvħ‘.ISĵ+Ç9jÎU´Ld+ˆµ“fu”ĵËÄ~mQĦħfsGñMÎb)êRY2áÄ>y2d‰=¸ƒÎğU•ñĦeíëĜüòı8†@*<*?µäĉ!ġ.ìyŸ]PhŽNÖĞÑ1Ìq€ïĉrYgî²°MŽ´RÇâ/‹êÁ -ô_XÉĜÎäğëru'Aßpue+Ë`Y>q† WòXGĵ6dïˆ÷Z’ żñĞe œċ‡˙‚”ġñúœTıĝ˘Éíï_‡…Âj^‹-ĉÑ'[n¤nyOZ£:OäŝÔ?UŽ”ާ3z;Fraᪧ}/_ ›-àDŸ'o²!OäQ'‹ÊħLÎö@˜ İĜ.!Uxò~eRj=U=ÎDqĉħKĤߒ&žu9éûÍq›ÎD<:ß µŻ‹áLb½.3ĵñ˙„cäŝ%Úx]Ğ׉;­ÁÄ ½ċaíĥ˜Ry†Ÿ ÛZÚ:Ġl‘Žö^ùn×z!Ë/rüUŒĤĠĤî4)ĊhO·’MMdÄÍıĉ’ŝÖ ë14ġ´/Xû‰·sa°0"îAĞëĴµÇġer™áĥ’lŽBNŠ rŸ8ÑŬ°Yç~ry9‹h‹Ċ?êchٞ–!ú„c -Y猅OŒ½Ûúc¤ġÜ}q5Ÿ—–\ĥú–(şyĠ!ŭĤ^âÙë(L§ĥ 153Ùjv‡zôhŠÒĠé9鷔Šĉ—7ÖZġCYöċ³€ıÌOÁàŞ:,!·’ŭU…C$*Úh[GÂ%4èO†ô#+¤y“–6">RR-:#ÉXL%żYž˘ÉD‰dĞ­,[ŜüĴ‡F˘Tê ¤ˆgËXc‚ħż½:¤o9LJ•\{˙ĵh%v9ġ'tŬUB´QĊ•&ƒúF˙pĊÔÛÔ,8W‹ċë—ĥöëFıÏFŸ˜“À-Q¤EWĵDE²zÑ5sž#.TD1R0„ŬŠĴħ:û$Ŭ}+ƒr*é­W”ž›ö€ŜUbżœ\]E¨vs|?Lko²¤ŽO¤ÔŝiÇF‰Šx•Í(8‰z1áùdƒú8w .b€"œ°%K^i5…9ÁC|÷]Jçä4ĦptjĊŠ‘C”˜È‡”‹Í -Ä­ÔGeè‰ċ/" #ò ß@!aM†bòEħ0ñ­Á›ÒU?Ż\ ábY¤Ó½ë‡÷Iƒ¤mʗġ.Ç`xò+Ĝ‚“2qZ:jħĤétWM½°KŞ;Ĉ8ŻĈĤAœ sì&qü\oq¨şŽVjQ %i3k’$nġóġ'=ŒE#* -WVV ½ IàPQ8ë€ôŭ>Ôài Ġ4bm ¤miûċšÊÑ.P`²W0ÍÑ'2ó†0ĉÖÜÎvûwl.]e‹l™‚íùŬĊ!Y——z›Ö"ËŭƒFßkR͙ĥĠÎċ,­š`ká%‹˜Iubaün\ŝRڇudŜ Í:tÜ?·°ìYĤSŽúûĦ/WXlOé]Á{¨j -Àħf—•ˆ_‰p|”ċê=ZO›Ç(ï+Şŭ`ëH -ş5 ~šœÑ‡7dhÈżÖĞ]VÛ1´ĠԄìœ2˘D(ÎW[/tG -W ”(µ ìz ŸKĝŻÖèÁŞ3Z!‹>ôŽL§‹ßW×aF§;‚w˘0Ŝäcż³èA–°”Ü‚ìÍÜLcğEa;° *DGµ5€HXÒ&Ĉs¸‘wÈ*ñĝ—Ħ’ÂËä;êäs(­#PBÙ hoOt%ŠJğ uÑöŜ.:üñô–ˆÛƒƒ ˙&eċssŻE¤Ĉċ3a̕*™ŝPê›v”*k]5öDû6ĉ?Ĵxĉ3à{Û%·ŻEó¨µiV˙À ˙jĈÓ¨Żı§”P£ƒNx[šö ïİnôP×Ú1#Wv›A8Ŝż6Ħdz“¸LíñtGîb5Püw,.½#gğĞ…ŒŝF:ÙÀî4ŭ:uBV÷@aOċ•2zšn!Á `pğgTwa„GÜ7ŝ”Ŭ= bézêsÔ¤½¤–Y@Ѝĥ}0Š{9üBî6$ʗԧ‹>ĞÊn4=#|¨hŭ~ùŜ•4òR_=ŻÒċÌ …İzŠYÌ,¨9½7jnĠÊÉŬô9ĥêÊVp 6çÇ :ĊŠ²_…Şĉ„ ùÓGdLuÎ ñ l;>Ĉ[ŝL•ÖמÛkÀ'àDtp\·X½L–Ž>DĊògöùb \/1}EŞ(˙¸yƒ Ma2r“Q³˜CšZԖ:’…ĤÄÊög:=‘üܔŻ%WgżvùeŻóĴ“ħ:ġÎĉí¸Ŝ "‡ŻICqi€ghÄÔʕicùµùġKŜ1ÑTĵŬvŠĴÍĦOi÷˘uóI;뜿W3;ĉ1t™˘ñ$HĈSœVŞÄÓŞîX1êĉċÉŜT~“ŸŻBÖh]˜– -*` ˙ĝ“˘;1Ż^`š–„‹ĵž´ŸWǛ`”`Itb7ħ¤ìÛ‹Í'[²zż·UYcŭ¤Ĵê -ÒËùÜ£Nçŭ)V~YƒûĊ5”4ß- Żmc ĈòŻaż,jóŠİ°èûuR iF|_żî"KBÇĉͤנ>ĴSÄÍŻ×\]oNŞ÷™Ŭˆ?î˜%ó$‘щA?- ڑŒ‰ô+"›­öŒÍ…ğnI-hìt_M–²M?9-?e§=?ÚÌ3û‹=jY Ħ€mĝÒ°ĉC28ĵqTL‹pà²XyŸµl’5Ĉ’m–µz˙”w¤ÊĝaîŞè1DCüg2ö;[E6sûŞ0tß|˙Ĝü§D;³-yKAĦ3QĠ˙Û\}4úò ;/Ü}{šü>ĵŻ3"É‘í™^Ÿ0ĥZ{>œ‰.N–÷<çZgF–ÑX;ò_>3añN"ŭëCB³ŭñ?úd½Ùĵıç_´Ĵa˜êj%Œ˙­Wĥ¨"ù,YÁ*‚ó8uëšuš‚_îÁĠĜ;–Ċ™”ĵċ,| úŜ_Œ‰”çNқ4ÉÂŜµ8QYgöE -)€tĥ˙żCÓdäÈR­ 8ߊÊNš:Ş”2ĊäL—Ïyoô·(9*µËЉ½ġu]sÛ`‰r˘_=ڈ€ù`M~ÛiaÉëoŠ¸/P8'íçWsˆK¨¸Ĥ$dáİlĵ˘ì:3ß ?4ˆçén?Q*ĥßOBó³¸>HÔLC7Êjf:uÔY8ÎÓüÉè$é64ĊÌ{–"Ž¸™f°´f™…ž8o÷Cl$G·)ÂĞáĜÇÜ"·Ÿ†ÎImtoĈ)¨šqš"żġÓœ¤‰ŝ |a™•2£a?×1j“Ù|_ĠZ=Cd(P ŭ[uY7‘Ĝ$ïğ)Ĉ‹àsG¸ħPZK´°¸5ÙĤèƒäPIRġòmvó/”zöĥŻż—2£”ünÓ!*€ÁiÑFşàö[ÛâÛ^‡ċµxTXŞ&ŭ‘+•ħE?·œ—~FÛî&mĦyN]=_Ŝ˜uġè0yrqeß·Ö,"CĦ#K ·P >œ'O=ĊŭA}‚w>ŸˆħjYÓŞ.r!Q‘˘D•ƒ1ĠŠ€\1Z͝}ħRÛ*ı'D!£˜0טv9Öİ6Y]ÇuĦĊż"Ù9ñO†™(c -K—ñdßü…ċŭÊNëŠĤ)ŸÌ^âÜübIŞ˙|úÔÙÙ_|KĊĵ7mfĠ:="<d‹Ú„ĦÇ`PcŽÄÀ9ĥ$+ïÇôû+ áĞÔ˙wgêD˘' -endstream -endobj -674 0 obj -<< -/Length1 1946 -/Length2 13085 -/Length3 0 -/Length 15031 ->> -stream -%!PS-AdobeFont-1.0: CMMI10 003.002 -%%Title: CMMI10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMMI10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup -/UniqueID get 5087385 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /VFYBNB+CMMI10 def -/FontBBox {-32 -250 1048 750 }readonly def -/PaintType 0 def -/FontInfo 10 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI10.) readonly def -/FullName (CMMI10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -/ascent 750 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 68 /D put -dup 73 /I put -dup 76 /L put -dup 77 /M put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 85 /U put -dup 97 /a put -dup 98 /b put -dup 59 /comma put -dup 101 /e put -dup 62 /greater put -dup 105 /i put -dup 106 /j put -dup 107 /k put -dup 108 /l put -dup 60 /less put -dup 109 /m put -dup 110 /n put -dup 111 /o put -dup 33 /omega put -dup 112 /p put -dup 58 /period put -dup 114 /r put -dup 26 /rho put -dup 61 /slash put -dup 116 /t put -dup 18 /theta put -dup 117 /u put -dup 118 /v put -dup 119 /w put -dup 120 /x put -dup 121 /y put -dup 122 /z put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ<ï˜ĝX2-Τ^tĊEÒ_á’SœÚKŞFÙÄ1F^jżNBqĝžŜ×ó{ä³´y4ö-FègbÖ˙öԓ{÷"Ö¸ĦW–B:§rĊP‹À ?dgĊS%|'²Ĝ“w&¨F7J…ĵNÀ°¨œL9VìâRtıbÈTċ5ô'ŸâmƒŒ\‰—Nš"K<ù -’wŻàÇÊÈÜÄÁ‹Jv‚ċ$†tE;ÈD4ŻVܢüŸ§vëš{bG@ëdĊĞß)–ĝ²Nòhäòë]!(”À7h`”fŒ1ìzùpÜB˜r £ĉŠd۞‡·Ç>“÷sV™iHÂŜ­âkJ‡…KyÚÔÑàüuK—I[ÏĈ„(,M’=ŝĴäì}µ%½vf†ş'°–äE+œ)ê}fƒ˘Ĉ$lÜö(…ÔW2[8˜hĵT>ĤÜ9„ş€X33 vi˜U/µçÇYö{z4ŝ˘óB&ÚqŻ‹nŒzà³Ü|š¤Ħúï1/É´c™ħŒCzwmáö|Żxá]LÇmo}­zĵm5íà׎Œo: žİêżŠ„.ş‰"­ÛĈġĴd¨N ĞúôÍĈoĵ3 -v¨Œúëzŭëš N -p´zŞP;VÒżg6ǢĊ >Ù,˙ñ>ş—O€J4mA0ÌŭR3ĥÖı*È{+˘şä9á…iuċÏM”äO@h}-Û(Ž ‚Qȃ钏ŒĵAàôıŸ‹)ÓħÔí ĵ¨=.9İçœëô3góœ=[_˙b˙o_BV¤ßúĈ‚ËĥòW"íäĥ›ÂàaòéoZFsO‘)„”¤%ïd2òıwŒNğ­ÓH>ġD}ġ۝‘ĊY•ĵí´ħ1jZƒg¨ż1bıœJŞa|`h§b)ÁwYƒïc[&0j”²X7yĝg -˜hS·…˘&}pŝ-ÒêfÖ^ aûÖ_ -Ċl4zVéóènRóàż_e@Ż³*z|–‘•Wi.·9Ì)ŽÇ™›B†SŽßs3Ϗk ,^Œb’šzËıa ˅4_BêÜûĈÎú1ï+ÑÚÓìWµ²2ÊpoœDûœĞ‰x>Êf×H³ú[]TEöÁjšRȊ~/+û ääê š˜Ŭl8äzXܒp²ôŸ›H!V÷܁dĥ!ĥ€;d4˘£TÙ5:,úv#cK*ÜÖ;+zÏXŒŻz k ¤QÓßwĊ>aqĈb6ċ1IúıÎK&…?eĠ÷‘=ˆêfıĥ?Úä´T ĜÈoîRwšÓá: -‡›eıï -/ò ‰şèÁyûí¸}„ ‡tĉÚX˘ƒş"7€òqt„àfú}Àĉє)°†8SRÓX•y<œs´2j•O^ĵჺ%À Uş…à{>ԍ/ ĴŻİCmoßċ0Î%Ĵ}ĦpÛdç{h4>ŠŠ^wDĤ@eQôdÄêaidYÑ^à@żµ?p i3;²BĊıAeûûÇôġ Ñ"­Kcéĉ_ - -ô>üÉüToÑ=¤*¸ÉËúy¤€Ù#p$™UÎaĤ€²€5Q2Z3:·Èw’ŜXê<âHY°Ĉxv½}€äF-$›"›b!(µzkDQRbt;³Çéj¤¸Äk äNö4­Ó4ù™ôß³Ü˙jA*›`g҇QŞħ² (Ĥç;ˁ°Q U„CpbèÍ@;ĝC9eé&F[(‹ -˘ü…ùùĤ?΍rŠí˜ĵş_ô…ÒfOWŜ¨Ÿ¨uù0Ŭ÷‘k/’&Ż5ġ ÉÒ¨ùµĠĜ ħ-ßLYVZŞbì4Xž[Ì0uÌj>EÔk²€²!XĊÀLĥĝĦǑU—°ö› M‡lúTHÈnÒŝy›ÄeUĈĈ˙üs…AܜŠo…3Î|] Ż]™äĉzıŬN&•”GĠU1@µ†./9;ÇÑIêÏFz”$Ĥ€UĜ/Kl×f6xqà  y -²w}ħ‚HH/³*%úÛb•k“ŻüYħyoxĥjî—x£²S½˜\yµ)n?şžVè‚Jĥù+Èka… [zÜÌf˜ħ€—×fI*Ŭ[f=M3Ó)%ĵñİ“qŞĥO(ż\-Z!ŒžëJ -H)rQöµQ5ö£TbL}/>Î5kì÷=Qw˘Oŝ75üˆ#:•×,˘U_LP?‘µÇÊNCĉSMöĠiïĠ Ú>•ĈÏ÷ˆċ ċñ3*×j#WDê8è‹$òÓ|òž!·FŠßÊ̊¸ŝéÚL“;_ -dQ–JI$ĥş–YÈ(ĜmRqè÷£J[’~fÖ9,–Ğ6³â_1ú£Ó~w ğëİS,?1?ƒ óÖAÔĊßyl(‚LıÏtğ ïUîìè ÀĞm@Ò*ûT9ÛEıWOg-ږÖÁŒ°HépĉaH"\z¤ŭÂ/ÒÓ„EjV{1‰ó1̃Tħ•VLŭÒ5yWK|z€Òó—|Úĥt¤jBdé…V=zÙ3ÚÀTÖJ~ĵĉ[²µŝĠ3`ŭv ŝpnrƒU MVWŞ›ö.çY-t虘鰭²2zĠñ‘„‡ -ĞìKxq3àÉ_t§­›é|ÑW×%ˆ0£Ì=ĉE‘@Żş”.ï2^àr³:Ÿ(H>ĴeèÚPÌŬ³Ô;Ż÷ĜÇ×Ħ„}mWœé-ñµMáAÎzs`sb}žŒÙŭs¸@_“sĵ/—žFˆż„O’EÂĞ—lî‹Ŝh\G`böa8¤š·$(ŜòÈ^U3Żqš´ÔġïóC"Ğ˙vż‹¸ġjŝ?˜ŸúÜËAÓ·ĉ5.¨s:]Ç;H2…½²?lż´²cäŝP÷ô!e£Ûê-t1ŽĜ//Ǒb<†•“Üŭkû/ċ{ßéєo›Î „ÍĈì8G%‰pÎĵÉëĈ·Mñ:ӕúnŭÂ$cS€ë5!Ş’žş0•ŠâÚ@…!–ĥ~äD Ó#8; Ħò´˙ósŸ^ê°=gC˘‘´Ŭ?ùèë×z;_]“ĵr~ef H“Ż‰/tü óè6Cİ7GgŽı˜ùÉ:ùB=9$ġñÇë$›*·6‘ġúÈhrġ!ƒ eĴ;èË€ÒWĊ.¨d~÷Gŝ0E˜áÎ ¤Ŝ@1äĥxi°ŠVŞq ‘̸ŻĞ”­Öpçg¤Nwy]ßÖ\œÜs2qmîŝ?ž.ĜKĥúö;{ġġTı4‚†ÀŸÂ§N˘ïÔàkëàÄdàxÁIhE=ǃ§ˆ]’]r T’À} şîI‚ûí›2Ŭ# ‡™ŝêĊ[ °— -Ġ’cuŭyıURkàQRbµÊ‰Ğ́ż†„|ĵXPÔ V½Ċ(ézŜÑêm{v½ŽNt*ŸÌñšcD™ħÌ’ _;tkÔŜ-›ê4%§§ĥF¨ùï™ ĝŬí²AOŸ(†sÉfħ%(ÜûpÎDÛH"2&˜-pŠ Kï~°‰bô3!=uEóQ锗(ëD<;³j°ÄÊ·úßÙIċù2s˘ĥßûA´g†G“ÍNSNJcĈ2Ôüş×r.†Ŭ7ĠCŽ^CB á‹è°=ŬrÑ`–òœlq­(2]Ŭż™NeKè”0³ì?§Òp1–÷ñ ^˜ò`P~S˙=KŬ˙?EùĉK››&³+ó‰£r\$2 $[׌/xÖp3ëâYUĦĴqƒµ*` r İ÷A ­“U8ĈÇĊo*ps ù Eölk§b@nQ+óÌ;R‘Œnž’‰2yφŻ„Ùĥ}ğèKéĜKVTƒ#Ğ8ጞ•pE:wʝžÑEc “ŸĴ=Iġ鉧JÇ`ɔX)RxïŜ’éÄx 5Ñ.Úh¨#şDHêŸÙ0Ècµ~ÁıJ †¸ï:qĈÈhyKŬ´ŝF;Œ‰‡K› @û3Ġ\îSN:8Ħ£'géĤßU?Ŝ)äÔRb%ÑûÚoŒ·€˜è>Š6 ÄÇ~)˜ O’ -ĞİÇXw5Í/"Ëá|k™¨(e$/ŜJĞG ¸à“ÇġÁž0Mġo#hpÑTé%Äòċ-R (>*Îú Ò¨ìÈ25ˆhĵèïş|I.5uÁ`QP£÷ւ)`ñİ—QQÇĥé(ü÷4“5•³^§ƒŜ„‚M߯oˆ5G*`?ÍRFM¨ à€ŝĠÌgŽêpÀfÚßnŝ5Ĉ1dĴ¤ı‘íKÄë[L -y¸q ´BÀĥ$@'ˆÊ6é!Wëà -ΐúEĥĈIıï6ĝ,ûITÁ$‡ŝÎy›Ù‡î“H–piıĉ˙Vchž]l&ÛßĦFŬ:ıÂO¤é$#Ȋ!D:¨‹…%)a›Mx“ŭÈÇ"_L—ú?Âd*ú:‡Ö0ï2]7x(ìş4p P8ĵ*.v5žsËb<ġŽ³]LQ†0ï*ĝĥKí•×+·@>e.-ÚoŞÓèŝC–ĦĈ€lÊïĈÑ\~R+$vo–D™Úg†ßŝyùê èaÛ|nŸ“)>1–Ħ°İ£_ù|hv‹D5²"Pt#'ò†ċı‰.G˘EîSJÏWË•ÌŞN AZâÑr…ùâ!Éoí¸ì¤"ŸƒXŭFÒ-ĝò) $^Yáħ|i RİĈA5˙=OgêÍCna8z*Ĵ2Ïeŝ6¤Ü]Ԃœpóc'S\I |²,×ÓqÒnL ĝ‹%HĦTz88Šżü‡ÖWqµÊs——˘.ËÁèoèpÍ Â^nCzüö„\ŒM”@ς+<.(Ü]ôwƒv„Éڐ($˙h•yBÛ[Ù£’¨'™ûŭ&Âk~Q 7Û£%R*>t[ëÓ £ĵĉßa§\ -Ž^{*ĉ™×yài‚Ĵı|rdÎI…'8Ŝ v†#8sÊÌĠP6ŜÒÌ7 is5ajABŽ½˘l²ĉ Çí½ax×QB)߄½™<2\eœĤàg8ħkvĈa8żŻ×3m !Âĝfí°-ßPh½ß/>Y²Ñ3…QĞ–3á>yA˙#ŬeèĝrqëĠ­Ï3‹"żÌ~uϛçħ4k<Ŭ@Iq“ôäëuò @îQSk½ħT3ˆbfEsJġG&³›[„IiÉŜÎñ&žÚiŻ>6ş$ÏÏèmıœ„n—po\áÈ+S‡Py3nİĵŞT˙v- Ötŝ´IÌcPâëD욨İñ˘_8—HêTͨ -oU#´Ûx2ĉ‘Ŭ!Ǥ¤nÂİl?ĦN‰œBÏà֕Qê ’Ô ŭ‹”äô]á{IÚ²#kÁħé£çB$چ„s(A9exċStlIrŜ6Ċ`ÉÍŞséû?/&Ÿ‘j–e:e·~Ëx‹ĴgNKyA÷ç-/yı^E“}M -ë—@wÓÔ}£ÇöùĊ76w;ݸ ­Â³¨ä êÚN}ĵĴHuhö´Şƒ+‘ÀĈyg í½\òzOù1zë`ĉf ż7ĦħrÑ -•¸‡ß.·,˙U\/ӕ;…+y=wynu޽"Ż9{÷°ƒçQàĦ½Z|§´"â€&Êi%[]‡Żêuù\ -ˆĜR<ާ·ŒìŬĠBQaÜ'ġé!H¸Ġàê ŝH<ŻÏö fîë0<"ükg–~hîé{íȞc^ÀàmuBôè?< H!ġş_U'‹%dÚC‰Li‘’y­ıáÖêû|>K6Ŭâ&Êûh7µı/ôœ` w$Áóï/zlܚgó‡³-Án}‘ùİüwĵ—†aŞı×İ‘#ŜşÍ&÷ži?‚ ßĊ€N îâF›Yİ!ŽI˙ıñÑh9$èΔÎħ{ÚVĦK·Ù×càŭŒwù-İSÒs£3kÊĉŒBŸxŽú…7Dî,÷{‡™ çê?”ż0g³'`ĤÇHƒŭÜnŸ„ĞŞĤLŬ÷-Ë ÍƒĊ™ŝú3€h5úe!Ħ^ĝ -÷PĈ — DÔZyŽêG›Q_WÉ-§fŸ+[Y5éŜ --ıaät6-ŭó@İİ1DKp§Îı!şĞicß̑m<µp2DšC@NğĴĜE™èD $7FË$ûVĥŠ>ÖŻĥ'¨żä „òYĦßxdyÑñV—1׆Ċ&$Š˘t:Mf´n]µö öÒÉzAEsT˙ŒTÂĉ}ö ÎĴFž˜µéD-4µ—dĠMĦ×"q˘·ÉŞ%r?:ÒÖoCÜx¤·—·ş÷úÖ÷lŝc˜ĉiO-–r “Ûç,ˆK.„ñŝ"oGĤâ҈·ä@t–‡ŒÑŠ£ L—­˘:šzmk<³‚ĈwÍÔlíñ;Hğö,KñIpŬ@è++dfÏĴÈpŜüÇŭ>(ÎE)6}pbr+{ĦÇiĜžçžÚC9…5î¤áşùcêxñVİjHöÊ˘9ÀÂt.·qCÄ˙#LÎöR˘µ9Ù^éŬ°×u -ÑÏĥHf nsŜ!÷+÷)Ÿ•d^˙2aAt†'À·Żë,™LĠŬ&pÄlHçqsJÍÓe7GÀ?ôò‹Ŭ›1w‚W"ŭ~ -ۈñq \#s´E.ŭƒŒñ2^rHr|ÙÏRŒ,:yì2M`Öü ÷ĦÈÛ31àÇ!û4ŽìÌ' -P^Ĝ(-Ät,5 •vaĥİĤp}@öC-Ŭ›ĉA]eƒ£SñüÔ c۟„w_5„š3ÚÌ.MğÁnŬ6nw #"“‘üWÓ:DŽ Ù˙֞7 ?x9›_(¸ZD`Ÿvyç;5ŠÊÒ.G‘'­ÏĦ(rYğ.†žÔ˜ëĉ˘ÉĤÖ­ÑÚ>ƒw“Wߌ1ĞGaİÙ@éıX íGêö4Ĵ'[Î"htœ ‚M:ş~3´½WÀ‘“ S˙ĦVúyߛC¨Ċ<îġĊĉ…ŠHüeÈÏfÚ‹”·ž5ŞÜŽżƒk”h@=ÌÒÂgŜ1ŭ~koE(¤8È7 k q-})ƒ‹û.eŸ˜žwdD•Żw·1\l2œŒlŞûc#B}0„}l…ÀÑÒaŝEĦ´$€Éuħ`ċÖ÷"èèédk†óñÎunf•-ê+Ġ8Fİïí -svJh޸ÚéÏ<ɖUME—݈7|aİ)Êô£ġRù¸€B.u1İU~ îùgĥu˙]{eĦYşS,¸ĥGgĦ:,èäĦ‘¸-‡Ÿ{áœ%/@‹²?üé7šĜ A‹È;‚Éôùœò„@™Xü \Pîhìü„vœ92  Pĵh{weĥ/errúDŠ‰&2^Ħ1_B((Ì{T˙‹Üí§p} -€3b-Ĝ\âôğĴí·Páa³ÇĦ½ß-úĉÇî%?Àöi>6xzÔÈèż¨€$ÎTĜŒµìö(ód3ô핧Wħ[äıĥÔMHgV)Ğ­ĵ?ìw²E8'§­Ĉ/Żd,Ğ´>sĦQgµ%!-âë(û$â–@"(^'/ĜŒ˜ÇħeßZ‚иDÁû -zzä‰?d˙I#óy¸İ[pÍ%1Z{·€ê^*иL·>:<î3Wœê#='Àâpéˈr~œgŜÑfB<;ʔ?[úµT~Ŭ =t›FĤLfCxU)Úf -‘ş¸pc·9€ 6³Cĵŝ=´r ĠbĊĠó˙š‚ĊïeÍùĵdžDslg¸.ŸXëècè턠ŠöŞK 5Âw~&ßmêAœpĊÒĝÍ_œÛ}Çù‰Ê\mĦšë¸+ħ)bL]Ĥ*óJqâír5í€ïİA×İL|Ò=Ŝi+ŞÎM‚0*AˆĜö\/Ì=@˜žïÍĥr‡QŒĥ³—ğ#“ è‹bżÍwßóżbّ6Á˂ĵ ¤—°˘Şr4˙‘ĥ _7 ÑġĤŸÁq]÷ÒrPŭíéŒÙÓŜBsÀ.Òm°),ŭênÒ!¤\êD_'µKë6UdubÂ+[Rà†_W}ïħ0P@$ûM+ğlyD­bo8îŞ]K!ĝ˜‰VüHżaKƒ4aT r;~ “2Ĉíô§ĴÄĥ™‹›ë ŠGτĠ?óĈ~˜sş |Ò7ĵßğ|ĜipOÇşPX‰ï˘<ĵ6Cšñä eC‰”ÁىHtŽ@Í9eĥ&xÊù²˙C¨)şvJê\<ĥ1 J|è=]ߘ͙“Ä…ĦĊD:;ZÑŒéœżŝ!{“)9aÛŬÑɋ„ĞÈwÂÙƒ•QO§ÊĥñM˘9|h4ïĴ+GžPŬ$$ğP–‡°yw/”ƒx³ .ëêúÌye¤9öj(ĜëÇ, GO E3 8;4îu‡R4­ĈŸŽ…䆗:Ħ /ôÖ§·SekĈn=ħİŬĠ§Pו,|6Çê†/ŽLˆÔ)QƒàKQ,8ôŝ›–?GEoÀ.šc-+ıßïĉĦA ììĴ/²KŠÂİqöž­Ğñ ?RjEOhn£°ö2Í_—÷ĉ‰f6CŽ;żÍKˆ% ĥÖöf]@È ÛĈ YĠÒ£prÔNê_lµ!kÛÂ!Ż¸ĞNËn‹z]=İ”Ġ– ĉ烽ž8]2u½fÄĝò­Ñ;½_ħĦ˘÷jÚĥ‡>£]ÇçÙħ/Ÿ1˜ -J|ó? í¤Z´lé‹­ÑMTÇX| Ï°R1mù%ZŝżíÄŠ ½ŝä¸LXĥ5ì­ä(ˆÑ-NE…´Hğ°´ÈyˢËö˙Ġ‘àĠ‚u)ĤD F:F*m"˙az|ìĵà}tĜ‚A]He ˜ ĤxTóúıBp<ŽiÎO1kž¤! Èي¨´oŻ54í_(iĴhĈ/ „ĝżÒ„Ġ*”]o m~jY|dÎ1J0aïu†–piħK(Ì'ĝï=葴‹@FˆTñ Š_p̏,Ŭ: ùW U[C×ĥ~­ˆâmeÇy˘İA{%gAc%ĝ´ıŒŬ#ÄפŬİ?ŭŝ,dĊ5vS½6^wúŽu§–!Ú ’Q2˘`ñË7ùp'Y›òÎÀ̓“Ğĝ̓Ÿ2ŬĠ…"Óo˙ߨHıïç%@Ì(K›XxÄsO5¸qċZcÇñVHO£‡gÍĥùàAÜ|Š­ú"sI‹˜ÀA–$´d]şÍM§ġĢ$[ÌċPV`íRş´Ż‘üߎ-%I0—ΜР-´Ú}œ˜´i+İúÍ´9Pš-sGÜĜTĝü£ĦÈg)—ĞTPk;÷½bCINo”Şŝ§%ôħ” eÊ6ĉ…YgˆnÎ}° ?ˆó~8ĠûĜeüŬ%ʲ^әîUjQŭw„@kàĝv‹yjŠƒ^t…—ÍRL4@–:_íA¤ÌTħ(ß ˆİ.]Ívı_`IcŞjĦG;ùúHôE+“E„ŭ9 !ï‡6Üu×~ßİ·Ï9ÉêJQ0J¨÷ .X‰ï¸Ûüф×Ò~ùÎŝ!Ií¤uÀ¨=ˆhıüĵ‘–ħ‡4î?ĤÍéaŜ½p¨„.8iĵ!êŜçU)HzŽŻÜҔ–yçŞŝ’}Kşêy6Š‘jMž>)‹L g²‘Rp™‡fĤY2RŬȳkİY¸ƒŬd`SÊĊܜy5œT:@^Ü£Eï’Lr½ÊğNXK -QùMpˆĥ€Ġ&TRKUŻ³è.cŬˆ‚ÑUÄ"q*|2‘A='ks?÷[—tÁë×›sœĤ‡ŭÍ?^~Ľs̀,pĊÊ(АvĦ°—ËϤÄ×Cšv¨:Â\d*İ„1!áÔ1ïşž…òéñ-[ĝ98öU}bŝéW’êX`È;ÀEaù·áŝ¤' `?ÓgŽsgö?AŻ›Ĥ€\1%˙ìĠfèñ„óċ`‚ƒvnÍşgA˙ }av˙oˆŭĊĦóo!ı’)á,Òé°Ĵór )ˆ°mGAŒ…Üġ?İzöA£†ŭӀow ìŞƒ#ÜqzñÒÓĜ2kO}Ó&oš/qÌ·dgȸ”'vSoˆ\C½@'6 C‹/'‚Ĥ£v·ˆĵêĝÖNm²ÀÜ*1ŭ­ŸGÚ(-ëx1tO¨%,ĵú'˙œÂ˙ċ~uMÄe j˘ŭyşê°•NùŠzlÉîÔ­qz ßߟĵÑF"'(P}Œaù‹ÄmÇ"Ó³Üż”¸ÏIÊd~H8!%íF™Ğ†žLĥ˙#;³––´ôż]nŝ<ûż]ŞŒž¨Ğ%ğÁtüXôˆ(ċà5½f*ħfáó‹é4VÖĠ§B‚˙ˆÀ˘·ÇÌaá,ñXtäV—ä]ôWc?hkšŝ(>JÇPV(Ä5ÄĵµvLN)*˙î5~Ù—,i>(Ë °@µ}z)â\÷Ġ!ħñËÁ (Y\˙(•8d„ϲP¸ÓPÜógê^Ÿ -—çäŝ”àû˙f’ç)§Cù?àüÁ|a:zGˆNl'ß}ŝ‡°zÉ[pεOq:MШ)Leè$]QMôXĥSišEŞÒ^ġRs÷Z GúöA9E9m4u‚-6 e%}£è‹9MÇ7¤Ô~Şħ˙?éOŬ—¨{Ñ˙9&;_šÁá™ù1%ñĞ[<Ù~Ó`Äa6ç‰ßğUı35ċ$Ĉ´_XíŜÚİO~‹Ôñ²^苨zİuQ²}ô.\vzËêá0|´"‡û*ŝˆ(Œà‘Á;,lÂ˙<¨ğ ;˘ĥç^uá0§ˆĥ>*Ì {ĦhE’"ÀHûehı@•r‡‘j¨*uŠŽĥbXŬ -Óg£èT.~ħ|Š§vŒ 4Bpŭŝ×$^,%k½èиŜ5Ìéd˜ Nb #Żlä´b–Y)ȍMN<>ƒÇ†ĤDcKšWîa׏Ž@µ*)¸ÊŽ{ŠáŒŒÙä)ɄËŜ#ċÇ3ĥiÄô{Iw şìQԝ $”ÑvpÉĤúèó\pµ8ó"‰‰PçY?ï€äj!Sdž*áLħj”kL:şy–Š„&dp4rĥüċ:BTÖa)—ïñĤœĥmmÖz‰›ë"Sw’*Ċ|•ĝÈgÁ½İJ”Ya_ي@Ù·~gR€‘àšê˜xzyî‚G#ñ+ÇÑ˙žqz,E£‡¨rğšA<úÚ| }ĝ˙‰°G)ñ -ïÒX²ÙÏïĴ¸X ”& m™Ġ+Ş[WNnĝ -÷˙\Î1ı>˙ƒƒı›Œ=A)J…ĤLá罈f˘Üċ­pDŻVŠZ]ġ|úsè1H-'&Ħ`b mê œ€sW ıÛW'B71ż·nûò -nˆPñ{ĈċWĝc `¸§@_ŜPğ‡ù’@WU]ßêènsĴğ^_…œÉŬÜdĝ‘[ -Ĝ,™żIŠÔ8Z§o·Ù (t™á5òŝ¸ŽMğôi ÑíšñÑİPpUŸ‚q-¤Ïî;GŭwúL›Tħ£k…ĝżÙz×Û(Z³ŞßKš£aΑnküò¨Ê)‡ğÏa|_Q"c›ĦB? &Ğc÷°ħêG8|6`„YÓäك_ô$äP úèÀŬ˙Ë\İ\—Eĉ<Ôğ›½žÊ‹Ùı˙À„µ]Ԏ 5jÏGˆ¤ÄJçDoòÔs$c…–(íÛ-¨|h‹³}^‰ù´H7^°*vġ¨“Eî÷p†ŠX#C<¸ODž–½B ˘í\ıè?¨Z~[’ğX|½Á?#Ï0Y€pîŬ DèwBX2§A˜óğĈcıÀŽ,ÌI]Hl}vÁġBs°oßXàDÒĦ:`pHpíd…ñ;Ĉ@*ÈO°xYˆâàQ^u…í–z3şŭ+òšT“iĤamPöċ ~B\;Ô Ïà'"qžĜ75j™ïTÒízDLjzpĴŭƒN…Íkkĵ?xHÎÂFhQî Ğ$Ìj£j–ÖĸC§\ŸWò§?°šc8+ŝí[’İ "ž^€JP`!ŒôfX] ^›—b­d<éMݏ ċĈwkġXĴ‚3ù_Ö%À§ù,³ü·¨Û6é÷ÊÚ)żĵ)Ègƒז"ztf˘ Üĝ^~E-Œ×Νa“f{Ï(ü+OİÑú/ ħ1„ ¸ş.š^7ĝÀġĠe0瓈,@Ñs´hŜ9×&U•D Z·ô·Rİ6UKÖ. +ĵÛeNž -Vù˜ĥcÏ¸÷ž˙XĜ¤^Ç'ž_‡Ib>ÔÍ›ĵ¸HäŠBFÔĴh.“”ß/4Ê|%†@l—hyĴŒKß7âë‹)‚Ĉo -ÌÔEĜmPiëџPëîuwéqÄç0Ikŭfa\ÍڅßÇWĊıD<)Ğ+ﳌóYĠñĤ-ĦSƒ%ÛdZëc‡ĝÍyóò$‹i;?á|ë²|İP ×ԋ×ɘ´§$óËr=dj‚ĴQïádÁCÑŝôuwÌCèÉğFÀÍ ĜTk*ŸġŻ$Q÷ŻGêÖÑ>BĞ_/ ˙ˆƒç4”ÍÚJʙÏV×vÛ²Ò7ĴQ¤rBŝwċc_ÁH&zšR‹(ĵêEqäfċ\Ú @gŸç'ӃsOŒĝQôG†]ÏTHÔèdcğR¤Àħ?xâ´ 0oT"cÁVÉR4u€aĥçfĵ›!Xo)baR7Ĥeg8vÈ@L›áp΂ˆŻZ¤†Ö &üNÒu~èÚ[ħò²O+O 7{ÙĦ?­ú³ •U”ìb”ò~Çİe˙ıU˘† Y‡4oràx“ -r%lwçñ7…òÄçqîñOgvŬô"ħ})Ĥż‡šFu26:†"YOJ08ŝ›'׌4fۗ?”á[šQÖwrħ: -Œr˜‘ë=à”fĦ³wÙ´ÓEĈ@ïúĝŬ`Ê°Ğ,öŝóX}ɧôëoî4Ê3ĉht`Âô Ŭ1lÛ=ÉĊ••–™9랂éÄ!ğö0˙ß–ĉGK˜GǃŒúÂĊ„UX¤8qôӁ§İ}9R ú8‚)DsM3 SZġ04ĠÔıQb½`S& $Yo}ùĦ’fŒ!œ¸²{rj0İRĞ“8&µç§.Ħ&ĵr#ЍQú–çÏ$èì9àhÂÁšŝ*à7-(ŝÍH|ʧМœd£Cy=8Ë‚¸·`2Ŭ§Ú÷D”aı‚}t==‰Ä*9 mşƒ‚‚%huŽ‚[Ž"Ş4–ö 0ħµp&£İĤoƒ˙HŻċygZuyz$ül azÜKRUÈïê<…§Žx…Ùˢe5ŸÜ´#ĉŽ˜€ĞA‡áĊb^ÎO‰T… -“-AĤS珞ùÜ ŜNÈf0ô -Ì@DhpŒ]½ŭÂWoT°ïĊ!¤SÂ"}‹ŞQ†\û\ĵX - ŒÉĥšÜèéRž’sċĉ†Ŭ‹Í3ݘÜbY;^o5yS‰àkTÌw² ê ÚBÍë’Š6ĵ -­Ñ:‡[ŠÛô5Kĥ2à8P¸›½XLG“aĝŞĝĝa¸o6ÚħöuèF´6ĥñç`xßËê%ĈG K8Ŭ5yP -ħ³> -endstream -endobj -676 0 obj -<< -/Length1 1418 -/Length2 6498 -/Length3 0 -/Length 7916 ->> -stream -%!PS-AdobeFont-1.0: CMMI6 003.002 -%%Title: CMMI6 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMMI6. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMMI6 known{/CMMI6 findfont dup/UniqueID known{dup -/UniqueID get 5087381 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /PNUTJM+CMMI6 def -/FontBBox {11 -250 1241 750 }readonly def -/PaintType 0 def -/FontInfo 10 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI6.) readonly def -/FullName (CMMI6) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -/ascent 750 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 59 /comma put -dup 105 /i put -dup 107 /k put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ<ï˜ĝX2-Τ^tĊEÒ_á’SœÚKŞFÙÄ1F^jżNBqĝžŜ×ó{ä³´y4ö-FègbÖ˙öԓ{÷"Ö¸ĦW–B:§rĊP‹À ?dgĊS%|'²Ĝ“w&¨F7J…ĵNÀ°¨œL9VìâRtıbÈTċ5ô'ŸâmƒŒ\‰—Nš"K<ù -’wŻàÇÊÈÜÄÁ‹Jv‚ċ$†tE;ÈD4ŻVܢüŸ§vëš{bGCSMĦ!R -ÈC˘”ıï\ü#Xjœ‰h“ -ë½˘šçho€—ù35ƒ8—ŸÔ"‡gŠ{d<ŬFR€ıׇÊÒ÷ÙàÊäl Àğ(œ#|hĴ¨ò~ËAS‹j˜cZ-.W eÖĦÄ*wc0 ÷ıG1—ĥWÖLĉtÊġjĉ˜†˙GÑ )Ԟl5 Ě4ëé6ĦŞgfP˙ĵ¸ġûQ›D’L:ÁïJ -ĝ)³T,§qVìüfĊHèeUċíŽÜŞGʖŞ#’‰8µÜ‹÷˙í.T‘Ĥċ,Ps,é!Ĉ ‘½„³­§tò M˜Óòq}K6½ÚktwŻéêa9[£~‹>NĴúœ’lìÍġylÒj\ÌĴH÷áLŻöòcšëĈğïĠ0?oŒú˜„%‹ˆ>ާÒ™Lŭíıu´c2ĉuĜUŝëĦkKòĠ0Ŭ³§xˆ–Ì ğߙzÎŞ ˘0aw†ŒĠ5Joĥ•ϛ$_ùôí֙WħòMZhû%²G@˘”L~/G2ɜdşg5žġNunmž0Ç! `ü—ëN1=ı_ñ^œ‡ŸĈkş9²û‘˙F ı$2@Èwk˙…d…DñŸMeycû‚ÜÔ î€ŬìĤ҈&d Ó˜ï&úXžY6—êĉ -üÁµßŽ&ĊÎÚ÷˘ÈÑŭÌL5%úhE„j4Ĉà#ğU*£ŭ'dÉğôÊgšö³…ž²˘îh#Vàş\›3mß[qNŬ<60!˙Ë2Ğ>~f[‚ñ-[Ĝ›żQìŒwkàp—s9·ĦĠCLFSġ…Äşċ÷qÈSĤÁ#rĤg{#œf b¸ĉÛÔ§~XŒDI•%Ĵ:`màÂrM/ĜIàjÎÇoÀŽĈĵ‹”ÊİyúLòmÑIµ/XéHÌç2½Óĵà&ŭ!Żµ)Äŭ[e§-~VÒ³şé§$?×á$oÁ#VíCgúSO˜GôhQ|û‘RħĦ7uîçuŒ ’DĊqì-xŒ<SòúTmċPò6ĝI+ôĜÄ֏§Ħ‰HàSÂ&óÑAb.Ö’‡#­Faŭö6KˆÑ>G„ŞSϵР›âÁiĥŻàŜ*Äħ˜hÚ½yÌ,ĵRóäµäá§gdӒŽTÛ;ĠğAÂ{]Ş.™IôġÎäİW³"ŻĠbĊ:fĞXMÁĈôE>ü“ÙN_9/—‰Ĉ!Ż—Oà­)"™Mî €nµJ—–Ñó;˘89,ZហŠĴÚĵ AĤ‚D¤ŒDt'Iš>cIüĠ,Ĵ÷ÒÈʃàîż”ċ¤šâ¨„{‚Oş~•ĵWĝCŭ“ÁA#BŞÒŞU+¸Ê4B\ÇĦUı”-Ġ\^ċÖñRċ>ÌÇ [֚WˑçòŸJü1ü͑pVĉycħŬǞCġŠzùç²ÚÓÔí·€/?ždġ-ü4ĥŒzuž²È$çLÌGï,<ï+‰U¨¨ÓĜ%˜5Sm€ñÊ}<‡O r€ü‡”ùž)Ä '½Wħ´àíe²ĤqŭĜ˜dùxÂNġŻ6KÔfïG #Mìe~•İğYĴ éBÒÁkYÊĴ ”kŸ?kwê•r֋ÄÄĠûÈjĤ"6àKFi%?ħÜ=Ş÷Ġ,`H -ç‘xĉeíŠë)ŸTθLH›e;Ÿѽ´AĊ§ĉì 4j‡ˆUk{žµpÙöEa'ı;Á0İĥ ġ“„7qŠíŠeÑĥÚkJMgú£–ô/Ú7ÒÙCec޳c}$¨…­Fx–ˆ‘d_‘d+'πaĉÀ{CMùñċxáíÀ)×Ï{#¤ĝÓQ›}‘qÓùĴżëv˜z¸!܉š#‘žÎÍ$"ùŝ AèÑĤ›WÌ+tFg9ksŸÙ/NĤ–mB`ĴŽ)Tê|e†9’Ùc’ˆ&bżŽW˘š{‘U%˘÷UpĉİC› bŭGz‚<ĉ/)FdX+Ó£ ĉ’`eò,èÍЇ‚xĥCrdç Pê@v5‰ÏEb Ċù`´Úu£dàiì#ZÓ ġўŠ'™JXù‹)0Vİ`QŜŞtPpĊüܔ@lhÊuĜ £0J|Ûݞ„,ĥ_LTc2ú›ï]N0ĵE Äèż;ġÉğß[qıéUŞ:`‘ĉğ:ÈşXÙC|Şpl B€.ìıà{˙‰IúLšĠ¨6á—I Ş -Š ˆYQâÜ÷ùŒ³´[OìFŽ–AA$.ŒGŜ¸‘yÂ#aÚ/Ğ´‰PFPiZdÏıSÂ׏°°Fk³0сR`Ï.ƒIÖEòÊQĴĝg.nğC@g!İóÊvÍ˙JEs“²‹áFGžtX‚ÎÑ+8Ó˘Ÿ††ëޕɲ4ÉĴ‚“¨:oܞ 1ñ„żòÎzü2[È™=ê½Ş£ìxSİèâC:VtĠ[ëmSi}ûíȊ.EdŞĞb÷ĞşVĊŠċÁ!4İĜ.m_Ûyہ³ü:ŬĥT°i 3ƒ’•3:U‰S˜$ß .†ûMÙ9µï_L#ˆŜ5˙Ò³`jß·´½zB}g^W3ëÎGy÷_;ŞàÈ+i¨/â?@Fú1Ĉ*MrÏ*‚)5ƒĞƒÔH°R inww´ƒħM@ ğkÄ$6ĥ"ßĉ;{:I*µpn™½ŝʅˆ.Ü(ïŻ6'´ˆÏmĵ˙¤mô“ıQZ^£0…kµg~§3Œd|,âY÷ƒ óĉ­•šñ`ú2ÁE`–šß$ĝĵWıçM%mçI=n¤Î×ó͉SžOÀ§ °- pTFúqĞԎáĵÁĵ6€·€"’Ôrè€K -Îì›ŭ–fU›,£>/\Œ~È -È.vžı@ùÌö•NU=çx€$xöiŝhĠëEŠ´ ÜŞ–´ 7 Äĵ˜žyЃÔîhïXϞçp2÷Ş[ıÓ½k~‡•çħY*‚έ ĵÙÒMcBÏrV˙ġϞÈ˘#’x?ò°Z‚>­,ĤdyAĝÔÁ|é -tW ‹ıdCßiĜıüŸGA‘TĊ„ïü‘ç}ËÖ_CıolˆħiĜ×Ŝñm3_„„SÒ˘ënŞc]ôSĥÁ!:LFŝ({Î÷îÙgPêp Îžd>)Ĉü…‘ÓUœs³üž(íђW1iŠĥ.ÑxŞùŻêƒ´£ 9ŬoĴŻqklɒ‰K‹4ŭĠ ÍŻ‚˜žA•œ ’eŝ6ƒïÈĈe=u‚­zJ(‹b‡xĥo@ôÜL Âŝ´·ÄĠ‘èey -˘D£Ùá2d-­QäŬêìï'>˜ħ9.èv!ÍÎ7áħˆÖ*÷y&{è×·W9šóyë•ĝ M™Ì<8ö˙%cô$Û û‹Z—:ôùĥzknp6ÂVS“ċĊ;Ïc|v><•Q#ñò.Ìrş†ll Áú¸ŝN -̜-†ü”ıBJĥ÷Ğ{5 ç‹9nù³ß´;ĵdŸÚ&ûZiô˘Q1Lm: ¤ü2ë@ä+ y~H˘šû™²KuĥWvNcP$ˆb7&‰Ìİó²3ŞmÍÓQaż­XŬÂèу "ĥ››xxaÈÇË z<Cî#èí%ż‰ jNĦ…Ïh¸rŽ‘66ߧGĞÌ_6×‚ÈsŬŝ#!q8³&GµĞ˜ŭûÒĵĊÇÁLğç:‚â™k‹ ½*VhSœKîĜĊ“3Ÿ‚ùùn·FFŽ`ìâ4pë>ğ½ë]ò)^ŽĵQŬA‰£¨|İ ñڛÔú¸ÇhF -‚G,î\_ğÁİÈÛ³j§6,ÄġŞċİ[èĊt`§b’^SĞ9 |İBÛ †&um´'+-ÒĝĈ5‘òj'Tg˘ĤċMh¸Ç…d ˆ -ĞQĠRÑ#R˘üI,ĝŝFXÇ'Ÿ£F; Éò -Â6êñ“fŽ²âgly;ĥàŒI?ȉM‰stÚ.cô+73§5•Izp£Ĝ)ܕ„ÙË7bhÌ[ ×FĈ+ıö'÷ŻĵY]“‘½QġUĴÇ6‰gÜĥÁôÁĝ›–ÄbR·ĦGŝ}—Ìe \šA 1Ġb1 iË â̔vKAŝ §°{§gfuö¸ÄùĤ[İnj}cÑŬ°ŭ6R?öĵÑZkUğà቙ÍÖ_ŭ”Ÿ{[òĜÊĴĝġÙ\ĦÌ:>MZ -vŬ˜¤•´ÙÍAFGäĵË U+²9[ic%YtâtĊÚ駗E •?[J‹wNy£p ßŠoĵ"Rİ5`çjŝ=ÍŜ&Vĵô¸Şĝfuö²0İĵkec•Yžİĝ†ż+Ĥ LejġÚ§r΂LèÚĥFE`Vµ!+‡O*TµbÒ˘B…VG›ĊÈgóĜtÌY„Ê's`- ˆéAZLDż]ì4[6ŻízšĊRòP|ğ8h)u`›ûĤ i6ċTBzáĉQV ´u~ô_ÀHü–v/´pù²á­%ÈşÚżÓOŽT–[F\ vŽ’I5%v›á+ïöƒcü£˜5˙‘)S§oK38ˆxWoÂğĞ7˜éŻÖœħż:ĜYÒ>ÇÍ7÷G]½âĝĞ.mèüŠ2AfÖ}eáĉGÂáfƒä|Żŝßç;~¨Â(ĜX¨H_Ĉï-„ğ!ĤµH-ƒ7ċ†2ÌÜm9Bޏ#ö1 -ÍFÂÒ\—Eàùñ6jĝMKZë"#K É=EAóBOŞ3rOĈì˘ÌZ>Fv 4ÜáÎËfwÄBgÚ¤£žéAC NN4ĵ}1ş;hG;ÊĥδAq¤zğĠg~Œ. câ¤+‚Ú‘Ò–ŝ‘<`Ù!I£›ËÌìnÊûİñ.ĤË×İDTFHRÁ,Z”ó;4nÚ,@ïŠÇA2(Ô‘È!ŞLÔ £ħÚ\OgmÀŻÇa— ]xX5íqMAŬı—SÖ 3/ëĞĜaâ\W@Ò -¤ -,›}4Tî†ĝ>¸ “ŜùsDòżD[¸wzjœ ‚’òó½eI.O Š,3ı5öuüžäiX˘„ğĞÜá=›8Ïğ]ÉßDZ0Ò÷6³{YĝÀò-ĉÉ$=Ĵ}éw²T—!2ċ|áÄöÁƒ‹ŭŝşÛüÙ<5ìxĵ? áµ[/[^×èəĝ)“˘°oŜŻ*uâÏĊöÓÑjıᵙTĴó Q=1Tàw8˘jÉBŸ5“ŸÖċĊ‡ĜduKwMıÍÂÛŜŻ?h`|nIĞäYN7½ÀÀv‰4†½%?½kÇ$Di3è'íÎüKž+ϖÀƒ-´ú‹ċží0³°T—³žÓ£¤7"G „%!~Flf÷ Ò°xÁh€5>ÑN”³Żĉ rĦÛJ$ß@ż˜#GGôÊF/·QȒŭhYp yñ$•œZjM3P3Ò(ûA4İĥÈ`Qŝîë -ğ§÷{_üp¸–W'ĴŬ¤şŜzĥ-ûĜ‰:ÊŽ‹Ï3"ĴdÏİjĈ ?(){ĈâÜ iM$¤| ]¤ı>ShġŽĤÙòƒĥ긕şa8uÂñNùѝœ úÊ'sȈĦ0p—I„ĵ´_³h‘‰2I{q)çÊÒV!vTÙVŝŠ¨‚Ħ9وGVnT!KU—Û{²hBЎÜçá8ïwß:2ċ:˜VZÈ Ħt•!Ĥü:,•—1¨sšĝ{4÷%Şœ8çòİYïK4ÓïġòŠ’š:¸MrÏĠI"8ê/½ËÇ,OO{̇ná“gġbÑHÄѐi„xğĥu‹0U7ë }|^£1Îò~)nKı¨Ùéyĉd'“ìbYgX£Íġ8]É_֓ 5[˜#m³Mġż uĥïĉʎĝ4 Ò[HñRÚ¸?΢ĈƒÜĥĈ—Ê“ĝp/Ò%·ä{ßİ•8Pġ=Ëqçv‘ċ‹WZżTTŬc{ʀœÌRı²ħKMôíL:AıoíĦ¤:Ç$r˘q/X m/ĉQ,cE@輻KI7Ċ¨áĥ€1ğè+Üiµ‰ vĵĊë„Ŝ4޲џŽŞĵüïùİZİ‚4poj ·ïX‚ïóö´ëì~G/;~ǎ‚ ċiñ9*˙8Iú -9˙ j‘u,—Úʏl_P!V%ŭ*<ù"Œ²-" Şöİ8“qŸ, Ŝ{Pô²ĥvݤ:ĝ‰ëv -endstream -endobj -678 0 obj -<< -/Length1 1594 -/Length2 8979 -/Length3 0 -/Length 10573 ->> -stream -%!PS-AdobeFont-1.0: CMMI8 003.002 -%%Title: CMMI8 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMMI8. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMMI8 known{/CMMI8 findfont dup/UniqueID known{dup -/UniqueID get 5087383 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /TWBVYQ+CMMI8 def -/FontBBox {-24 -250 1110 750 }readonly def -/PaintType 0 def -/FontInfo 10 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI8.) readonly def -/FullName (CMMI8) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -/ascent 750 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 67 /C put -dup 70 /F put -dup 83 /S put -dup 84 /T put -dup 59 /comma put -dup 101 /e put -dup 105 /i put -dup 106 /j put -dup 107 /k put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 114 /r put -dup 118 /v put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ<ï˜ĝX2-Τ^tĊEÒ_á’SœÚKŞFÙÄ1F^jżNBqĝžŜ×ó{ä³´y4ö-FègbÖ˙öԓ{÷"Ö¸ĦW–B:§rĊP‹À ?dgĊS%|'²Ĝ“w&¨F7J…ĵNÀ°¨œL9VìâRtıbÈTċ5ô'ŸâmƒŒ\‰—Nš"K<ù -’wŻàÇÊÈÜÄÁ‹Jv‚ċ$†tE;ÈD4ŻVܢüŸ§vëš{bGCSMĦ!R -ÈC˘”ıï\ü#Xjœ‰h“ -ë½˘šçho€—ù35ƒ8—ŸÔ"‡gŠ{d<ŬFR€ıׇÊÒ÷ÙàÊäl Àğ(œ#|hĴ¨ò~ËAS‹j˜cZ-.W eÖĦÄ*wc0 ÷ıG1—Nׅè‰sˆ'î&X8óğôüÛ°²ö3şĦ˜—¸/żż`ħC37ôVl"ʀÚéöùbŞĠNeP@KğVcžR„8Dh89Şëûġ˘ pz šLï›F]Ġä˜ĵĵm[YüöĦèùĠ´]”÷ óöŠ_òhV`×I1íJöäŭÍÙŞĤ*<ÄpŸ{v?÷ \ğGż—]ĝééœ>D tÍ UĤ#ŝï8̓,Úûe½˘èG- )Ö1C˙4#è9âĠĥB~—Ş”èD‹Ibŝġ_ 6,Ž=;܋o,NġIMœj_üvVoċ%ÈhĦ§ÈQi ı›5X<ŜĈŞĴl“0šLƒ„Ä ËöşŜï’âc0+$ÊcŸ:íĠ4#Ì3R+h~y35ħŭâ42K„İĥƒ´ömċêŬWz.˘gċ!jAĦ|ÓÏvŽ9—eqöËŬĈyF[qÂÙĈ—lj… -éöċ§“œĉ)jҙĤs>l§°¨–2²ŞgçјpTĉż@M/{[ğbîK1NWžŭ½ú^×t€D§É$Ûò;áČ,,ŭ…­êĥBYQ53˜}ÀQ7sR ğË|4aÄı‹ûŻˆ=8×İ1• Y 'ò;lÖ3#pK‰›Ñdo‰ 2{ÁPĈ?ÖÜkùÊŭµKuÄU%Ú¨ğ5@_ÏBa˜*ïÔ{U’ĵ›ƒ-ǸŬG˘†Ğ1ÁL‰5UÀF0éû҄>êMR ×1)dqž÷a,<ׂR–•ÒÂB§YÙ_Ħ²– ·ıÔĝ1;˘VİÉWú*]Xİ?û ?÷"KZ¸ˆƒ†j@Q8'ƒeŜğtâXğµè¸<ÜĜùşë•kĉ{öÉs-ZŸĦmqq…rÄImŬÔqt/9aŸ†N‹gcZïÔF‡fD|l¨êLYùÁBj÷g­ú…°›§}`Ż‚œ°h$šĉ$šTHĊ-'‹‘ö‘RàÀuV×x#òœ>ym‹şÖ›&àġxşŸï‹”œôy †kùĥ˙ÔkxHÒ73_‹ëĜ‰Ġµ^0ĦZ‚SÏ%Ŭ–ÚĞ=—jx5XWYDœ˘è!ˆġ¸<(ùeÖh6‰£µh· ĥ×Bĥû@‡ ĉ2OêÉR(!éK*°ÜŻŽŭ˜¸”tÊ^çĜñí";!0*Ê -tG³û -˙lŻ8JY|’Ú -şĞ5K9‹„ïĠÜñòmœYÓİÇÌn FÈ÷>-?)ĥ"ȧ·9V”ÇÓ*Ĥwj ÔËgĝËڕ–ŒoœLċÁ%Y~ZMËŭÁ : ž´¸Ì ğĈçÀ …Ï÷½ĦŒžèĵ!P!Ïl10{FÁtê'Xꤞ‘ğçKÄEM×8ÒáċtġÖˈ(üŸQ3kZ¨ ˜ˆŜ›êĦ4²Ÿi_9Ï&y£ˆsÊlAÔʗ3*ˆâ@xk,@|xÀäÜ/ „ÙÑÓʖ×)OÖcİ*ûDeE| fü° Gv6\„‡ÁU8ë"½Äm1ġaè0ŭhÛeA·fCÈĠ+œï˘5àìËÇ5 oéN–wÍ^‹kœĵ:ßG û\û0a#ž ˆżŠî}]xü‚vRf·)t££sLÎè¤ûŬCs_W@#ÄèµĦ7iO–żÊX§Ùà”t&{€biÒ˘ğğYnVÁq¸‚Ì à!Xƒ[oíÍ£wü_î "Ğ@àäÑ]Ñ J4 ‡êÒrSEħÍ +,µ0–Í9ĴĤ–DWŝF²"†‡C˙Í@iÜĉ[ԗ @í~8”öxtvžŞ.ŠfU³$ ^xÄ{mé³`†ŽŠú#èZÛċ,ÍñŭQûŝR² ­ÏÚĥĈ ‰€ˆ %„SÈcí0áğG˘˘ĉ.ÚÓĉ;Û=÷î”ê°8ösyëżĥ'óZ]Ax³ÊwZÖêjGµžOIĈ†7ŠĤ,Ì5ċoĉöİßżħÂ<Òk@Ĥ%sI\``AIħF-•Hëb`Ĵáën€Ñú80ñ%ÛQı^p›ÏĈÄu‚s]”³S4›/³ُużCé³ó4+‹ŒSZ€qp`Ñ£ŠlDà”Ò™04-RwÜ$0•:ŭĜêÂÒŝ#ÏzÁŠ,GLÍLwüÒĦšK^ÖNŽ˙Şbñ•)àżèQ˜o•Ê5²ôU7‚ĉ˙ˈ*ÏAG¨4Â1rmŽé˙ í͜=`ۃI<ó*V­=(Ë8˘ĝ#+ĝ+ċy7é?n?%DA€sG­Ŝ˜;3žáŝ5^*jȜHëùUŠ1nĊ/˜°w³`Sĥ›’gŞ@aĴ'sÒHvĵx EĉĵÚ^)•şp‚ҏÓóœ¨)$ú—³ĊéZvĦFBşLG—8v2Ğż#a5X -çÏÇ4ڄžô9ĝdNÉ@3›\9WtžšŻÖTL÷%:íäқĜ£ÔX9ġ-]{&_ùĉ1b7}z&†Ğ#4]fÉ5(°l<İ Í -ÀD&-]° Ó;ħ‘OĊ˜R6ò“Ïô—êBo†;£’˜ ƒ–Ž%.a4/ğÁ-[zòp_d—³âSÇä2ċßka½PŽo)za}†>Ú焘kGïĜ~D˜5żñ5Ôo>@]AIm_Òĥ“Ĵ ïÄŞJ¤°‚oìŠ^ɒm·Ï†o‹‹#6PUA"XÙ꛸ÌûˆÜ/B^ùÁ(Œ•@n$#ŠÒïHÁŜŬ褔0´ğfÁÖr,ÖädáòÌÜ"ħ„ëïq½ĝ+˜sü? n¤¨½~ŒÈùD’˜LŒŻò z’CÙ ­œ‹û⒎Œy¨CEËŝñJߢĜxĞÒŻšJs÷›!§òèü(•Ô˜>âÚgs]÷Î8`;›Ô­V=¸Ŭhk²…“TJĝöXM*•8Ì^Ùzëce™²Ñ…E)ŞR• ż!—6ĊwĥñĦ…âñ›Ô3–½''6"sÉméƒI`=0c%gxúƒf‘2(g1íŝĉQ&#ŝšpˆOŒĥóvY@ H˙Ôb‘ûĠˆG[÷ï$њ\L5Ê˘–ÎúÚûĠˆ -f/Â6Oööy”‘щƒTÌ9˜|û]OÖÇ`”j­éÙ³1+ˆ‡šWƒ'dĤNšÙ(Œ§lßĊ1ŞBÉÚD^]á£ĵzò+ÁL4°1—†˘Q™Uq -ŒŞġGš“Bĵ˙ ܓVA'ĦîSġ§üqÓ• jvċĝÁƒ)Ž³4î°ñÓ‹ĵ e|ĠiĊżl`uƒ/‹ĉ”oğu>_Ĝ³T)^SÑ-…nw}ŭ, ˆZN¸ECôŻ÷ Y ReµzÂÔö3ĵĝsĥp€úĊ$ îŭ2…ÍRH?. Ħp…ĤŸ#Á+N—úŬe>Pò£rÛóIÈ%yëù@İn-Ğ°ÄâS4ħÙÂĥÔ{·Î֍Y[Oîh„EİßiŒŸé\*Bx‰C֙#İÌ(~Ò#=ĈÁϑ ġ“ĈX\§ÈÖyàQÎĥ5éìŞ_ŭp&R5‰SJÖ^ šÎäÔ·rô•Xżĉu׊˘ŽŜ œ’˘)žĈ”1Ĵ,B§7îG„ħOĠDÇE ċÎkÎË\³ÌO…ȧòYŒ@ĝhn˜•:*ñ§ĉ´Š@Q?š•ƒµPED€Só\Ż‹úİê ŬĜ äŸ°„ŻC³úó…óMhQQ“ŸÒxMϗ™DvĜ]éŒğ ×öúÒĤĞáJŞ*ıTâ˘#Ü"óÒhÛ…×ñiW_5ʙ•aKÍT¨Şó$×#‡‡ı.êî Ĉ— Yamç€=ÏfòWâ#ďétĈj&zl…IàX@t›Ċ߸àĥ”°*úïî½'>`rÂ/XšµV(ísoŞ…G„ÂR…ñÀĠe'´Ââú ¤,ž˜q6Že: 5làûŝÑPî½ÂÌ&•7‰ù/œ²šöì -E“x*Y›÷ï¨$ĜċÂĊŬĤÀáÓ˘Ĥ ížóîކï1”5˙Èœ\>ĤÓöh°#ĉ1ÑF̍\ž`A­kÇS?j¸Hâ–Ĝ:+S D·:]+HTĊ5‹f‘\V:\Êg­ġ0Èïİ⠔IÒ²t} -´oDkòs˙>+ÔÉÄDĜŭ8Üú5ß}•láŒí‚S,@ï˘\.ÁöX ŜŬÈê:éÏ;ˆšĥÍ Ŝ}# z—;d?=èérXB›˘ĈPuš 2ÄàdúĊİ ċâÄ£˘TµÂ\ácŻ²ó¨Î!§¤—$r·P-z)£~·=‘ŝ -–àşî(a\/5:Tî`â2â˘ZsfÁûöŠ5œ#½ĉĉˆĦ’”!ä*dµ H‰Eî}94~Şk#ÔG|´_’F³Ïżp`›U2u£Ġż'ġœ°alsĴm >‘€Ikš‘BeLm< -—ÀïÌ< ŻóÁÊñJ(ú¤Ŝ.“~tG2óüĉ?pĥivŒÇĞnyÚ2ŝÉí‹HÔçó -t´Aˆ‰u…8ZEb­ïÀ&+£Ñ+Á8ÎÛVçĴUk€°ìÊôĈïϋš2È:Q ĵ׀àԚW{gLŒĈĉŜL žĞ}uCۖĝ5}"KòíĊb7;ÓÁKĤ^yíîíħÒ‹ëµ -Úó `d;N'F Ió/Á-‰ 'ŽşF_„ô›74óËĴĵߔS­’Vm‘-M'wâk¨ìn1V<‡ĊN (J”Żğz`W -Ĝ‚;ĝ›hC7WñÉ$‰Í'XYĉÎĥ›u) K&і~¨–À–’6ù›ħgó r×FĈ./ÈB$âêRì•éŒàAÀİÏŝòìÔ żĉ[-Ħëm:‚Š’Ħ˜“œEc 0Eb__#ğD˘l< ü2Ŭ=diŭˆà™ÂŬòk҇b ´IK A\ÔSšÀŻy;t\2›˘m$Z"Ÿ@ĠÔ ġ…a+ÛK›Èĥ.\°™§–?Z}ċšÛí˙¨mVbIQ†FA”˘ÉÜ -*#?—ûŬıĉċ2ì#ŽûPŸ,;YY‚Zĥ˜İ0ʚ67Ö}s6§ŠZÙj_Ĥ˘^ĉ!ëP8ûKĊbEş§Ĉ½żi…/éfMIrş^eM­½ÖKżŬŒNdŽÑMBü -`ĤGZulX%˜0•ü˙ÙPá3J0ÖŭñvzÎf5A)×tÜÂâpí~L–È‚ëwj?Ŝŝ˜\Š`ŝq)~mğњ½‚ğ¤œô›İĝ 5tñZy%ğˆ´Ë_")­r>ob|7ž¸ sĴ°kbdׁsWĈ¸½káĦP¨ŒÊPQE†•M¸k×8 "w4½Rzz{êD+î²ôĵŠAè|ž"q£Xµ4ıµds F 6½äŬÏYTÄîµÚ‚h1ó|DR…rµğA¸gğ˜EÊ?aYdhV#ŝ:ĵ×.äù5I…Ä~Ħ²ŠŻĈ­aˆx6ġ.Ï2™È=DGÌ삎CħëyvŬ|[t‹‰d‹ -ĵ4@•’QvÀÄĉBm\Í9îG³ÌdCz6mĠù™Ą‰T":ĉx8GU"û“QÑGĞ ‡­=t™OTÔñ߉3Y”ÓB%#û&÷YıÔQ?O„|Ċ8Ż·Ûejİ’¸n³Z5è2$B·bcĤ@Ĉ}~~6SÄíÍ[ËGtŝġPÚëHàâ,ċËĠŽí•mIŸT\€A›íŸÇa 4µ“Pà`€°áJèÁ,†óµôjS\Cp ûá!JšEĠĊË0ŻÖáҳș°Ĥ,÷WôLêôX -K›R{u:³Uì˙Ş -³½P~kĠC˜ŜÙWD¤žè†/óóÊĊÖ!rt•ïĜ?İ˙›ÁGÉîNQò<6Î}íBÀġBt˙—ÑË9á%\·eşéîğİ—ž³şáĦWżĊÒĉ+€WxÂq÷ê22 >y{-u#ÍcZ-î+f÷Ìàċíû,ü‹_ -RÊ"Ŝı_1ŝvœµCşttğ!2laż7Ò2­üĴ½}²^úĥ M¸Û}]Ĥ΋rjtà64;˘ß>áùÛo]R çq/˸’ä&ïÀ÷Tt Ħç#\GCE9ħ[xƒäœ™{~…ż2íÈÎ'ŭg°ÌòPĉb5r-¸š†öökpC1V÷.#pj!Ÿ$vˆħ J>›RŜYĠ2ʧ/;MŽ­€RĴu7Üéëġ!ĤvŭÛFaĥİ°×dSP…Á ¨'˘è‚ñœ’Ó²Ag â ŻI>ŬLJ ´êä# ëÊñ‚ï†[äƒğ~ÖÎMîâŬ=Jp1'Ŭógŝ0 =crµ7u#LĤè$#ĵ?&lä™×EĉÈò›Ä=‡ÎDùŜgzvŝ!Ëŝı%˔' -  ‘íŻv^hÔ`Í_ M¨ŠY];ĦÛÓ›oĵ"•˜M¤îĵɈŠĴ?G°Žf{ìvà×Âclŝ‹Ížœ¤úC]J–:bK÷3s“!ş1‚ġÀċú¨°‘s‘ EPfÚħхsâġğŒee_7abĉ•")HudnZ~²,IŞÏĦ‘‡ Ĵú…Ù^\=\†ìk…w²½Ö0–)ôĵ˜^ˆÑl 6–‡,ĊŬż´!mÏyŠ`*Ô‰·N÷şïw<…d.ġFĉ¸êû -˘ĉٙWvĉd,£gĴ ëu~ıP™%ħëًàŭúëß?ÒUµn~“6·ž`–,ï4 -$âŻ³Öàöëċ5ġżÛÌü„ıċäÛZL½e -Eî#àCĠĤkïTŝ‚Aǽͳ m° "#P.ÖdĥŽŸ‡”`r#ɸ‰aoĦżŝyğCù•èá‘Hş-A¤0–òŜc)ôÉóħt ¨û</oA·Ĝ÷4ĥBJġOKç}.LjÍgŬ ÷(‚×ÌL3â{XÛ1Ċkf¸íV’+­y[:è£Lïš% e¸OÎ;êù‡İċ>bfD:€r „ ıZ!\\·îċî'd˘%ñ¤Xçc„ĥ|@ÒĤE8óŒ˘ -2ŭĝÇÀ͢¨¸4‰Œ@E-Zîúpg]o(@wNÛZɖÜ<Ŝm‰¤l2nĝ@>ï…ú&^^7†8.eùiÑmS‚Ùƒ·„W§ív´j’!ĊħêÚY-ƒĊP}ZžÎi£ -*C ÖE8feÉî$2ŝŬ)NÁ…vnœ}ghŭC}˘Gä0Î]÷ö-²ŠĦۉû´Ĵڂ@è_9E">^ ¨}übZ”~¤´ÔÉNӜ†1TÀsoĠgĦ^ÉAG‘ŬS \ƒWÓä÷聐2éïĉ+Y˙U¸ß€Š~Bd/¨i0í/Ŝ¤şSŽ|7–µ×¨ı‡™ê½vvz4ÀK½$œ,ÛI8‰g{°ûŞĥ_8ŜxQ³:ŝßòş9D-‚M˘Éâ hXšqÀÌÀ%homQ€ 7/ŝŠFr³*ŻpaV„PjĝÇEä“U×Ğ^¤ÛÛRá´iċ€xŒâñNQîôÇà²&2¸qC¨yÈZí$ÛÚ%Š7È?îp°ĥNu,Ċ{È&¨'Ê×.ȝ;YpŬ&+Ña̝Ô„ÉEëp[Y Ż °uäI9#§Nş òq8pÍK#qqÎ3>àë,R‹ÈUHéRnh}55êkÛpĠ=DAŭú-×*X[‡Uu£ä³OÍáCTêcÊñjĊw;×8 ?3ŝÁšĠ[-ı—îŬK$ÛgHˉè€ìSñÀü€xäoù糳ģö˘+m„ĝŸY3Œ•S”ß:9%œ½›´~ï9äŠ(ú{ìŞó„çÛEä2Ŝħ½èĥJ  -3>Ż„B„8^·>²qž3²ŒÎ*·Ê_WëYĊÊhëB]ŝ<‚S^ -îKGñ|ĥ -`&„£f}F5MC/0şĥJ ğĉgŜ4+ö1N ˆÖCó „j6ˆŝqÒcਠq%  I„‰r·‘<ŭĝ¤È… ‘^’OÁ ŭ%ŭ?ïD'ŝƒĞÄhÁ\ĜjÊ|˜êäċìK1Ż@gfîJeëöViĉۖŽ×é{ĵA\^uú͘–,Ż”<+çÛ]*ìD•VŽÁgÌiÚ Œu4úZ+&ĴîúÒ` ‰eÍÄ.ŬäğJŸA·¤<ÛZô=(1lùN2ìǠۆàĤ(d•íÌËBÀ+­ƒL§„N†²™ú(´iC ÌûDr<06£§Ï’DÓííÒY[څv†O& ] `vçŸÀBĦ£‚<œÑnĥ ÖšQTàsĜ×`•ŜŬ/gj,ëÏ aÄ+$Ô(‡xĉ:ß@Y ’Ĉ£: ÛŬŽ ŞX‹ŭÌx&_ä|²Ÿĵ§u5ĴGóI‹Ĉİ|Ŝӟ[i3háŞÓžbKr¸·ÄUvvmx-òDßu0eéÌ,*âWMLßuäD‹)½Ô~Rœöyİ;8áDà–&*ƒcPÙÌâžÚó$×~ßhĠ -‡ 6ÏÀúŽĝlÔӂò >X—4’ËHÂswP…>OÜ´Ŭ@ é²Îßwš_ıò˜ú9´3Ê/ -endstream -endobj -680 0 obj -<< -/Length1 2717 -/Length2 23393 -/Length3 0 -/Length 26110 ->> -stream -%!PS-AdobeFont-1.0: CMR10 003.002 -%%Title: CMR10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMR10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup -/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /DKEMOU+CMR10 def -/FontBBox {-40 -250 1009 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR10.) readonly def -/FullName (CMR10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 70 /F put -dup 71 /G put -dup 72 /H put -dup 73 /I put -dup 74 /J put -dup 75 /K put -dup 76 /L put -dup 77 /M put -dup 78 /N put -dup 79 /O put -dup 10 /Omega put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 84 /T put -dup 85 /U put -dup 86 /V put -dup 87 /W put -dup 88 /X put -dup 89 /Y put -dup 97 /a put -dup 98 /b put -dup 91 /bracketleft put -dup 93 /bracketright put -dup 99 /c put -dup 20 /caron put -dup 58 /colon put -dup 44 /comma put -dup 100 /d put -dup 127 /dieresis put -dup 101 /e put -dup 56 /eight put -dup 123 /endash put -dup 61 /equal put -dup 102 /f put -dup 11 /ff put -dup 14 /ffi put -dup 12 /fi put -dup 53 /five put -dup 13 /fl put -dup 52 /four put -dup 103 /g put -dup 104 /h put -dup 45 /hyphen put -dup 105 /i put -dup 106 /j put -dup 107 /k put -dup 108 /l put -dup 109 /m put -dup 22 /macron put -dup 110 /n put -dup 57 /nine put -dup 111 /o put -dup 49 /one put -dup 112 /p put -dup 40 /parenleft put -dup 41 /parenright put -dup 46 /period put -dup 43 /plus put -dup 113 /q put -dup 92 /quotedblleft put -dup 34 /quotedblright put -dup 39 /quoteright put -dup 114 /r put -dup 115 /s put -dup 59 /semicolon put -dup 55 /seven put -dup 54 /six put -dup 47 /slash put -dup 116 /t put -dup 51 /three put -dup 50 /two put -dup 117 /u put -dup 118 /v put -dup 119 /w put -dup 120 /x put -dup 121 /y put -dup 122 /z put -dup 48 /zero put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ=Ó%ċW˜)-{Ùr½uú•)Żœ‚ßröA•ÉÂÜE(ġ@Úŭ{ëı´‡ş“Qğû|ü_‘RÑċğ -ĜĈϤëA³Ċ -T@ĉ|ŭq|VkıżJ% qu8P˘ĝwÄGx³ĊŞÛ̆ÖċQĉŻ6K üŞÒ-UŒ\§Ô%ĦbĠ"t-*xÔġöÓŸÏ˙J‘+ -}ì3{Zà2ŽùĠzŬĴT2sÀ$ZġÌÑ&{Bè–J×{¨ÜĈĜxı<Ÿ ,—Ü-.è2›ŻiR‹n·ħvÌÙ1䠕 „'Ĉä“ħİ·_r"OŻğ_‹tħ3keèfBŬĵöVÁfj—Ú9Ò³˙ Ô Yh뀸Á{û´qŬÉÊĈ-÷†—şĝÉ·ÊÁ}W§?Ċ?gw1*Eh[ŠÜÛ:›—ŞtÍÀWeI,Úv•8üa…<{‚ñBú1â¤00Z8Ìî5 |ñŽ}­µNàÔ×lw]ƒ˙ƒ6N˙bż—¤h3E`œ†(Ħ›EÁ‰ĦŜ'Q;²eµÔƒŞ/à­.DİyL’â5ĜñÇ$4IGċ×Ɋ\‚yjù9£.îV­Uğ5£Q!äì‹-Í赁ÈBƒ…Ä9ödèâöĞĞB^éoVù­wˆBɎáT7„Ħ‰R€ŸÀsO™GA‹Ĥ÷Ġ b#íTBv!m·WT=úÍÀĤüw,ŞID%'ÙMĊKé<‡|Ù]ĜD°€@‰ġ·€2²½Oĝ( œŬŽ%œĉÛ#_½É·VñŝBSTĝ˘#zà×ÒÍ!ËÑ${l­\§4ĸ ;5Œ™l‘&!׀šóß=(ŒŠŝfŠ¸ŜUwA´Úħ›ÔĈeßìÈÌB#½30>ÎìH ¤İ'œŜL+˙֓žjâz@ú¸=s\²Ŝġ<…Ğ=\ÀY$ßD?ˆUê ĉü6•ŸÒxGĦQnÇĞšŠäiŻ%֔ž!×Ñ -L2ħ[žšô)!Œf…X‚cè‹<Ġ'Ȳ–ñRP3EĦ!„-:ħ'àŝAJŻ.ÙIJCJÎJtŞ&{76ħ -#VÀëĠÖHĠ“ó‹/İÊF×gw"F5”wñSˆ$|Ż˙oQ<ÎçΗ Ñ`~ĥ<10İ|™˙<ğémï´·ùĜœŜÉhŜ „߭逵µ°°›?É`?ó7–ë _Ì [•ó8xP<41Ġó=tÏĝHÚ ;6™ı¸}rKu1é3ûšUCiš´Ht­²ÑÓ}öyÖŝ~c%\ßqï€\şşĉ4O4v![›_÷Iş˘°ï³ŻüĈĉc‹0ßĞòMJùMŸY0Ĵ̏v{6ß”Ö\ĝ rŸqɚ"3=÷”TÒYK.ÜKêÉ)Á,GÊK{aˆCZBGž½ -yÛ(ŠK'†2O0ÓV—6IP$$lûéúĴ¸-“à[ÀëÔeÍɋĝÇKÌ×&2%g”bŻz‡÷JÌ™,uo~MĴ2ÄzŜu’™ ‡Ô6*šğ*Ĥ Ċ ĞÑ˙9żÎ¨ß?Ä£K”c)ËÏ÷á\gŸt­&?ݎÏÄôûnTëw½“ĉĵ$ dN\C¸›¤ÎÚOöÖÏ@W2xè8q!LdÒoë~ä1V/ŒÈB=@ħôúí!0’ÁYĦozù$íù÷ǀ%Ä­żÑÉwáŜá2]oŞß _ŭ?IhËuèĦBmîF:µ1Ĝ–dİÈy6÷‚ÀÚŜ F ¨„Ln5Sòw&İ-ëÓ°ŻžGzĝ¨9ê=È'’ä(ÌŭĵIühNú´Ö{äO ˜1LvcĠmiµĤÀ&È"MìêmÄ@·WĠ†­¤­mÜb%0٘*ú`šëÄĦ“ß“/fġl½%PE2Ħ:VA)SBL/ĉ<Şî5ŞCžA£ß÷l;{ËÀ (#şĜXnF’"‹˜„8{RĜo’ÁÄT(ä_WbAŝK|oM _ÖӗWßŝ‘½ yäMè˙6€Ğ ħ^½÷atž@O1ëĦ/Fñ”ĥ3y#™cMM×GĊZŭŬ[mĴ˙şzόF lŞùĞ"ÂJ>eĜVBWB}çV)ÜSÈÛi,ĦïŜ§ïR¸½ğFÇ޽P.è½LрxĝĤ_[ÎXVˆÇóôQ Ż TP˙ġvƒ ù -eÊ,’pŝÚƒrh“ú¸“uñ„Œ`+l{÷eQ÷֐_@f63HßPavÑzUÍ_°ŸÍĈZĞ1*ŞäǍŻM+Çbp€†;{ŬŞÌ ­Q3èVV;ĜĦĵ͈Ó O.Ožài,ĵ88Ğփ솅gŸ=\=à@"FàúKFĝTĦbû˜‘VŽl(lgÁÚbÒ­Ŭ!¸èŞĠ–ĠË\áŭùa4Q1°Ì~ Ğ9âqV¸§Ì ’s^kí˘sdŽ›nz‘Á­£ç¤:ÖLžz]ŽŞr Š˘ŞƒvND‹MG79$ILiŝ&“AĜgánl6y‡J FOµò;,zÉ´Ñ% -oğŻß xÈ0˜s‚ÖÈW1FxÏîÔè—ß gŝm‘µxVyġµÚѝ"]#z~—§pvòÁ †‘™öĜĊ¨.rB9‰$n¸YC­C1úÄtŞd@#÷¨8kN‡Ô‹K° Ó;£ÀêԓlFú( ĜŒNóŠĤ;àádŝĴÂûí’­üß*ĵŠ<ĈĤĦ•Ċ„ŞsÀĤ9<µG CE`…Vé˘hà½ÉÄ%Q“ÎFoP½Äâу$ސ½"Ñ33ĵ÷P9×9ìZs9‡'`­ ìrÚWù:N”ìÈsÓġǔ·@fƒ œ^WŬ…&24wİlz ĉ$Ô2Wï²wŬ…ĈìO9b˙£ċ"OĤŸÊÍW*F]Ŭ/Ĥ`yŞŒQħ ˆÉ”\Q•ÂF*ŞÜiTñè^N öd_£M`ƒ¤†S%T³NşK7Ż+R™Öì[r›üÈYġĊíYqe}ĵħĜ ‹÷ĜY‡Púô -ÎFUE˘ìóŝŒÓKƒÀĠHŒ'²µ>ZQ@ÎIÙàt%£ä˙–œÀ[¨)7Ä&ü hÎn ħéY'ÔÛaÂĥTñ'XrÔߙ/n_n•JLĦ (–@ -²ç Ëš -­µN{KFµßÛ^k›bŜÂnê~í`LŻ£]Ûa¤UĦıĊ{üˆvâïLßÜşĉ˘4“ô1˜$rmA˙îs•ÂĈóònZß*™ğ=İ÷Êsġo›b@{‘yÖ !CC‹{c.WZĥìïĉ0n àbp…gsP˜d$-Ñ\öŻÎԛ&L27JğBŭóµs/îŠĥg(ôİxQ,t>[â8͓GsĊ¸:R$9]6&ˆúmy)iµŠvÉéjÂöW¨‹LÄRB^RBalżëx³_ ×Y:²5M§ŻßĉîÛïŠŽğ­µ¨û/j¤…àĊÙĦ!}Ŝ`”îëD&W€ÈŞäÖQXı$HߧçÌtI¤­ĵ ÈĠ.ÙYñ@ĜnĞr–_ôìn܁ OütAN-L n–‹—?_Ŝ^_…Ûg’µ~žĈ;`°í¨KB‡Ŝ6eÄĥÁÜŻ‘¸ ->”èlżQp‘†Ğ˘Ó)À†ĥùµò/;S' ^ıġ:ätJħj@êxгƒE(0GÊ;ÎşÛQqŽİǔkT'ıž;ž<qnĜäutlLC1“XÄ 5Í— -q‘×Äqҁ?ä‹z1CS+À£P1~eÉS2Í 3ĞJ–MÚʄ•l(ñÓµ$şeÉQċ/mpN5K7WŭeŠ|)ÛĜŜaŠH–­àZıÓŻ4uU}żĊÄçô¨U Ñ!˖Y•ìêù!ÔIÔYċ¨ÓŸK%ècEŻ¸ìû›=BÙÌI]€S1÷ #óÓşhÌ[Q†LhŞY-ċ‚~Srŝya5 MPYGİĠ;9]İÑY‹…@5€’ŬßÑ( -ĝœ‘> ƒ·ÉDHj‡˘sr‚xܖ -ĉ.Â>ÚÖŻŻĦÏk—ÚlÄ;&–Ż#<çښ°òe)fÑäFz›`·Ç·?˘Ic@SH&–<˙ĵ’îevn8F‚\VħŞ3Ċóa­A!yyĵ:ñÓ+žc!£x–‚bÏMŝ։á/f}3ߖ›ëËĤÇ"Gİ–­ç'fMsÑÔXWUŭ}üöµ·¸Yĵ^ €Ô×%jÍÇ!Hï‹OH˙É͎_ùĥ‹;臲Îò‘âJ¸vĦ²]Ü# -$ÙŞÛ'Ch?5™<„SŭğíË°Áñ@“­ šaĴ´€-™AcŠ†éloW´M(òr·§#Û`×nY{jÛ`3|lv`ş'Il ŭàħ!ċ´üĦġÓPÂÊì{”˘EŻ˜ï=Îpaè^ ĜhëOk`·î›pĝú ­8uyÜ$rò–Ŭó•u -f}cq+5Áy~!ŭŬ]ĠúĝÀìU,­t )ĉi:Hò O…ÄÛ(_eOéFVŝq>ĴuèàÄ-G:ˆáñÄzƒž…›HZ\%UívĜÀ z^àËBy%€NTâ¸ĥ3=Xëà?ĵmJ’ĝ-Ó3„÷i×H@ܐfσŭk¸R.ë›ġŭv'€Çm.'ÍSÂDğÌÙlyü7“˘ YġÖC³­Ċméµ^ĥŻGu5_G›ĝµÙ1Ĥût/ŒÔ ŝàÌâ -à4‰ħ1­nˆ_ûD>}p+ĉfŞg9h$ú¨Ċ]@ïMù`Ĝ^ÒıGKö;5ФwÇëğäIrqïA¨3fA‚ßYiuĴ€ÂŬäò½ÑïìÒYréDġö:ÚdRŬ “At ë-ސ,)âşaŞ¤ÉşhâÏ9[Ô§u˙Sç9K’„ÄTKİaX$äwgɓĥOƒ[âx‹qǃ£yI(–˙ĵj5L§ŞIÀcµ}|hÀ$‘zDâUϐwğY+½ŭĴZ:ÎïçÄϤĊœ1żòµlÙeÀÇ`uĝ@|ĴìÖ܈贚Ĉ^Ú6î/žyÑû`aĦĤÈ Š[ŻÎŠ`ÒÌEž£ÂwÁìa ĦzĉiòLa„}jÊ°çÉ@û£Šċ}ĊxĉïWĥ™ċn‡sŽ˜0n*{Żl?Zİzó‹•Ê‹>¸ç8íp-LÑ&È£ûïK`> `´¨%Â`–˘îŬżÉsŞ?şvËğĈ^\ü‰*’ÖŭQÊá¨Nbf…+ÛĵŜ„žo" Ù§U ĵzÑógêgÍa䎐u´F Ñ™<XúyŬ¸ŞĴú*ĵÈgö˙4?X2]4¨HšÍ˘›×òš^ÁqLeo²œ˜Uíó~ ÷’’7>ì)Ĉ¤ó™Hnžş¨­A7"é{D†Rj)˙עÉ˙~áeàíVDJĠ|—şşX}ѧCrŠÈĈTÈAÈè fŭ˜£’”P};Š"ÓĵKöÓ#ΑT ·F÷ú\çŭ÷^ԓ ;™ À|êR D\Ă HuÔ6˙QĊŭ˜'Q3Èb;x#¸Ž3óSÌ:ŞjbíÛ%¸tJ‘/>ÊĦO˙îœrVŜÂx]°ıĵ>)âïŸÁµ]€lù5o[çĦF;,N&¨'iİŠ\ħNQÁIòHÔÍôÀ?T:í@ĜFïçN˙ SXÁŬ0ħ<Ĵ)ğhàWց½4fıFD·hÛ.Ĝ³T)^SÑ-…nw}ŭ, ˆZN¸ECôŻ÷ Y ReµzÂÔö3ĵÒ\ -ĥĜtíŝŝYá5`F~_›xÁƒUž|‹'X’µÇ‡„G@UÖ6I \™„çÜö>ü:ÉV_ûÉ>ĠĤ9*I0}Óµ\"{Ĝï3UÚzĈñÉuäFœfÌÙ¤…ġPߨÊ)Eˆ8‚üUœúw)gŠËqÔ:àdj#ıŻÜˆhqÇ œĵso -ı@’ -KG7"­|Q‡ĉŞúċ Zòzs|…‚}£ÄLĠ´SŠ:€fŞĠmĵ§ÂA3ïÖS 2Ä=‘Ö[³d·Ĝ“üJœ\ܳ­òcìÚ€üù|Ëtj1ÑĈ›AçrŝŠÀÑŝÌJvÂ,K| ò´…Ï•VŜœ -˜ü›Q„´[ÜŜëı^9# ‰ •TϝżÌ–µ\u˜Ö×Ñaá2ÄSU;·}Çw„–ѧ š‘]*êz24İc÷öÇL4$ñ2ÛFħĞëw<Ĝ`â¨à7)ĴĞ_Ù 0 IóïĜZƒğlfı˜ŻŬ5ïà\èítî~V= Êĵ&܏£ŝâ²3V›˙ÖY‹vEĉ9cé7xßûXÄ ïçy’ß ´>}žÄ·e½Œ½Ä­ç&ÖÜnúµe½4{şçíù…£YÑÓ êë÷Ĝ§‹½i£6*ÖĦgCżV˙j81aĠÂG­É[°‘ßQU ƒXú×âW'~³7?7ÜKOğ   wƒÍŻ6ˆċudslĤwSÙ+B”ĵÊHÏubĠ֜ğ¤ò`àİZ„¤‹Í“e”wOŒħò†X ú&ĤĴl~3ê—÷ÓÔ¸fĤGħ‰”kâĴˆżËDÂżDr)ğ}çšĥë!úm[ ÊŞˆp^êá"ƒeš*EϨ´ħ]\YWĵ\k’sˆB,íIQ ²ÎZì1IàŬ”Q'™oTž´4„aĵ` áìV‚öF Œ)ĴëapËL|y ÌĊî6>àu\"$Ż(WBĵŬòòAĞ&|Ùa§ MÒ+8ĥ.˘/Ò¸rkġdĴ)íZĞ|*û_?˙f[;Wä ó£{‡^*Zl3:Syáw{Ŭżċ˙‹ġ[8}JëSĈwŝĵ¨÷dšòĞ˙?ûÈQ‹ŬİÄÑpžœ…+4 сá!!÷P—°ċ³C@Í{Âû:E@’NÔíİĝóp2á„ŝ{²Ž&Bܑ0%ô–f žrJ ŠLW³Ím_ ĤÁî)uv–ñ32²öHżżĦY°~ĠÉCSċ“xÏь]2YŜ7÷ċ]ÁNnjÀ¸ˆ3*g˜5g›LI§ŝÊÁîSVZÍWÌ7è1Ÿê™èKÑAĜkA£"]†NyĤmœÊ Ñ0ùŝ/;“ü?gŝÄWCHş‹êñ%´ċ4<ĥçı;sLĤ?bSK!À”Ò!‡K0$hħï4Ñ÷=‰œħ(Ĵ€’ FğĦĤ÷ż–V4İé…çAA-ôL'Pv&ˠ܄À )GŜ(&ê ŻŒŝ9ÙUŝA¨“BvĞNŽW[d&¨/QŒY7VÑ£[¤#í›dèĈ {R`'|½Ştş^+Ğ&y]וĤµ7€Â‘Ôò`ċ.˜/Ú|žüÜoĵŝŜI˙¨GeOVNêM.Âßb*#{ˎĴ ô•ëziÜáj÷yÛ\?‘}í$â]²ä~=ÈRˆı;ĥ5ŝÔìßŝ\ŸÓθbÇ i)bböôŝOßL ŠıÛNß‚SŸğĜ\ċĤrşSk8òT§K˙ò>ÎŭbcOטBk-Vs,ibék…£Q(vÓÌ)çb-Ò·ŭ&ùĵPmzÔé5µAġÚT#Dmcŭïŭ°J³FPߧQ/7˘Y ÑĜ•Ħ}ż îd)H ÔZÏĴCE{5Üt˜z›€ }äĥaŠßĠêmâgßħŻR˙€§ĥ·ŸŜĜżnЏROŻô¸×F-^Rnwì3íßywtÖŭkÁIŜiŝéÏ^ŻÄvĞúÊYìĞ1[’ü€Ò5ÑìxŸ>œ2 WŻğDÀkÌX×7÷Ò9ëîá¤ù·“+]MÉ°êì}$5‘Úà)KÄN™€:Uĵ‘ğTb;P1à'V4‘`ġżpNuÁO(#Ğ9™bà°Y¤ŽLŝ7ÌĜ³!2ÜW9ħê@,ʵÑ303F:|8U Eı‚vŸYüQ -nׂv›‰AĊ:(îQĠ´ÖƒÜ*1*ÊjSםħŸ„‰‡ÁŻE?ĴÒ0hñ„r¤yI·7˘ş<ıéÙU†ü]ÚħMÁ.&:2.z€Ş€áJÉÙ8Ŭ -¨ä’Çaן-Ñħ½n]CІ.„µÖWŒ*ġcšŽedF M^àl$Äġäë`% òÀʨ†k!ıÙ -‹‹ŬXpNoY.em0N‹²ÛÉwˆhƒnÏÔ¨ÔŭÒëLç†ÚŠaA€Mn1ÍŻŠ -¨èÇu²s8~EżŸ’ŭ-³8ŬteÄ``œ'`Àû^IÔ=ÉÑTZôż†\§y^ßAĜ{ĉħF' ´ Y1Ğ$iíR)7!ċf’ܤR”Y‡hƒ¨ôşBIÌzӇ´Ü@BfÇ-ˆc"!\8Ž_™ĥH˘‘ĥò‹ö]üü¸O}˘çoB9!9Ĵ‚ÔLîĞ:Ĉ¨-fzNJ §€°¸ĦG‡tîë‚FH7ĥÀûôߓȴ§·R ŞO(ñT`qâBŒŻÒYħjOe_|O•2*fAğg -x[`çyZN;#LAŭE àbQo' ƒ+ĝŽċ4×À,ÁŒYyÑ4>VYdĉX”á†1ŽĊM}ÄĞ’O˜^D9GrhÚévO âêÁĜ!J†QĜXŻi'mj'Ë+ôLµ*ÜG$cáÙú„Â<%ï:6XsĦ+{4KÒ ‘ĝ`Fq@üÇĉ|”eÁž/&ĥ³°Sİñ$ïĜ¨İ -—´„èŻ …üZĝèk.şdCg{uğxÁAS­‘ĴŜ[’è)i ĈWWÉ˙ ³3Ae€~§]á îí¤—*mŠÎgœEÏÙèGe*vĈÛÖ£ÊN| z -ĉEm-e_L”ümŞ˙Şi9wV²Ëŝ‡Äùd¨#œÛͧNüP1)ċ5˘C\<5L€żĝnè>l€ċÙbb…oê+l˙Şn¸ñ{µF#ß -ēH@Tƒç~–=\eÌ ÍÊӈÎû=İ4t7×v¨|p³§ EuqŒñ,*JÜ~|Ÿ¤ż7B6™‚üŻÊœÊsßÌPŭ14†*<à{]EÜÎSnè‘J8Ş0îXĜCM˙!áí3ÉïĞ‘YÉZlŝÙâŸTÌô-‰.ˆN:üAŸ},·’$‚PpƒĈJ"9ä•_ Ñ7Ô+e½šĠc­Çá˘{â§{-·ñŜŒ1zeĠ~„*cš=~ë£jVÇá#ÄĵӔû6>(ÈĞÜÏı¨}g°U-ÄÓIÄxÎŬ\ĥ‚ż?ualQÜğ>ŽĥÂ2T;á⟽ eÔF(][‰Îr‹áéd–fĈdġbƒPı£Z5’.9~‚ħéyûüç1ÍÚáÙtHŒ1"Á#BïVñ4Ğ%ÜcŸOP|Àù,idŽ"bGŸ/Ğ -]ñş”W.SáӑP:>R+ÈQ{×!‡WcñÔ Ħş*˘MgäνbÏc3Í9$eV6ƒÚÚµ´&xîcÊé‚œ½]NˆiÙĵ:êPŸLĦ³'~€Lk^+H5)4ğTµ †, 1yĊöŒ2Ïe‘‹ñ‘Ĥċ‹äöŜÄG’1Î,ë˘,Ġ tşuäç"Ùä]òö;ŝ%N·ċsHNöqfO÷dĴ1ĊE…Ÿ˘½ñ–}Á‰8Z]ǫ̀M2 Ú>ôxĥ@Ü3L]á퐲#Ŭ}YúÎÁVY“ŝı7ÓlğUm 4Ĝ5šF…Û,­È -âh‡MĈ%Ëġ…n‚]U]-ħ8ˆ‘:Š\ÇwxÈË´.)gн@şfFŒ{Nkè9–‰3&yX…Êû“%v•*çÀ‡§€Tċ™—·3Të\‹MQ6 î&YÈ1À…GŞE1´´[ÁĴŝR¤ábS¤™d3Ò“Ñ1~m‘„İWÛRû/KĴ‰a¤„ÊÍçŭÂĉġ:–} -Sè;Á7™6bÒ[•7Üà†×ÄĤ–ÄQSnëşÌ'0ûÖIA‡Ž2X0ì—T`Ú­\ù…öWˆUıNÓ˘s˘Ĥ½ô\sŒşĦĦ…Ŝ?ƒıcQ’Ça<ҀeuĈ|ŸġŬ§Âŝ?Û\ŸŬê(èĈID-Ħiġoìj"‹(äҊw]ú9í@˙“œ‹# ë€D6yĊş5hC°ôú FÂËÛİÒ[i!‡•>¨J£n@mfŒ]Ïj - -ĦR=8“ßzû‹°›ÍyĤb7‹2”ÍQ·#ƒ´ä\óDw™ħÈä˘İA{%Bê43££Žƒ!e\I†“Ñ•kg(‹³˜Ŝ2µ6–I0½GEàĊyÙÑMXMDi3GHœ b†òŽы{ŝ”¸J•f3ĴSˆ·'Ÿ,µħ8GG3fFŝ„ĴI„ş*‘˙ê>V,ÒuïnëhħżXréûĜ^Lx'—95•é¨U?lŭıF•Ô]…‚û!£´ma;úˆ–SiŻ·FĞ uÍ>ĜL„›hĦ=rŽġ² !7XÑקhŽ=—Ìëï\ˆDIßĠ=b1 w8½JΈ'>w"B‰ZÏá!•I$üHċ”xÈÌúüöÇ$¸|héÏMò˜Ŝi âW;3SLi4*¤‘Ğ´ßrن£Z…_ġĦ8ê)^ì˜ı`Ĉ4Všeêßêµ|fˆžbŠ5—–´&ŭAw¸ž‚ĉ÷q‘İT‹s%´ùò)óĥÔÛ#ž_éû²³RâóŻĊĤÜÄ´ġU½ż\²Sérù¤ğ¨|m|lq܋ğÔ­—a1†˙ozD›X’µSŽĤN¨ä¨‹EX,Ÿ{Kz™ŝ­*|›Vżj?LL%m&“-$ q ä£aPNvÄ9&NŻàlÔc% Ĥ·Ĉ's‰Ì;˘1Í0ñóäÁë—(:k™‹µ8GÊ@ĴéÉŞ„ÒíÇ_@VÑr$šÒCÁœË[ŭqgU2wĈÛĜY?Ğ+×œ6h.OœÂsío>fWÂrŽ<Š!K|ԏšËêÒ˙·ÑñĦñWĊfİ701üi—z½€ï?•?˙ ğüd¸2%|U{ç;eŒÀ1¤îuèċ]dxr‘L¤—I§ô†ÙÜì)‰4†g,ċ8dĦjê€Áë#R;Ÿ‰ J`Ní”X9]ÄĴ@Äw²Ħcó˘Áy]ŭ|ó]ŠGpM=š ĥrm}ƒÇòĊâĈ-ğı°“úĥ÷ġŽâ˙ˆ½ä -f[8sMĜ,ÎıżXŞCl-—lK)³wÖ:KQBïñJG^CšĴzµŠR3¸Iŭ`ŸYğ?˙ҝüLġÙ~\%>)öàlÍğšÁË7ı\ çÁ­ÒċÁß kO"ÉçZˆ$‹€™,ÑòĉŝožÀ½LWŻ˘OçRP³Ŭ'Rê‡TĞ]nܐw“Eߍ=iÂħ¸!%Ö^%Ĵ,÷Ž|Ŝh=òE’>É ĤşƒÇÖ}àêÀxŭ.;\ߐÙ¸5„ FıÏW۞fŻùaDveGl— <‘kĦ}C›alB¨ĴJfŭP¤ùÜ|Ó.'ôŭ°şfĴ×÷9Ú=mʗ'~RK OˆŞH9X7 ÍÁGfGW†²ÔĊ7 ä{³E.ô+2£rwœħ××àjż½1‘£‘ğËR†ħÁï É %LĦû(?LŝÎ 78ÊŻ°m0:ëAw':¤@Ÿw‰Ó›nż,Ù_CyµğXSò8­oĊxĈ^9¤XCŜŻ’*çpĝ³íÈôk2ĦF!Iż°&·KŻž§ĉl<(KAïĝ·*DzrKL!*ƒŜĤ ŭĠ6ô!·ĤCêàmġ˜7kÔ}b`Nz]ĴĉżıŠÜÚ\)ÌMŞÜLċ‹(î}ıòv}‚ÊjV·g4úŽ­àâ‹<>§–Ÿ™=è”Y— ),a?³Èyşĝ†ù18á˘ßm ?¸y>ócÏâZeTo'>’ŒIƒ´Ôß< Â4£0Ei¨§Ĝ(ĝ -H–ìŜ7Â+ĤjİĝËT6šF_MdŠÍJĞ—³qAsÚq`×ó°Àñ|Y¨'2³cTNY÷ƒ*FYĥ âò U2°q=Ó?qdìż„q\“™ôÑ^$?ùPŽM ßEo⨝Âĝù÷CiŒ ŬÛà†|9 àCÏ,àÌ ÊÁ:)÷~ UW­ñĵÔ£•ú/gĤôÒSÛHĞx#y@.‡³˙ĠÍê;ÛŜj)½È닅Żèt¸ëĊ<éç$1Ÿ½- -5£…›x£1Ȝv‚ħž”dR,o$IçLòÁkl §2ÛŭóĞ$šHw*şĴ ‹O/ÔIYBsDŽIìcy†ë\&ç7Ŝ´vË5ò>‰2Óiġ„j-ı˘Ġ3Ç+³H1í6éż4X`8Ĥš0ŝw%ĉˆ éĈˆRP1ì65öSÖ%r˙"Ĉ€ ŝ~Ë °ZÙ@귗ħ„ñYâùÌ2Ğ9ZÈB´C7.ŸI!Ïb,ĞuU“Ġó˜ġk]Ŝ -Ŝŝ\ž­eÙv,żùÑŻˆżËDÂĜ=żÈÌbŒ/£5³L.ÔÏ:@Q€]§ƒÊŸ#œ×û‹ÖĞ‚qÓ~a{÷X²Ĵ€ó|> ™‹™Ÿ? ’vĠ´™””R^Ü9²´<Ŝ&İhn ŠS›Â)²3^Ÿ°JOĞŻrż†ĵ­Z÷bÓP(÷ôfk´é™Ö:*vEˆ‡ŭ—£>ĥ>²…œZ×ğKp: jÒ²42‹ÛDÚ\ŬŽÁ0ş¸}'ŸÁeÀ9'báM§‚yËĝÒg -´µ:Ö4Ĥ׺Ñoó$P¨3~u‹(ÚnĉÌ>ûĊâÉhzÍ–ûy&_¨İHĥyE°“Ĥ üÑSLçÑ÷Ù½ôx‚ġ“ÁİK·.ħêCü`–Ô0`,Ż‘b]ĝÜOíRµ1Ÿ'iÑʌó³wÇw–~è)LŒïâ¨StĜĦÀäRşgŭD 1?§Ž£üëñŸÍŸ§2m­YLֆ}gqŜċbòlŬaVïŻ™ĴEɌ @ġgPöÊ=ħf“KÈ7ŸÎyŠ‚·–!Ûy›‰Ğ4ġˆàĠ –ĜC2–ÙD)RĜħÔ[˜W³M^'Àŭ=á,uÙGÙsż=%Ÿĝ†•Ì~MbEsL…+9Ì/!ü֕_ŭyñîĈ7'³aĵUU6ä!4ċÍD„'b7ĥ&çÈ_yì,ÊŬב=ë™ÂÇHgZ`QúŠĈ_’âXV½ġIÑĜ‚\ÍYxF4ËáujKXìïDŒ„UĴêtšJ )¤2öE}hÀ$ÚVÍQßïô(ħc#î’ïöŜ6İ9×(ż 0ŽÄÜa07à¨2š‚Ş;ŝ› Ĝ“ziʜÖ1€ñàs‡Š/úúÙì ó|³|=Ô)/l#)ŒoÜ:$Ŭ+u1˜³k'™!‚ÖŻBarö_ğíL2­Ġ· Ĵ9Ê]›Œ-ܞóÒ 1*w>ĝC(ì KyC°ĥ.ZÍ\~,Ŝ+íS2“°_ <İ‘ÉÙ=ċC‰ĜT6~ùùƒßgq’tÚhK/QħOjzı5µ‹‡ÁS;ĈÛüc¨m”Ú,`ż‚›ñ·ÏDeqRĦ]%ÊĦĉ—$S‚&T yñ­×Ú÷C‚gMwäèġċÈQŞ0³Ŭ:#ËIÁ*cV•ġ_MÎÑC3šì;×?¤£Úż´dU³ÛBÚûón´á ¸só‡Ş°ş2šxŝĠvˆä@Q­ß}ÉǕU=,~–´„ıÈ04ÓgŬÙ:Á¤ÂWFÍËϝӆì6ržÌcħa҉žsGĜ%ßʖ C¸˘)òŠXR’…£àîPĤVM/ï—)ÌÖĞ”p½:Ël5x0Ĥ”|Ŝ:Â,ʘ3";ƒ¨+FE§ĠÑ£62Ż‡h^h†·öŸñ­ -іż /VSç`Ìb‚Akdܛ6†d8¤ÈÀSï艴ç×ĉ;Ïtš··vˆ72]ċúù%mrĞdŠ RŸpüÔä^š™’ÇZAP½ö볆 KdÏïéğ„İum3Öĉ†t ñ_Ŭ>@òܢ“kpŸ öÙ ò‡İ‡Uq.K{ÚcóK@ˆ§ä(°?Ríż›U1¤'M ÓIèm>óÊ(IÍ>+)’´)}(òÜ×G ŒÙúŸ×“”jùŝ ú; Û=Ĵ|Ž 6Àĉ:5j1\­+䀍mF„ÔJĝ×KB§ÑRJÁ#C§‹#˘ĞRHښwIò ¤İß]9—üŝÄĞ~:€×Sƒ`1ġĠ_tŒ‡jbo4l06` ÷òN =ΚX˙Ħ.p3ñVµÉÓ<²Q_Fĝĝ€Ĵ4œNXžo~ŞÏ”ÏRŒ4)ş xzûó+qùçíâuÂrŭÚnœĥôÁŽĊ5Ù k7÷г!Vƒr2‰Ğ7“òĉhƒ#Ú£€Ĉk^ }Žċ˸ -³T‹ġm ­5(@ÀXÎż£ıFĉXt`Šñ/“ñ3ë<”ÚŠ­Pİ˘ŬB>3ŝw<“mµ`Íe.ŝìĞ‹>âñ/Ix 9÷Ö›¨H"%xúĞ!ĉ€ ş‡ ZB›Ĥh–…ϳġĞ`}Í.VjğµTíñ÷y ¸Ù¤FÌ*) Àé[óÓŝoXTÙO7*ÉĈC/kPò É­gˆYžîX-&“ßF+ÂÑÍ6‘ˆâÓ•,ÙÚr˜0ÊFÌ ­0× ÉîĜÙ4CYŜôħàpġ_ôċÉ'h?½X·ĉ›żĝfi™›‹ŠÇLR(MÏLÉĤœ °Ä°=z2d„´á핝ž -ħñ ¨rDÚéıxâ–íiKhJżnfÔCӀ KÙ?Ĥcbè¨GZšúĉÁ]1Y”‡nl@cKsIjTÒ:”°îÒm:B"X³÷ ŭ çv~öbğ¤~ĉĊĠŝv7FҊ”ŭŠĉUFĞĤŞ&‰HP RNÈRjĝ_jRû’_èV ĦçeÀ>Ż€şJ7üÀˆÉ0[jlġI>ġ܉~ùP’=Ç - ?˙ĥEPFˆĤMEù’ÄN‰4r$ü1Ïôaŝċqžnd^W˜hx&#bı^y W1ŬûĦ*ż-c$6(Qì†ġù]_Dĉ`M€ÇSŞ/‡û̋M­t†êĠ!·ˆ¨‚•bϚÍ0S’kô5 6mĠ’ŞôjDäĤùÛħğĉĤ¸Ğ({>i³ĵ>"ċÓoä%D#JúdĤe5ç/™6żË™ùU5ĊS]ò°ç¤ŽÇ -Gшù]*&Ŝ–jUóëdehüÄr÷ġA]ËÄtnż£ÀCwÀÓ è"›kïï;Liû†V"‹d+zğ `ˆiR\üpJÛĉħ^ ċO¨ :;ċDŸÓöPĥ?›n“RĜâ°ÙDĠóŝ¤Ï'-ġSÈĝWŝĜG_µH_Ó~²·W9İáSċí‡Iħ!?_<ŸCYĥĠ+•ßçĦD5Sâ{xòIĤ"JDԝN‰–×^{ïú´’°ˆE‘’dĜİ²|˜ıÚŝIÚß hXČ²|ĥ[0‘‚6tƒ§ùĦď딀ßéĠwá{áŭÜ6ܢÑ4ŽîmĴMĝeâ@ĜŒ”t+]ŽKĵiùÉ:vIĝŝh}zNûL#ÔoŭŒZRt+—ò‰ÜÔûœŻmYĉŠQġÁp§\X|X$§´^Ağ´`´eżħTd -‰¸ŜĴ=Şú‚°¸ÄhÍ‘Ú‘R>Jm¤ACÌ>Tmí/™N–b ½ÑKŽÁ›¸=ݲÏEò‰Ġ 6F¤rĈOHXĊo4Ѩ=²5Ċµ§mœW—š~É͙{$öyÚ@œ7­•TĞXûşÚ˙bûĜşï‚˘Ġİß V£BÊWĈ‰ëÙċ)Hwê -ÇGÛFŸ™ğ_ġmûO ó쏂ÑÄ#'3kŜÄaì—pÍëŭhmĤ‡EmšN„ˆ(µ7úmç÷,‘݉g0<8EÌs IN*·wġ#ÈÀŜ:Ŭ$[Ĥ_âħŠpEjà[WÂĵŠHşTUĥm*ÑÔ´%³ÂU£ÜaÓĝ:MċÈ)1Ú\i­ ²ż9™ÇĈ‹şç›…:˜,ÇŞĦ`Ça=%}>*¸,"qç‰2sĤĥĥÜÉEjς -‚AM×} ê˙Â& •ëá5…]pñ•ík^‹N™´R[‰Ò559Ĥ-™ż¤¨³(É÷Ó8șħ‚´Ò]] ìËù­KiĈ äİĴÜĴZÙA>úp -NóÍ0óҝ̳JşN7vĜ°Z˙˘zrĴġÙĦœšöò×µPğ[~ĤŜ(Œl;<´k[ıï2‚x‰ż}żħÔD‹ôSüÙ¤ñ11)7ŠÀDç4ÍXpÜù W£i-ƒUvŝ+ƒ%JòùguŒmi쓅pĝċièıLĈëĞ£g ŭÜ}' ]ž£ƒXC.}¨'e(_`„Ğ*YŻĝ0”‹Î˜(ìÔ?c§ĵZ%üġ”uÉĵIY;}ˆ6mbˆ]8#ZÊF²PpĈ(×J£D‰ĝÉ(˘{êj‘8Lĵ½e"Mn–EúaJÖPVŝİmż6g—ÍŻżÖéú,ğtäħnċcwžıp´ -Ċš0`*‹Ä\>êġİVĝ½mWMáBÄg›¨8x°SÙ¸‚ -9…Œ VL”~×ħ§½‡Ùf˘ÄĦáyċŽBCµÇÇĊh”{":”z „Ì£^Ëó3ĉR¤–œ—ĉ„ ÂĠĴFjÑDŠ/$M‚F÷aW ”şÈñ˜UJ²ĥUÀE˜ı7:µ²Ü¤´ïÁŭüŻ žŞŒĴPàß1ÌîÒ%•ÏÉŝyú‘ÍÄߍ÷FXäÎövföáE5üÙ ]zè"]HRĉuì1S5Ĝ‰­Ò-r[üvÀuì×%ÙT–ehcŸ=^nT-^Ĉ˘ôWŜ6ÖÄu´cgȊŸÚ[Ho8Y ñ:Ìßž Ğû:Ë2uG;s­é³µjĞN9÷”^ћ”ŽQĝTĴ%{oè[_^Z – ŠŸÙ´7ÙòxûĈĵÇ~”k¸L;R’Ĝĉ΁ ŽÇ­üfà5èĥJYòH>*Nş#àˆlڃÙk!HyĦÎï˘ğ2ĠG¨ħ1Ü­£[Zî–=¨ŭR‰)ŸsoŭÙƒ.vlħôċĝZ4!ÛwO3T||Y -ô XvËÍà3O @ĥN6½EsßrÁġċŞÜ+Ħ2+Ž"½İy€şÎK¤1IĴë0&òô[“<ŸG‘Zï!ÙjZı~$ßî{”k*[Ûxoc{Ë ÖĝĜĝĜĜVQG8§›q˘Î§kšċŽŒX'›S¨²³G·}‰7‡Ëö,}çÔ -Ûĵ5T3™9 ŒEwÖĠnŭíÜ^8oŭE…É̏°=peWj­•Kê£:î²ĵ9yâf½Ŝ6|,İÒqL>òHžŬ!gaêüúA\ÀôB:™°ĵŸ$‡˙|Ğ€ĵ|·:ê._4_ÏuíAî´8˜j…K‰ žÇ°Ä…nƒ×BvÇy öƒèE{l”’}–(AGÈúcúž££¨gû Ċ¨ĈĊL¨íP;Úî2âzÒ_­5Û+$›² ˜0g½A'/1/‘{†Vŝztí@ƒeĥT4éU>f–ìÍÔnİğíÉ1 Ĉ„ž„Óí.‹ U×÷/Là <rj½L]›ÔXˆSġL–şœĦ²£ -“0‡‡ä…(Ş:j˵íAò6z5ôĊA¨ĵ3ÄĞ„6ƒqÍĠ£ŠêĈ::ɓ(§0èĤù! &c ' [x°"QĦiӗYO(4''84ıĈ×Ħë\u&Ŭĵċġ¨AQW\Ùp£˘u‚³+À"÷ĈRϲÎeÈÓz ´‹Â·İĤ –úÈχԗ¨"òç˙ˆĈ¸4òßánÚvÓäÁžûŸĤ3•-˜&<BÎ))ÈÂĦÌĜCI ž[~ğÚûèò=ĥ8à1AÊ\³òaHeÁŠÖF4ÙllF[,5.ˆ[3›ħùï·ĝöÔoÊ&èĝŜÈreû khĈT úRäWsCċŭÀ}ŠşrmğžpÌJÎ}`ĊÑ\Ĉ_SB·³ĉé?(pî -DġÑTj Ħ £B•¤ĥm}Ù -/Ìfòs?4Aщż'à Çy‹ääwâ}ċĥâÁŠÄXˆ0 ħ‡“á¨}İÈ_µf>×tBÒVÓÙĜÍ`lŝ°Ž -p,[P~Ġƒì$fığÈĝĈZ d4&<¨Ñ4˘ĥ³ -Wí”üµ'EŻ7lŜà›SÇh/:jHW𤀠µ HdŠCW8żïì¸u°Ğü?xL(˘\­wğ#ĝâîƒ0;íOt:[]²ŭO0[%|ö=j8ĵÛcKڟßÚ5£ ÚÖĠaCî -\G`Yż Úĉ‘eħf.şyȍwFZ<Ü)eòAÄhƒ7Ë9?ÙÊ@ó¸ş$ĵ“”ÌËşğ+,fıŜ éÎWÑÙk´—,Ŭ0\ıu‘°]qĜ$œœ£Ï4á@×ÛB+}Vì$ 3èÁ…éù.“˙N[ò3g.t£Ĝżl÷ZƒÎ‡´èê­%V]%/'í²ddÊú%/Ù:˘–ħnq7èOlÚà~+*qµż×˗{{׃šg‡‚w˘>í]‘0ŠÄ% ˆâb•İğÚ} Ġ‚ËĞRëIŽ†O–ÈùÌp ²}d€çébV²PB /´Kş*rz·ZĞ„5ĝ˘ĥ˜ï€=˙ ·:òƒ"§×`ĝ*@…˘¤\ meŬ‰ËŽqDïK€—ŒZĦÚPh·Gävĉ Žˆ€*Mt·dßë|….’kÙı;G†òÇÌ!Ħ:)–OżáPaĠwcSŬ{]G]ĠiAKŜ‘X+ѽŭyK ½ç}dRoùÂZE*E‹R G6Â`S?%·ĞçĜΐK UŽ.ü/7ƒG…a:Œ–5f)4:¨¸$hClbE\àÚ—–ہ|…iT€T{ñÍİ(X†/ñ0!ûĴ8sçmŭĠçê/pJyg4›Ş‡d“D’|€˙èvmdşBꛙşSÏ„ĞÁKYÔuċ §Rs -V[<Àñuġ„qĥˆ/~V8§èûa!•R›îs÷|££ògĦ´÷E·âŜĴs·RĥÙá„Ú§8eé>Ó‹á,ŭ‚”~?ÀKQ&bŠ½e •,2ˆìím‹ûş‚S‚÷ßIÉYŝ-4ü¨•n6ħlŒü ĴWżûPp>]˘M˘Ksä£+ ͅİÔ×(¸œm$ŸMÍ'ı³\Á‡È´Âó‚Ġ>ĠŜsş÷Ç+£;fw*”ĝâVSÑPM|`Ž§ÁTNŜgŜPrÑf°QáŸâûÁü.żğ$ÓĊ%Š1ĥċ*,…ër:gŽûÑ`ïm]/#Ê@&5&e*NÛŬÔÉ)(ŸßöĈXJÛ/Ÿ1[_ŝ=Aş[u„YáÈJĉ+XĞk8ÔB‹ÊtŞĦ—7AÇÊX4÷żŬ˘ŬRaP`x"! v!Öĥ7·C…: €^)Ŝ$_‰ÏXÚù‘Ĉ½ž6/²3nÔ Á Ĥê ~ÖJb´ĠoßH5ñó ˙…Î,G>IŻîġX]ħ=>œ!ĵqœ Ή]ëóżüqx9#"À&Úŝ]Ëá³ú$Ğ·PÈÍ˙öt&w <ÑԃâÍÎWŝÓĉJïâ‡ŝİ6ħbçŒákB— IÄŸ)’k_üÒ^ŭT1Ĉî—mrE÷Ü7ߘp×Ä*ÑıµëhÑT>Œ ”ÊêĞ°!“xŭ™(ÜfRĝ‚5hÔ˙>ĵÀIş&nŸ…íh7ŭ#*ċŸ§˜těRĴ!D˜˘ñ;޽îTUN Ċ q:œġÈ]°m2f*àkİrċ@òˆ-ÑA³Şê’IŠ#ŸnEˆĈVƒT3ëÏóœ[’˘ÌNGH06P·×7ĠS<¤ġOÂe•t_Gŭñûù¨P\ ĥLvìĜë pR½% ħ -bŜë2•Ğ8ÎċŽğ¸Ĵ×%tÇĊt¨ÊK`nÁÔ3n0Ĥ)Ĵ•ƒàBĞéNlħŞ7ĝ>fÇIçÎvß5%÷ -(° ²€èj?a—[°Èpĝ—ħ3RšeWĥŜÈ0{ô8ù—KV`fâ}{2úĝŻO;ĞüOM•iqĈqŽÖNô~7ħÚtJıŝŻç2ĦúÛóTŒĞy–ħ_CÍ´? -›(‹ÄĞ_w²ÄVH™Yċ) u ĤßZb€²îGÉî ¨żgÑ]ŠĈĦúS8†öoó½dj3M„‘ûÚ~ıWcìŻĜtŻ‚onşš×,ƒ”;O³>i•î‹Ħtiġ*lĈ”B&°|;DĞĈħkĠ…ŝ"ÏD{›ĵGÏĠ³¨\VHȤwšSqÓɀUGjCIŻyâŬ1Ÿ›GYáŭŸx2üÈ&´uϟ>QàŻıÂÑħ_`!aßvĜ¤yÎĵóŭ™+Y'p(Œ~íñĈÜ먙KNp|;‡%Ŭ· -Äôñrtlƒ×g ÁG8–'%‚›)jqŞR_üßܜĴ:1ˆ]¸·*GCxóŬ8h.58<\hĦ -h܊r ÔöQĝıá#çŠpŭŝ„2PѨÂ}‚ò&üçmé]ë‚ĝ"ıÓèòtm8{´XĵWLOc“Âó{ú<˜2úB&˘>T†$Ĵ¤ÓÊO“\êlrkK~Ë­ċ˜ó ‹ĜîYsB‡Xŝ"ñúĈߕ+äDĦ>V>ˆ³˜S錉kJ>A˘ŭ%&´£ à6[Pe9Pg‚ĠDĞePùpzIM,85ê²ÚOġUv"zP…’Gċ ²d^’ݲËĜè9ÜdÁÔF2Ş~Ú)TÜ ?ı €á'˜êÌའ-^wû‡‹)öħV6‚KÑÉĜÇ.Ql.èʆ”uî[ġFĤ:@ż‹,·•H½–’ĴĦ³íÖŬ½µˆ£~/yâ0·öHtsûw-˗bQ–˙|!ÏW‡ƒLoŬío4ŬĤññ$ÖàŭkúYyÒŠË ß;Œ+JY$-y÷iÒ2U úĜeİ-Ü­÷­)”p:Ü.¸²Óh€ŻtV“wĉpHÑ+×ôdÏ´ïLŝŻà¤Çœ!×~”ƒÛaühïi§@—3D ¸ħŞ·•; ş -jħ3ÏflÓfÈ ^ĜRlaɘò¨OÂgÇbA…û÷‚Ú˙ ysŒ{‘A0aa^ÚÊHw97,b½IWċ„žD>k§]B7 -´˜ƒċĦ).4{‘ħ$U—è,΁/fä@ĵİĈ?5êIo³tˆĴQW9ÒzĴ-Œâ¤9Zѝ9üzì GW$/WÖښ·]jvÎ_Ċ¸Nl÷ĦٚqŻxt˜Nw£ |°0ċ*ü³ĴĊ'·4LĞï0ΖUcnìÚ½zfúâ\„6żôG…Àp‘<Ħ“FT|Ş:–Ú%Ġ@3q“m),1Áû³(İYúĈ:³Ü_Ĉ ™¤N‰oeš9İä=LŠD•Żà<%şùzĊV=‹@‰s´ TN*êíW,ö,¤ĊĜš‘|ŜıñL1ĝÛ"úW˜ĤĠéġ=0HĊ²#„¤ıxċZ˙Ŭ–µâ -@V“ĤĈ°ûËóĵW‰ÊĥĊm›œœ²û¸ġšKPR‘umwA"p™†AW /‹)FjWá£YôpŻdĥU*~ĞaÛŠ£‡wg]u=ÒŻ,Ï@ŝže6eħópħĜl<¤Ú÷kaò)|ž”Ż²Hk~aİâĠĞôR}%3˙Lĥ „ßy×Ó<TY— 8˙/ŸšTÁ\;TH(h’ì&€Ïşïó*Z›Vxħ)Š!PCC–½ü˘ [ÂaİI‹ĵċ·áxú€D`‚M÷–R3èÌòÙ' ]e&ÈÎcÖ꓅Rċ˙aN˙û™…ŠġĥÎÚ3Šw÷•ÀżŬVû`–_F¸ˆž‰ßż²–‡–ì˘ñ‘Ħ…çԍ„˜ÖùnQoĝt~ĜĜ7œ`E$ -â˙'lċĴ|è+§Eà Ò/Úöʜƒ. ÍBĦ>Ġ§qÀGĵ~yĝ* ÂBŒ_UMÙ=Gy}˙ĦEîÄ÷QL. -&¸Ç sATJ¤Ë^ûhŠs/8Ù7§4 ë÷ÒE8X2)0OÑ/ĦubŞŬ´Iñ×+ÎchF†ñyß?ĤÊï -ĤÀħvĈMrî8>³Ì0•ÇĞZèƒLû|Ö#dމĈb‰ë*PéB,táĝŭÊÄ 8³‡šv -ğµĊN-ħ3<:ÈĈÓEÙñ4.Ş^I›Ĵ[`QŸ=q' Â裵ħ_5lóJcôIĤjµ$CÂWp×ÏN½%0J¤¨<öħÁuÜŜŸûœùÌÒXïgCĠT$l½ˆĝr=쐙PˆĊ²vwJó™¤"?^ä›ߊš à}I}L 3qf‘at=é´Ï/ÑÒRJk!>ĴÛÛ"àŠ8‰^ĤX’djĦO£ kœ bŬÌ ¤°§˘[ZHWC3t­u÷j‡Ûcœ -û蘇ß)ğ#~jšÍúz,iÔı÷ÑIÀm͑š×?ĞŬîe.6Ì<½ó>îòqûgóEëÀù5÷Ĝgf re›Ĝ^7Iì:Ÿ\_ÁħĦ›ìdë燐zIUΔÎĴ8ceġ Û^8­eŸ‚Ô -'·OhĠüŻ0á’qÂ}v%F‘­HHôǤ˜% -ħµżFˆfÜ{–M÷³6(Ş…ûwoĠFdÛ%4ÈZ‹Ë—ĵÈżJ…<‰O_½âZYjdŝZ3½p‹’×büvž,(ĠOħĦ&“Ŭáċkd/bSê7ĵW6äáŠĝcĜb{'“1Ÿä˜  -‹Ú÷èGóŻÄĠ…À)JÖoe“Ğ͎Ċe;§d’ŭ|;AŒ`Ì\4Ǥ‰bm÷]YО×ùdí1MĊü:£Ÿ{Ĵ<ëĥĝ2@ƒ}}\ĦàĞÌŞ½ĉ¨ĥ"žxĴ Y™&'Éx‚ÓTìègħ”’d´^ä+’LÇ´s~օäĥÁċt²5Ġ áêeEĦ#‡äIœTU$ş'âuğ­Ï]Á(OıÇŬşSy›ĈşEä+ˆ/éŭô1ßÈ˙èV˙J¤Qp”-Îôž}ŸŻU3Ÿ Ĝ>G0k îŠSŒï=ñÛ -˜½È(îM&ğ„Ú.‚óÖ;’=XĈ—Ä'-"·/#1yé5À bÏklû_óòtOĞßÄ­ÜŬ:0f`_!ŭ#wĵ 3tH^–?â•~–·ĝ$¤–ô'œ½e~ĥĠŜ׋zZÖ0—9ŞC{Cóóv9So‚ĠğäÚb9Ô -Dğ“BöZòvÄԓŜȤĵ¨͇)˟òu(DĉI*2`>/\Ş3 -íÔĴÓÈuŸDޘ³ ä<¤89y2sN·Â}|9‚²A8éÄ˃İz˙úÒ:?OOGM6]Ş+·I‚ôÎÓİËÓı&dĝŞĊİ=\‡ÓĠ}>wÙ.,J;“ ´w6…Éq‡ÒJ„\]Âχ;NuuÎè"‚Şœ_Áϔ+ncJ¤ -çlŠà£,œÛ<"ò’İ -V,ŠŬ|w  -¨éĥÁĝ‚İX­’ŞÙÓú!*NŸÌŸn­’ GÚñGß‹ -–8ǁ³1İYĞ}M˘•ħ~2°ÒÙwû^fǸMĴŭI/Á,ô3˙=–Ü÷ÂŭĊó(5ŽÇİc’…ĦCuTP!ŽĜCħ·+†QŭµSéùf°µ +Y ûƒík›µLÓ1bVÀ„\Ä Oñ=ڋCċ!â‰Xó!°³Í‹²é1=ӝĤx>²sJsÊec„ôn”şOfÓÖ œÁiù¸D qĤ” úK ‚@ •_q߯\>3Żüò$ĉİGOÚ ĵœ;ĞÚPöŒT:LŸ“úôĞ‚ŽZĤ‚˄ï"C1/1-6âûz,ef´b™Èü‡.·K;Ü9ZŽ˜§°P–˘£?l÷jÓXڍžċÒiĦŸgR%(ÌW63Ż5EZq‡€ËZÖ£€²‹e”zïĴcÒygÖ! 2EMR½ßÜé}Z~µŠ­˙Ŭ;r­‹™Ñ`‰ûŽ]Šù{žÚ_ IyÑO‰ġ!óċöÒÊJZó:>À3Öf(Rħ4}ĝŞħAfîhŠ,îĤÀM'Çâ6ĜÇÜ­¸Lia<žFM!]¤ÂırŜ,½P™ÓŸâUûëD"Ík_Qœı½"œ)ŻŠ–è~d·hŻİ3Ž<‚ ړ²£˘ß 4ùqßQvNĞ~_mZFíû·~í ƒ6ˆÉ# Z“À5<ÄĴ'÷ -endstream -endobj -682 0 obj -<< -/Length1 1996 -/Length2 13162 -/Length3 0 -/Length 15158 ->> -stream -%!PS-AdobeFont-1.0: CMR12 003.002 -%%Title: CMR12 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMR12. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMR12 known{/CMR12 findfont dup/UniqueID known{dup -/UniqueID get 5000794 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /OIRSPO+CMR12 def -/FontBBox {-34 -251 988 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR12.) readonly def -/FullName (CMR12) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 67 /C put -dup 73 /I put -dup 74 /J put -dup 75 /K put -dup 76 /L put -dup 78 /N put -dup 82 /R put -dup 83 /S put -dup 85 /U put -dup 86 /V put -dup 97 /a put -dup 58 /colon put -dup 44 /comma put -dup 100 /d put -dup 101 /e put -dup 56 /eight put -dup 102 /f put -dup 12 /fi put -dup 103 /g put -dup 45 /hyphen put -dup 105 /i put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 111 /o put -dup 49 /one put -dup 112 /p put -dup 46 /period put -dup 92 /quotedblleft put -dup 34 /quotedblright put -dup 114 /r put -dup 115 /s put -dup 116 /t put -dup 51 /three put -dup 50 /two put -dup 117 /u put -dup 118 /v put -dup 119 /w put -dup 121 /y put -dup 48 /zero put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ=Ó%ċW˜)-{Ùr½uú•)Żœ‚ßröA•ÉÂÜE(ġ@Úŭ{ëı´‡ş“Qğû|ü_‘RÑċğ -ĜĈϤëA³Ċ -T@ĉ|ŭq|VkıżJ% qu8P˘ĝwÄGx³ĊŞÛ̆ÖċQĉŻ6K üŞÒ-UŒ\§Ô%ĦbĠ"t-*xÔġöÓŸÏ˙J‘+ -}ì3{Zà2ŽùĠzŬĴT2sÀ$ZġÌÑ&{Bè–J×{¨ßr̗Ġ½Íám”1lè(zċNRĝréò^&%Ï:(/I‹ŒßşH’m§!’4ÜJßxIò7ıbs,O’i˙Ol7³5R 9ċÁúŸ³zè(²X*‡Rh•³n5‡Ÿ³&ˆ£ċgÇüŜ\ÇcŬÊŬµ¸9`Eı½€âgœ²wéŬT!ÉÜxÈIÔñJz҈vé*lôc›oĈżĉÍsdm^•%µµ‚=è°ş•ŸD +‹³uö9ı#•œš ı3µP Ç_]²ċë )›ŻèğĊw -ĝˆĊêŞUŞ˙AŻ­ 8œ¤ HŽù·‡áÍuGá:DŜ‡áJˆŽŝ(†˘óW­ÂóÍóï]£-0<.ŞgSB Nl”ZžOLïÓĦŽ5^9´ŝ:§Kş*|îF -‚„˙{‰ ڇ€ŞÖE,ßžûqĵ>½j0^—x떲QĊŝ'Xéí酉ĵi É;yZÉPġt¸˘>˙ħĜÜpç1SV°}Ç:ĤÀŜŞaód0hÄ×{ŜJžŒ³AŸ)žÎ˜Ğ‡[Ä ğĴšU‰=ŭyï5ġp”¸RŸU÷¸ò&Ç0ĵş¨‚'–-à›İ²8•ÑtI˙Ax*Ì£$á!ÜgRH€SĞ;RÁVíUà€ì?!lĤMÙĴÑ2gOèÛ.…TÄ7“úĥwϓ)?ıCß –Vb7^âk›žİġJ;Ĵc -NÀ”*ó ٍGÀĤ¤àÙ|›’ÔˆU¤˙cÍߢèɨlÔá“6Òhš6[ 2ÙßµŸZàvUôšâlĵP|%)VǸmş×Н=&ĵa -çĴôJŽs˜„_£Ì²’™yŽÙ|{R‚˘6Ä´žÊ—B—7jI÷‡€È˜2—ŭ³a‰ü§% ˙˜@74 @˙ê4(’ĵ.=î Í`žÒh'pĴÒ+x•vÍX}†²?‹ÌGÖ3D:—‚^ĥµĦӟ*&ı4ñpĜrâxüá5e ^h›k@ñS_̎ċCl^^Ì}Úĥ-q9@şÑße˙Ŝ @ħğŝĤ ·|ŠwMŠr“c9ßP(äžT½Ïk°áéru…°Y@MnŠ·uÎW`%?Q8ôwG3g€ŝ;ĵ d¸ÜlÊo Íı2ŭ “UáóġuÀ6â˜C֋%ĊYTġ'RôŒÇjҟoÖ1MŞn}Lŝ+“:Oŝµ/Ì`÷@ƒçӟӎċÉ4¸Ž´ĞJ -„B ‹ÌÈ$ĞYaĠ°H A‘g0IQ”ó<Ŝ;—ûv|<í6ÔGÙä@tqX†Œ>áɏpI­%°(Xôv•Êĉ7}1´9lĞAŻKڀ6––]“Á+šúàħl‘ô_6ó'–ë3Ü`k*T ĥ(İ]ž65RĜ-[Á(E­ìAJ!3s:e*A˘êÜ£Ì ZŝŞÈEs´Nьm´cŞñ..Ûù> ‡ÂˆÓòœ>Qż‡&ı–ÇxċëÌızn˜żˆ†kC¨°fqW-ٕŭƒ6q‰o*˜p+.ögjlZ rhtÎ?3:2tÙñÙy&F™!w<öqïí°ğF.MÓ{İá;šA0núb’?vÄYNÎ+J—ĈŻĊ6& $ì›û< yê#p÷Ï°nƒôj°.Tä• ġ‡è&Ї8ċԟzħĊGoˆ9ÀÌÔ"^­ù€R¤x‡|Z!^ĊwEa×fħÒîÉ·im˙œ44/bN˙ì'™öKÛÂ3ċ½ñòéħĞOhÏJAǙš³ĵ>^§9vŸÓy*'Imt¸Ó:dN#£”LÓĉaRx !…üd!½R ”›ˆšµ*ñ żä9ĉ SĊDdkĜ’b$°úVñdžŞ^t–4}h5e‘ŜHNˆrÄH­I,O·6'àáÏl˘³†› -„˙†NOêÚ#xa ÊOTžVċ-ğ(·!Jµ·ZyXß ½¨!]Żz×Ü@×.ĥ€İù 5í‰Ï-“DL´5_rÙHċé­qg‚§Ż/r秂ègÍŻP%“‹x Ĵdêż–Àx ÔAŭcëĊ˜ÊşÏĦ˘üYdŬ(„*:žĝod`ˆ˘˘AMúPb„Œ†-n¤‘‡éŻt’]#µ‰Ĉlg&ÉÓe¨—­è–b5dÑ*OE 5 ħUThúŬlvż9ğ_)ùÔÌ$pC›šĈë+Ì(¸MŽ ĠĵÚPûV‹’OpĦÊÇtcC`şĠ â0›ŽÄ²€85ĴYA(Ċ'针1Jš ) Ż”Ó=Ên?EpŽŽáaq˘Š\Żùê')Ë_4Ù}KYĦŻ+µdÖ>^cŜV‹6Ĉ0EZĈt,Èŭ)Ĵiöe O³­ÓŸ5nĤi8B5ŝ*ĉĈ„—xàn½@ÁEûDP˙>ş e$IġÛì^¸nÙÀa YŞ>ĝĦ˘k#àw?Ápá´˙͓ŭátµÛÀ!_1 ĵÓÄdr²{üd ’,“Ò@ò]+Ĝĥ‘½ŠCÛzıġn{é0RìUżKñŒ,&ĠÚé°\Ĉ­Üä˘1LB°ĞÏ#Jä²µÀóŝñ¸p0Í ÎX…J‘K7ZLD"a£•ôfĉI1¨?Ôjt'É8:/(ŒIžGĦŸÚʵ6ŠÇ‡˜ <ƒ+Ħ²İrö ĝœxžĜjË=ˆ´Żğ9żċzI!ĤĈĥreGNżXNpA‰–4Us]b;g‘-L:çŒ÷/ĴÚÌpaĜ–:1xùǔòÈä`‘VÀ•ñ&EEŸ?ĥcÖĝ CۗǙ77²-`ÇÙ$Ż­Mvßêê|³…&sČΠ6X!Äg#ndχ[“w䄁n(„dَ—oÔo÷§_…ì”o2<ŬğŞ ˆħÇ Á‡xMIż^ -½ô­[$dDTêZÖù ÒjÄ·à‚“i|O.çE9wbSşsĊBzá֚ȴ!µš2g¤Öü6¨àÛÍbcr˜ıòۑW1A"ßnX˘Ìñ1µğ4…n‘KÁOC-NAİá=9g5=íW^xÍÌ(x´Ä˙ڞE°ÁÚt8}NŸôÖIŽDʄ”’˜‰żĞšż!ÉŜ€"]}ĥFżĊÀ‘ÙET2ÈmRi< ĤÂr3a0ÇëĊ!fâ’ÇèğŠSœ&W{VÖÛ_˙ Şàħµ/—™Wc - ċ1“Ĝ5Ÿy‘8³/ şÖVşŻ§ôÙ§ıò‚*^F}#? PĉŽ¸€-üï~–m~j”œ’FvVĈ ‰KĜ.\'Y˘öĈŽôZ‚ŠŸ‰ˆÖ|ĉ9&œ½ĊŜfr7áĥ€Qĵ~n·- L5‰Qċí/[Š½[“‚€ORue§ü>ċGÄÏ zúŻjPËŻ,jW灔RÚu7´q ìğĝjml -†Šš3Ÿ!Ü9r’„ëi é`uÄ8!²5$³c¨ùUU™üOÊ;~}Û¨¸ĝd>„ŠÈÊ̖ù gşlUüovŭŠŸ+³"Q%z=Ä$¨Uu<·J6RG—öÊ´Ü̇vmŜä³%ġùğŸ³Ò]Ĵ=PC}„üÜ_2ÜÇÔkŭġ&ëĈ é;eħG7גI–ĝŒ½0QfÁ/ş‘ö Šûße!Sâ|2Ž“F;Ön€3:ġGj‡÷)~k•šÌÙM'A‹§ÛR>CşßM^}ú]†dLBu¸(w˜ÈĊ& ĠGJ*ïÔS0|èCxĈożiNŒ€K@N@˜Œë˜÷fŻÄäŬùƒ2Ŝ°¤ÂiÖrĦ7ц%˘xŠÑÍ47‹í8˷턀ħ‡È˘5k~Ġ:ŝ½Dwp"Ğ;jñ°Aú­ Î`SR\ĥYħ.ÒwNàŭCħ‘kċyĞ~ŜuH#é(8ÏN7³ vß/I g;è“0Mf{Ĝ’ûF3 “ƒSwHnp}Dħ0íúëôyġäaf¤ƒ€¨œA3?EöŽ.RŸBßċ—cÏU|Oò¨+ıU$´rÑ=ه‰nŭ´ç5`̕£,àá/Ô^r;5?9ÊĜ>QœN×GZiƒĴß÷œ‘g—†p={†Ó_ș0ÔHÍ>(Ë´uW½Óz|›TÌ´VIMŻf*ߣ„6ÂÌcçÚ^<—œR5Ív-w*ċMĜˆùó–1‚V˘Ĥ i‡?䢂JBf… ëRĤi{äH#´4h (… gĊ~ĵ -8-֎×ꅽÍ@ĝ(}ì›ü‰ĉTœT M—œ„P­ħ‚`ïpԈĦ`zŒ{ŝ'›œˆx ‰ï+š’ -Ë<îÉ֟…áµ}ĥ@ˆ_Ï·²˙İóW&ç¨)#ùÎ׀°šŒÖû+Ħ$ɐ2ĉi_™İBzvï`]CéÇ]c+老ьş„´*ƒÊùµċM0ıĵ†÷Ħ×\ÍÈŝoĈÛóŽómşV -İ,T[ĵó£ÙÖa„ï'ĊrŽÚÙ·Î=+ .ét_µÒ,'€ĤÂP)Úó§žr*Óá4W…p×$  U{-Œĥ¨Ñ‚B‰ó ŸŒ†qÚ ™˘ -a`OÌ|q‰d˜ĦŜáÎ3éÓş$áê/ó|ÒMRú·-`ŒàŻ İ;6ĉMú|ĊŸg~ò€÷Y uŞ[ħlò(oĵÙ˙ԁg™lEìw“·¸Áք+€ŒpôdÚ³XlDXu˘žG ıb2Me­ ċ‰*e××ĝßiRÛXx8ıAè—EnS•\RĦ y—EÓၛ™ƒjÏüT91ïP“§rŻĥÙô]T|ÄÑu0™zàWMŠSç=°“ónŬƒÒk›ù›ŝčeԍ,èÄĠĝA£ÖFĜk´/b\ġè²vIŬ÷ĉÉ· ĦQŜóDħÔêóûkĝs–˘h>ĥš`…‘ŸaİP°(~j%P†¸ÈÉ> -µGWl•LÑ?™‡äµùĤöŬ‘İ&ÁŠhuġ&½A†$Œ‚Ô%úŽ9c\P "G("Ŝ ĊâŞùŭġµ†áìÉÀÁ•Òz…ŒŸ—+"“䀸ڸƒŞVâHŠ™’ġÚµ1Gڟ÷HxŠâYĵéT²ÍÒĞÉs-pSŒĞÁC³² q: -‚99xec]RÓ{zCħ‡ş?yOşSÖ.ĉ+àT#`ü`"Ĝ  Ĉk‘œk2A›>ċ&ƒ^²ŬèRzÑ=f‰é–)ĝgjAŬ“'x‡bBPd<Ż^Ҏ,Ó!ĦvĠċmĜ J!‘ħ*<ħ/S²ÈÂ=MÌ9}X[ÛR3áúA2+Nƒdë"âvF6 Eġ’[ï.ĦÎÓZNN‚DÂçhŒ£|Kç>5ҋ.5(KáúÓ>+†ƒ+4ğyĠ@¨ŜŽBĠî[Y¸ĵ”ġ Ĵ-`üŒ•‰”‘ñ͑!§-|İġRVMr6 d$j÷ĞweŸş­í(%.`.öò tÀ“ -`ñȈžèö´n1ċh nzÑÛeRà€#nùmäŜO°ŝنwÂwOu*NÇĝkxcŠ™˙V£ÔÁ9ĴHÂq8°2ɤÏ3ñ˘Îòò×Ġ›ô˘ƒ.Sš+È@&½Š‘\ÄÑ]ÀbWßĦ!˘NŜpÙaî0’fĵlŬnğÓ -ED ´pèCr:ñ°óċÔìQ=£ä‘èâ̝Wµ8{‘mCUĜ·;·Qtŝ[ŠZߪjĈš´|YQ4ÈĉC<ZeÏĜîoäċúD…r%`ÔÊĥ@BĤˆ‹>:Ġo%1+Aħ%1òë{$ŜvKÙ* ë1u+†ôSpĊ))2"yLŜoŸ¨)5 ?İ=› t³pşB,áî›ÎRbĊItßh*ĊNAoٟ£(Òž/'ıJÀ 2nbq„Êğ°oHœô˘µs˜TòV}1´ˆĥaĝÄ^½/°îJ!ˆÜÒFĉŸb,ìôàŸ%Ĝu·ÎĤ*˘} M-Éóë8³p—y‘|ğÏ/µr,g˙ZŽhç½ÍV|ȝ1íx·ASt­W[*äÓáVÖ{×~ħöR‰)Ÿsoß˙@ħœío1¤Ë ÔĆl†Ċñ<¤TĞ]Ċ4Xùró{—8hßSb° ?8xâ3Ÿ2EëvŠÑlßF(ĠûêlġmSFĥĥÁÚĜĜ3)—_JĦ†˜/GÚGӉ /ùz6­}EÑĉ3N™1yÄĠ]Ĵ‚ûÎU2ÇdŜè:I ıËûÏb’ô%ó“İJëeUğEÜ/Ö>1;Ï ĉ‚Ùžlĥ#Ħ[êŒâŸÈxXÀCVâ)à5PU’Ç|„ĝÎŝìÓċ̖Za×2¨{¤È\ç:qy<ƒiv<ŝ)‡­üġë‚ê&Ògéےùŝƒ…­g -´ÉŠŝö"pŬħCšWïµÛîïĴÙLyÂÇŻ›iJïz)³ìA•l‰ˆĦÑÖ ü{Jİ?ëóĤŜ@A)ó$Q½ƒĝ·ç*1sÓ˙꜄4Ĝo6êç$O{>&Ì&„ á‘p%<ÇkFjà|o{ÜPyĉHt‘şzTÎĞ°?¨D‹vZTeÛ-óŸ4•îUŽV€Ï•}€kÛyZ˙ždkŻxEĦù½CIm „rV û—Û Gú;ħÒ¨*Ç8ûx=NS˜ĴÈĥ˜ˆ@Ĵpĵe÷ŠJ³gst.i> ˆıYžĥ++´ÉÙkí¨Bɸ*ŝòŽÙ{Ô·4|Ç Q)#‡ûß_Ae·Àƒ/ĥ²ŬwD­¨Çz"—ÀnÛbùŒŞìÖL”B—êSΆaó…îcĦ­T×İŭB³ù hüH$ĈDĝQµq½Ħíî•N§›=…RÑ|t ŻàD­Îr\}ĴcŠ*,ŭ3|âÏU ÙÛïaÇImĜ¤‹T"&s&,IĠŭŜrË×Ħ~ ĥĊJrï£ß/˙$%Ĥ\˜Œ—%ħ³`ìx´à†Ò”§Ìdm0İW4áBm0Lj#8NçcMM%™§Fdâ-¤#)İî,›&˙0˜@Hó“ħä1´ACaÎ1²J^’ Ċ KHìí#ù'J…MäÎċd}w'=ĥċ*öù=ׁUÑ\&:ë–.éŸ/X¨êšĊ. -Û˙ĝı2ÍİQĵ5jBñ·Q\x@é)oBlrb_PÔ¤K}ÏFƒ¤Ï †-¨‰Ó²§µÂO-ž³/;à˙ÌrÓ' 8͌8 äê°¸éÏc7ÑfߌJšƒêD_ĉYJӍ²–ΚvMħ ™9Îö {ê;=aŒÜA½¤˙öçĥisŻ²LÍĤŻS;à½ġĥr·½½[§Ëc9çi³(*3ĞÂĵݸ^H"1ò¸R†ĝ pÍ/ÚÇZà£V–o=§mȎ7Ĝ8íxsZ¤yFš^“ċÖó5Oꂷ’Žl9 -P*ıŒ1v–§ƒĜxĞ ĥ>VsHLÑÀTŜĝŬŜñoˆ{›§÷¸t:¨–‹ùà FgÚ ‹+4Bcúë>orQž wİ˙ħĜ|Lkô·mdg ÜÄàO˘ğĝàâĦNáµJ%£N‘YqC{Ê%mK§AM %;ġLŬ…ólʄ‘T*–2 ƒ:È5 hĉÛéN­Z¸k°›ğgĝ1„E“û·Ġž Ç —éL²µĵ3{L(ÔÎĞQp>"×ĤŜÚ -À*Ü5%&_cRTu9?"mUħÍìžéšŒ-Iuù'Ùp· ç2ñhŠ*½yJj-4äl6LîÒ^ +Ni%/Ài–Ĵ¤ہ‹‡y+Ħ×%:&“B e½~xÂN€gĠ>“-³Hı‘ÛzÊY+wƒn*B÷uÙ$ħ£CĦ}¸=~hîÀxۀİ1éö—}ĵânÁRÙ}7-Ù1ċL¤Ċ¨ĥ™™ÙA|è1Äô#cSİì~çib). {8ñ@‚Sˆ\$ıèğĈĥÄÇĤ÷$£üß4ğH@kú4ĤyúöV̀Á²…‘y-]SŠŜYÈ+µà(;‹`xĞy—3tñWlž6T Ԁ™ĦÁC#ı™)öX=~ÜUĝœOÓɗïl´Pà)ĈYĜ­İÑl²§oÁ1™-£šŸ[Ŭ=úŜ[›ì;·VĴ7—ŭé,7ÄKġ“ñy -oħÎSˆŽƒ:²²a>FrÖ;ê9[ĠÙ/~,ZÏ3J7ç/™ĜÁĦˆY+ëȤĝdŽgĊ)#ûä§2˜†KBbĵœŭŻC{ĜûT“ûê_ħÒg‰”uA}›wL$ëtA #Gnۇ²e˜ –âoÌÊKyQRÑSŝĴïË6ıWéÂÀësşÜ•oò…z AĞĵ/Ĉ¸Nso%€Žñn9Sĥ)èŭg -÷=›ĤÒk(à‚’8˜›1cdĊÊèméŭGĉnóG`³•F(I |†ŒĈŠ¨mt\z-ó²&](7ÇSË[AesJa$Ş;/œˆä%Ôu v½hçlD£.¤ÑέÙ\Ġ·â<áû¨Mv•ñ u˘u4ÁT3k=:2xš` ¤ĥÀ_"A­Üo#ı˘ž µ6Aè–_ÙG4V0l9/˜ïK9xí˜_‘FJĦx$*ŭˆÏ?Q„x²ŞÙÎ ĜŸó//Í|§Ċ6Ŭí­ÊèCveÓp‡ë½+Ò,0<Û-ùÒ+ ˆr(Yò½²Û°â™ıUŒ…’Š(­IÉÀ(ÌŞÂúäħµĉÏ2}ŭı‡a¸€ŸŜÜGGHĴ£Ċsĵġn²³Enŝ6ĉ‡òUc~'`1 -O³sµÇGĞ£mB ÊÚA–  -‹aˆ_ŭŜŝ…M×ĝf`}hÀ1ÍAË u!“@iqx>b•˜ŬSɅjòt;=§]‹Ż_?N܍5‘lä½­žeZĴQ^ĊoúYÓ ²ĜÑV˙|ôÎ[ı]²z#ŜĠ–-FŬ§0„E­½f²Ž³ĝF0óMñ÷ÚE¸×ŝïÌĥŜ˘Â›šÖ,@ôw<ÇÉvŸ5t°Žšxäċĵñ²„ĥ‘ö)ŭËïÛn)}ËÁIaKG›9TÚcZx½DQĞOħÛô ġ~ÉZùöŽí‚wp˜ü­fӍò}G1ZĉnNr0mg2BşğžÁ -pµžç£Ëó}Żšœ—ŜxžGëŞD¸ò£6ŠÑËì~ 2£a÷1BôĦ›AFGĈl0Ĉvĉ†ÔèARb³)Ö{âÁ)`* vŒž|şŞôĵ -ĵ>תĜfĊİĜÔ_8Nµ˙VRç ŬĠ˜èoI535›mg•ĉí>ĦW-,½•9.@)ŝ€ObK7g6:Âĉé01G׍ÙċšöĀÇ„…Aˆ“‹j+²é*ڟÈı •tCmŬËĴüŝ_IU!J1Ëĉ•¨-bàùlĦĴ µDÍcŽ˙Ħ-/'ßş´ÁÑ\Ìèşĉ –Lò{ŒpÇ@ÁĵÜk>ÔĊY9 ½@ƒï=‚P4*\‰L ¸^nÇgt³í:ŸZPuĴ'(^2Z/ÂŝÏnת5“ï‰V›H}€ġ('°Ŝ„8Ġò-ÊĴ “!ħö7OgJO`4(ÉŞÚ”—£˜İÚèĉñyÒK9DĤÇuDì,˘Lò#Ó1TtwÒ³uÄDĠmW bċçƒ ú$´m ÍğğĈŸDĊëí§›=1²Ïš"½à"R1k>ıŠ§üğĝş5¤ZéżVÂw\ŸÍDEBüÉëżs¤·;’YMĞħ;Ô kˆżĊe -ùĊi”jŸÏŝ+Íż§xuúZè´Cj†*+!EÁäùٛà…é½:žžËĴFÒìÌč~](6œXqT÷Ż-UÄAÜqéÂFKÌŞ!™;°`ö]dİî2*`ÓWĦ•`A"öÑ` NL>×;ş÷ĊO#6wO…Zħ‘6& •ĞX$܀$ĥ}Ú{0k½ ‹j]iĤlG‘ħşh•˜ ôfŜ/ċUA~ÛÙLUÂw YˆĈ/Ŭô éë^âĴâl ohˆq ŞöĉNšĥDTSñéC| Ó Tm>£ZħĤïŭ“üj¸"H!ġŒĥ³ôç^8<ç…璝dlğŞUsÇñĵq3çGNHaM÷8È`~È£âàLž -' É9$›½d7™íZż}ZŭÁ’Eáğ=Yŝ ›ôš°şÖï^lU"„ğİBÇz‰mmìn”IŸÖI—[k‚ö…ŝ NĠçÓ[GovŬyS‹X'ú9ö.ôĝjŝşC‘”–ĝ¤ Ŝf„E…Ä˗Ùiîv‘Ĥ£ƒĦÜJżwߣĦfĠo@„eò AïğÈtPĊĵíp^x—Ö5ôGG‹uÊ@·*àëĴ`њuĝ¨~˘tŝÖD (<&ĊĞ\Ñj-–û‹öQa›É\ leŜĜĈ‘•ßÛv‘÷ıÑàÈßóK[†&xRĵZjĉƒ -JÒÌ:H0¨AXk6…áS²6Ò}€ñÓd9UüÍKÄVAZÏ)[üċŝ2!ü­ÉVĊÌe‡RˆèÀí_X>dzÑN’ğÄÚĤ²V -gĊ.Óz×ğÒşĵ}¤!E ĵóÓI§Uĥ5ÊdV£ÑŒ Ŝn³˙°ġ>'Ĝžé³gQG´ò‰)7òB\nĈ‰ÖòĤZü×nòƒ›á7Xyìk•‘>ġkG×guµMŭ7;SŻ‚ĵ–Hœ Bê†NžOĊYô߁Iü~U³N€;Ú$}Ftœvħ;˜ϋ!—ÜnĤİ|LpuN§`çtÀW2)yXŜ]uòùŻ}ßxԊ‹Ħ°à³’ÀôšĥO}jżJžïÑ$$飴 Ĝ†)]Ĵ/=…%[cÚGÚ%úZʖżp2ŠÙ= ŝŠgEeÖ&v›vàÀ2œçÏFĤÁLÄín6‘7˙ѲX@ÖEœ†²ĴM71zšœ5‡O ‘yı £)~Œş…\²—µùqmµäO‚EÛġ—Ë…ÊöJ§¤ì×òdïúIÑíûєiiĤËKä „ıNq“^·şġk ²şrċ:×ó𝟠–y20‰^µsf1rÑ1‡Rĝ!_pĊGUċŠŝúİÂRŬĵŞBÔû½ğÏ0öŠĵ+=ѽ!ċ<ŭ<6CD´ =ÉEB°{‹à!ž•TĜ#l´Ô,]79^Äß½´Ii'·ıfXëùR(µ_ÜLjÛÀLçKnm{Ó°9ˆ´°@ïğ9ŽÇÊGžIWë€Zµtu[ğ2Ŭ҉Ù܏²ÈàSşf’†¨QŬĠJœóʽŠŬNx–0úôR†Í]Ŝ”ĵÔ°ñ¨‚ùƒ\O Ë6’^ä1KżÀ <é6³Ó$ ĝX“ÌİĈшa¸î[Z -Ŭ{ŝ´'>áŞ>*ĝŝ,¨ğ›”‚-Żáë+Â˙ƒĴ<(‰rúcħ2Żí]ž¤ ġµÒÇ-]0' ‰TcÁK½ ğ“*oç‹ûQCÜ]Xp ˘ ÑĝŒmĞê[²5ï>ggŠğ·½QÄÇ2—c§ñϵ3äcšgĤÓĝ4a§ĥ€†q%ï½½ŸsşeîĈ²Ì˙ˆ—™9£<áñ…U6ԔÒ}Áˆš}˜³”Ñ\m ’tî}L4k˜KgCŜVââ>ÇöŝÚş=äĜş%ÍÓ÷¤ò,´ì`çôÖÄžİ†İÈÑż%KÛŽß Ğİ=şĠU÷ŞvĤ‘5C˜ïჽ+4p8EHĵ\i„n_›ò\xĉĤmû‚{"ağ’á[ôµÛXˋ?5ĝìÀí^ö“µä×ÏEô …N7]9"şNŝEEbÔ'lF*ïèÓ§ċûÌ@{ùĈġ2³úMbħôç=ÉŞ;Q3m3œ&M’ô‹€Zġ(6ûaŠÓúÊo™ìÁœ”Ğcbˆfğ•o‘28Ĝ!Ŝ}–ĥP/{Ü;¨÷Éhö×b×üvĜ7çvxŸh‚v ŝâiÊ0|w´"ˆMPk£ÔGÄüy”},i&Ê҅˜ŬŭaĊ#A?…$ڂšıŻÔşÁI%ÖoJŞÁäÑ´yâû”•éx˘ÛwI“`kĠîû£NŬ([ -mÇNùZ˜‡Ò!H;nŸeo r‡şrÓBĜĈĵX R ˜zužšjċlA"-BÊl İkg´3 t:>ÄĈ_0Û/|Öħó; ŒÈ:¨™ÇxŬ:ß˙÷µ@4ĥ|7â;Ġ~ÓHËÒ\wïÖÈwqۉaœn„1Ĥ+–‘`ö‘”U$Ş] yŬ6÷_ĴÀ?˘Y·–€üïyê“çX:=Ġp¨ĝW½ä8Ĥŝ^ʤK‡Ŭ~<ƒÎG^½&ŭÇ,A˜İÚ ,xûy¨Î"û˙G í4íVr¤%(Qç5Ï4f#IUf÷JJÓʑ î}\ñ@e,"$2x˙íhîôxEiŞ[›Y˘+Ŝ:ÎĤ -ĝ•;F8IwÊ4ƒ&˘CRĊ”Ù¤ŠĠ`ȏĊX†‹Ĵlâêë>Ş!{¨|ŝ/‡'ğŠÙğ‘Öà“ĈiÉiMŝ‚ŸSĜMc'ƒ´ĵ’ÇŸ- î[lÂt²6و]^Q‚ı£ŠF#L=ú~ğ -endstream -endobj -684 0 obj -<< -/Length1 1392 -/Length2 6243 -/Length3 0 -/Length 7635 ->> -stream -%!PS-AdobeFont-1.0: CMR6 003.002 -%%Title: CMR6 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMR6. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMR6 known{/CMR6 findfont dup/UniqueID known{dup -/UniqueID get 5000789 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /VROLGE+CMR6 def -/FontBBox {-20 -250 1193 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR6.) readonly def -/FullName (CMR6) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 49 /one put -dup 43 /plus put -dup 51 /three put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ=Ó%ċW˜)-{Ùr½uú•)Żœ‚ßröA•ÉÂÜE(ġ@Úŭ{ëı´‡ş“Qğû|ü_‘RÑċğ -ĜĈϤëA³Ċ -T@ĉ|ŭq|VkıżJ% qu8P˘ĝwÄGx³ĊŞÛ̆ÖċQĉŻ6K üŞÒ-UŒ\§Ô%ĦbĠ"t-*xÔġöÓŸÏ˙J‘+ -}ì3{Zà2ŽùĠzŬĴT2sÀ$ZġÌÑ&{Bè–J×{¨ßr̗Ġ½Íám”1lè(zċNRĝréò^&%Ï:(/I‹ŒßşH’m§!’4ÜJßxIò7ıbs,O’i˙Ol7²ĴÓĤ!ĉbî^ëßĉÑ´Î-êE>3§t;GŒ<ċ;lñ: ĝOS•˘áS*O?9ĵ ÏßÙáà—ô°ŸĝŒÑ-ŝ‡ûİĝw yg8LsYtÖ¸E” qH°p0¤>ˇÇċ -è,qàêۊı”q°† ĴmZD]7ÊşıOk-G_Ŭ\âSË°yGœġLžôŭ”š†N8úg›ì2Q}:é¤ĉ|úC/˙  Ÿ´ÌûÔɑl ѓčCŬ2`À€ŽLu3ÍŬàğDÎ*ĠCÇİ5½Ñ™ċsÔÑLƒUkmHĞ FqÛTfÊZ$èô­Ò|™Üĉ¸2ÌxlÚO‡u×x’gGè/|:ì&Nn$JÉEQĉïyüçŜƒ4˙óÔ>İpy'ä3˜ƒ˙jiŬ.ÛüÓÇĤXË9~ŠÎÍb0 uĉb;FŞ8(PFY|×DS%’y=ŝ†gn!QZ–‡˜ž°ŞOi¨ˆ†öĉ­¨H,†ça7`ġ–ĉ_Z<ñgñZżŭëÍʹޘeߟŸĠŸ‚q•ˆ/~j'[E1Ŭ Éwg,ÈK­€”ôomÖ>M8´;°rİ ŠCXĥ‡VkgĜ-/„ĴôêR@ÒÙ|lñbC/ĵÏz‚°KĦ_Şi,'Ö1ÏQñ™7^“3şEıĝÓŞïì‹9$ÀZòĠdy]ltŽr =ŸššÊ>ŒK€%ÌÒa1½\î(t.EzW(ˆ#‚MN̑ĥ6Ú~*×E;Öż˙CĈ˘Ża^1÷y5§Ŭż'hıyf -ħsÚ.8Ï°5ÀciG$5Ëg0ïKTlŝpü×@Ù>]˙fâÙWÒç„Û7QGVë”àĴn¤~˟=]éZ`Œ˘î“†*ĉ~7 è"ž ÚŒcĉĜ÷w0¸Ħ§ŠŭU{Yn.Ê_xIżP ­§YĤQ]`µ‘İĈMN!“ġÁáXwé:ĉ³R;†t­šĜœ“+]g‘°êZÔɅŝ ŭoswŞ“èQU)œ·8‹ÈaŠâA^aÇv>xĈÄËH‚ĵ_nÊÙ~™‹}ï˙Ü‹StšÊGŠ7Ĵ ÒKĵ7ˆ2f­CžĜi0Gm1u?‚ƒĠ4‰&–]ëçژŻdÍ˙F€Üpmê¸UŻh¸ Ó²ŸÁ$w\ŻJd8+ÀS E=§ÀX‰˙n·ËV‘%ÓÛ?ÒŻÖŸGÊ[4ƒŒDÏ)Ûíҏ‘}êƒ<µ)ì%p˙D%qrkÑoò„X(&‘ÇĥcŠ<^ÔşOƒ;FI¤Ħ·RC™çKú-fġjĵġî—ÜzÎğ·ĦÑÜ œëìühŒs+à*“U-œŻß\Äŭ(Á=D[d)@üŜ%t€ġ–)#¨Ù’‰MٗA=ù5N$¨1Q—k­hĞĉÄ|Ż½)ZÈcïÜ×ĵ‹=}•Ï6À^Ìw¤'euÔfHŻ p!x.ôÀ"s!ùÖS¨pĜ²vNȗy8•~ö%šž‡…_ímÔD8Ǹˆré°É³h‹wWu_ÁĠ6Â[ĥ’=ĥ -ŽVÇ]Yи2?%ĵ -­şĊê)Š/KR”ı|e=îÛÍŞĦ‰b_„˙ĥ0Sè„Ê–5şŠ…31ĜżmÉxĉ>– Ġ˜´Oú°ÀX![‚ÙĜ Ž`ùÉvfò|}áRú 4"‹~)uív ßE$UĞ™\‹µW;댞ÒK0­ 6ğ$Ö§ĉ‹­Pk?ĊÍyğy˙ˆ4…ş<öŬŜ˒q=CG$ –¸@dÙÁħ·~óÉA1Q8‚A-|߉b1`z­ħj ´–ÛĤüZ\˘.Çrïİ  ~äÇsż™"µbê]Ry™™™&rÈD0hLšSĠ)êĴz6Mĉ=â—ŝ"'ıOOè–ŝĈQ—k {2+•$Óô}°<×àğ’òÊW`ö²ùÔ É1²='œ,ÖŬhİòƒkĈÙëCfEœ5úF]Š‹y–nh|Ìd/(ż~&ŝçÀP°B9µC˙x€Œ9 -ùŜê %á÷,9ŸÏOKìÓíL˜ÜvH,Œ>Ҏ…ôŒ,6´”"+DĈ¸órhL<]A+6ĉJÂJµ9çċÛżî2÷jQ}b…FĦ[êóİzó'p &S½*U´$³Ĝ–£Ž‚a`RÑI=Ġždív”_Ĝ\ÛWİ÷Bàşġħ_½5ĥ§Ċn[™ñß&òUêŭĥXi­â‘NğŻcuÎżrvI—]VI¨ß†\Sîî"IŽĉvŸs ’qYpœÏP]˙5|˙|rOډ€ccéB0óKV|× ë†4÷Ŝ0CajpâĤësÉ8AĈèğ—çÍêµ˙ĦY4-ìÓëL´ċç ³ÍŻÄi ïŬîFVħ{%ĈxE_ ­œ*`LOUìó -ǔKż­GÊÉs|ŞmJ£Â%5ŬŻ’ÏïĤdAv<jà‚²-Wží:ß,=BYêĴŝmĦŞà˜ìe"r5t­˘€ÉíúĊ§²ì>,àwÙxI_ ġe³s‰·áÌÙx–Rt˘´Qe‰ĵh;˙ -[œGf”Ò„(`Ħ*ùñ/ĵI²{w4i˜Oa"û˙čï\Ÿàı%{-ĝ+Ħú`Ğ8Ŭá@;dZĦñÈŜxŸóW'àgA‘à$vÀq%“=@Ğ Py_w§é§€{ŠĴıpÁ6œßÑìŝL˘M–ŭmM#ŭ -R -…éY›´ĵœĞÑ$ ì­€ï†ôĈ|Ĥ6ı™|ċ™ÈGI—·`Äfkqa}@t¸Z&'‘Â=ä3„ÔbI§gUž5ƒe€­ÈĈŭİA½Żä },ü§ò)ç:iĈchZ:lżéŻÒ‚ 2W#¨3Ĵ0çërM$­a ˙ Imv›òúOê"¨, -ƒ:( %CëşŜïİMi·@ïÍ\ġ[ħô -Üġ‰t•Òà=èUMñn[B_È2–_@nu˜?LÒ,DWUÌŝŒÔx¸=u}•#mĥ•6ÓxA x^QZû+% ë‰*{ϊĠ·r RH [*Yy—ş0ċiÇ­0abŭP7İÉy։pvk§TÚÌ×TR+%Ċ7îü²Ü!‰ħÚfĝ´F gGŜàPÀ‹2?S%|ĥb%°ŝŭ—˘ìN&tĈ:>EOÊYJJïJ˙¤’ZŽ“Şé˙BH-!~yĵÒpĠ̊ÒĴ „ˆàÖŻdí z/ê¤úß3¤àj‘¤*À(JP›Ċ$'Ż¤­AäTĝĥ·ËŞx"ĥĊôb˜4~4]XĠşĉ’÷˜99T<½ÔŸÊ›Kꣅȟ9[I{˜Pú>ƒƒ5Ruc&(îŞöÓ0ÜŞv²ñ Ÿ;{é3ŭx}ğ_%.bŸeW îŞ˘2eSxìD‚8£Ğoì™èá{ÛğÀé·èœ}żwn,WP z›–Œœ;Ö+Rˆt…VÍXñ=Í \ÒuĤşB•ĊíóU(CvĈw?H× jt˙~DŸ¤xtíúӃşúŠEP’[ÈxĞÓ/²„Ħ2·‚)Ñ+à´·™ŸÑÊħÉx…Ì4·÷ݐ6IHg°oEÖ'‡˘Ĝn²bĉÄ\l­ÌL’hcëüb/ŞK}kêVšŝŜD u 6#+Ûé9oĴîÂÍi³(gy5lS‹ñ‡¸û{Ç Z½ÎQ‰ Œ·0µdġp‹Wg-LbŸp÷ûy\Ûz(gR§6àeïÇÎÀĴKµŝGĤ=9U2Ŭ§ĉჳıC°ŭĤóĠH âÁopŽr'ùÚFSëÉ+ U½ÉËÜ$ĝĥÇÎş ıh;Ù IĦ~Î–¤‚:oDĝÈU½­EĞùF¸yo;0Úŝ€?ŜÛÒÛmP>"Ë#ǕĈú° ŽT5J!*ĝċùS@§Mĉ7#8&Öì-Ĥ§ù ynúÄ9›Ŝôù“Ò5·°G„ħTŜĠÔɄVô -÷Ğ—í+WħS[Oêm3‘Pmd‰é,Ğ+”S€Áŭ§ñTìĦ†kĝyġR<$ ÍäŬ€ á2˙a&Òö¸ŸĜ=CÔ öï°áNÎ 97ĥ#޲â~ÊĈM‹ġġœÜTħÀ?´Bzò×RÑÍı ˘Q²zĞİ×]s‹ŞTëôÓP@P„™ …G-ÇŜ R9Mż€ċz­ċó€ċ)3šîMĵöH­žxÂ˙V'’.(Ós°ú;àË|ß_OTŸĠžXëÒ9`G„ ü$PWÙ¤eYïƒñÛÑ=fE%Ô¤OŽpdDŬmôzÈİÖÄ]áı†²µÖzÀ‡K”+xIVk -wħ:ôôMş mÑ×4ËüŞYV#Ħù⺸šıMü˘]Ĥĝ*Ç˘×£9ˆtù5#rmÚâ'E×eo$Κ˘§•ŬÒ+z8n/=?njѳžÑ(­×ÄË(,šĤO2w é<6ĦFnc 1!ċAızVRúÄI™ğêĜ²+TkÀo9˜Û:ßÉW\ùˆv.y€A5”ĉĈÂgòf]?j6)˙Ĉx›ŞyÛ!N5˘‹g,Ó:2‹šˆîFĵ%çuĠE`îíÓBèxw÷(ŬŻÉ†š&´^šó͂‚‹NĤġVÏèħ۞¤ÏAÈB k+&Â@É'Ïј†sƒ†ş†_;ş™Ĵ·Šqġ(_İŭ¸:íĵ.Ù:)î‚[Ñ ?bŝtĊ.NĤ|ÀÔPÙmĈ}ÂÀ/ˆuŻà#7A"UĞ)ĥ„T\×ZxëH ro}o2ÛXŸÑÄËa/ùvñ½D3kU•ô[ÀÒ×+,ëвÖ,ËO í4%߇$H'üĊħC/´ŝĥ‹‘ Œü˘ÁĠ|,˘v=ıï}醜CˆŞœœy`6YP*¸ĉô“rŜÀ8%{o4c”1ĉşOSñBĥ!dA6ë­]W%gÀcċT òœŜŸĥİd˙>Mˆ2Áı^NjîÁ[NĠ@• *Zµöĉ;#hhÜK7ç#2;ŻCŬĥ˘‚ûħ2 wCŻŽ‘"ÓĈ[´yDĞJÈ,#Íb‰Z„ˆV*7 xߘKä;ž‹Ž”yËv€•96I)I" $!‘ÄĠ/¨ùµ8ġo’(P˘yRêÁ´ƒUS£`<ù!{ŠGĤÁeĵ+‚ƒĉ(C‚³uA°ÂqlèTcu[– ĝ•jÖ=EšñĠŸ2ĝC4%Ëó´Ĵ°2+drQîşÒ˘/;Á‘ Ú‘ù}C`µ‘İ@|˙&c„Ċżï1ûIÈO}ş5áî& ‚!v,+MŜñ1êçÀpp‰_ŻŽì­0iP€ŝ͕•ïŒ‚ĵĴñ‡¸gZ1ˆ:€…~ĉi(’lŒŠ=kqaŻĴ.À1äœĜŜ':;)ÖŜ]4,ë6uxcçLÙAħaƒÙ^!İôL²‰’" už›â -ɜ~=ÏC3„[ .18ŭÜjIùúTOĜQ -Qƒ˙ž”yÜ(E*Àû>żĴ'߇߃5ˆ h „V€—Ŭ`,èġvr3TŽTÓ{ß˙½3OÛŭï_ĥŽ<ë΄ÓDì+ §˙ŜhŜ‰²3ʂ<áċi.êwH:°ÓÎ$ĵ2D(·ŭĤ=Ğ­îĞÓKoĴk$È§ż*;‰N͓ #WF &İ÷#Òû³è4}˘zrZ?ÉÉ#ó#cñġ ñϛÈ ċaċĉ’Œp÷~‹mšôz‘µìK(²Eeô%†fÙSċwdùv|—J İe‡“üOoC€ïü,0Qti$Œ}ւ"|"gÄO›I -/ħ‡<™²EPŞ*×ß&ĉzhĉ£·šDĵJˆŬ.öʃcDÇZñâ -„ı˙ZiÎêħ÷ߓĊhšû [<TĈe²| „ڍT)Î"Aê½Ĝá1W*Gà|t Ví\]Ÿ£•?ğMàaˆġĝuċÌOu…9‰Ú äééüĞòŝè8ÑêL~'jÛöÛ˘îŝĈ›>¤pSŭV#“Áu:>½f`Ï"_Bon”!wN— Ïy/C5£Ïrb?ڏ7ûÎ@£?+…V5‹ĠÏëĜ­Ħ -BŒ…6şÊöíoYñqÄ^­5”Zp ·r,ÜB’^â:NĊJÀ´˜˙0ó7Aϊߧr‘Ġ§}E4 ÉzA­èŜWrÌä%`ÖHÙpZş÷p=É{Ÿo.À{ç#'Şġ³uMèŽTħàò•Ċ[‚góI{dLAN’Ĉ }beì†/F? A¸]buÖvÉÁĞ¤qŬ“[3<Ï4MBT¤pa·àrN½[­0…ßüO€4\Û¤èŻ†BoĈ¸ÌšFĴ ¨ŭÛ>’Ë'ĊdnxĵN—#i k_AŜ›ĥĠ³ƒ°˘s#;ĵÚwÈö͑2ÖŠÀ¨‚’²§]š&o$c稢`d‡y”jJ€Ŭ8XĠsî™@ĉÛĠëS>c9ìT”1ĊŠ(ÍÊvn6ÛÏÀM×bĵż3ċ‡‚–~ÔtĜ’ĉ{à -‘ÂÌġ·!Îéğ#˜&xó1ê<âĤĥY€ÊèfL&ŻÉ\ĉŽT˘y­ÀÒĈ)dÄ5—hĵ× ù("1{ˆĥâċÔ -Ĵ &]Iİqñ%#ÎĥÀƒv"ÇPaĦ&ÜÖ"ÄB]DbüÛü˘­U%d|šÉMp,ûɚcêĵ‚} -iĞÜsŞù‡ۂ÷ k’}_ӊSĠgŸmĝSĤÓM F7ЃşÂŠrjh×cÙ%0xï[Yü$WCOċ¨ŜÑ?š#~‰Œ—3½€AXħEŽ€¸îë·ĊšGâdħaÍZìÍjë†LEOß1¤=ÔĴ˘lG#)ŭ%mÊÓĵ/žJ9pҗ`eL‰ñïżÂ…Ô)Ȩ@“y7ŬèçLêŞK|ĜÑäa+$ç?½c|wÔQ`x[˙ÍÎç(~‰ÁB ~@ %3Ÿüšü(şöÀżë­t§$'ħPzœğ’ëkí+÷hDaŽ?Ÿ"€Gî oZS89sÈíeVZŜ,6n‡m*3]MJÌFÛwxLĵİÒÌ,ċè!™ŽúÔ×­âóDÉ߁Rqè™XzàdQB}ĵÁU£'­œ¸ĉjkħËçyƒ›ÜféúŠz<8Phu[ -endstream -endobj -686 0 obj -<< -/Length1 1408 -/Length2 6296 -/Length3 0 -/Length 7704 ->> -stream -%!PS-AdobeFont-1.0: CMR8 003.002 -%%Title: CMR8 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMR8. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMR8 known{/CMR8 findfont dup/UniqueID known{dup -/UniqueID get 5000791 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /ABQBBP+CMR8 def -/FontBBox {-36 -250 1070 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR8.) readonly def -/FullName (CMR8) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 61 /equal put -dup 49 /one put -dup 43 /plus put -dup 50 /two put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ=Ó%ċW˜)-{Ùr½uú•)Żœ‚ßröA•ÉÂÜE(ġ@Úŭ{ëı´‡ş“Qğû|ü_‘RÑċğ -ĜĈϤëA³Ċ -T@ĉ|ŭq|VkıżJ% qu8P˘ĝwÄGx³ĊŞÛ̆ÖċQĉŻ6K üŞÒ-UŒ\§Ô%ĦbĠ"t-*xÔġöÓŸÏ˙J‘+ -}ì3{Zà2ŽùĠzŬĴT2sÀ$ZġÌÑ&{Bè–J×{¨ßr̗Ġ½Íám”1lè(zċNRĝréò^&%Ï:(/I‹ŒßşH’m§!’4ÜJßxIò7ıbs,O’i˙Ol7²_Äógѳ˜½s6;ĉ•ÂP—€—´¸­}tx´,ÀIvJŠ3ÄYžìÊĞ]ò -û=Üí~Şĥ™çHârl;H :Ì(x‘P/PÉû”˙L™òÇ͍SĝI'sbŜğ£×~—|Pżp•NcO¸­AͧġġħB°VĈ")Th‘ĤÏ^Cx–(Ry•,Às)+Hߋ;mÂ*?ç>Hœ½"‡Ì%Nğ;8'bóÚGZ•À“bÇdà ^iì$­¸şôiaeö”s ·ÄŜáƒF)l:}˙Ż3äX -‘ Mvĝ¨%GN×Ċ,ÒĤ½/~`‰÷"›ìJO238ڐi Œ-]IG‚cä½f7äԀĤÌò2×Í‘Ú£}T ŝçĈ İ@ó &xß³8h -„Ù{ga´5ßL€ÇĠw'~=OıôLcgĝPâħêv‘9ħF˛zú%‚Şĝ„e|ŭˆO—/Ób‡ĜûêêV ЁK â’^ı¸Ä†8ԇğ<)M­À…Œ†<mߍ¨;Ì疑’­}Od1]ZSÎçmPƒfÍ4°Ôş)˜}M‰›PĤÉèg2²l1gÌâFġÎéšïŜ˘p —V·}òŒ{ĥ§<[5iJOYŞ>ÍĠ5XŠZ€$ìöŜ15’ï7à~ıèZžİڕÏíĤ¤-U…DÁÑm?3δìİ„'ìùˆ£ıâ¨VÏ+RÙGŭpžyDHÏvx{p€cL˘÷1wĵèÂŬÒĉ ¸FéMNg(SŠâ ‡?Ô)ìş?;ĵ@MÌ£íBNßĴGXġDiêo n PÙSĵÂSXÛD[këöŒgÇ[îtœÁóħU^?‘ÊÉÑf2Š¸žËñ7÷ö‰#€xíUè½mşŽ½ġ`jcÉk´$u:¸RŞمŠiEçUşğĠĦΟ<ìĵâĥĠ.^Y&ħ˜Û†oŜ9s>¤ ùËğ‘şċ -Ż8jzIÓÛéC—%oğÓüЎšOn8òRg#–;Dĵ–Ëž2‘(J+ƒËó|ÙÑÁGœ“§èĠíœëàk9ڲփóey˘ŭ¨/È9+,-b3wı9Wĝ7}×êÛ íëzĠá£ı¸ŝÍÓİUyŭTpúÀt×û¸Ž‰ñ_ü•24¨ça6Òs¨’‡ç!ÔO› #Ìi׌$Ŝ³\àAópr$w5”¨\Ëplˆ ˆYn1u¤pd[îËílkÁ!lRìävò€‹4Œ_x…ĵè_$V[ïû“HZŭž÷KŻûr\wġĦĵ’u%î_²šF ^ ş=£ä‘è•ÔÈ†C†f½˜%-×Û·ż³R>ĵâŠQÎt@ôËÇÄ<ı‡Cr´üàîz£ĉä“Dх˜(öe}Żê:EÏ?E€…ġg =óÁÚèbö0"…°qTO]L\€ -A̛ĝÑĴÒÄM͓ġMŽ•…oĞŸxLş‹‰Ò~uÉ]ƒğ_ÑÑÚç 9.ÉŞ@Ó·š‹Ç/oĝĈžI$[˘ÜY,H†ŠĊIÚ>2šÙ )ë üşİż´Ċ~z‹xŒ6żĤm“…XöFVŠ”öCEOxJ†ú -jFmĤ„h)XɽĦĠ‡‹8ĥƒÇ‹Úé–{u ‹…c£*ċ;¨Ëe?ÚbċßÇlVĴŝ|÷Î@¤ÄÑ-˘jëAfâ9µVübôĦ³ 8TûÛd²j4!éVĵş˜äe²ġrŠZvÔZ,eVĤ҆?0 -ZŬíWĊG¤ùv˙Ûl´~éîĈو°[5rL‡}qTvmjCÖċĞbMÄ:gžáíÁ‡ö ÄVOëiÎĉç“ÚŞ­#|Ñym÷-4Í-,Ëñœ f…FöxWú½Ğ½µps¸X!6q-„M'îŭĦĊÚß"1ÇĈ,óşsxɵIS£—›ÄœĝV˙"^íj7ċ3œEÊvV™™(˘T^îKö-˘k?ŒñÉïšÓ’.á;d{)ĠápBh+4ĴèuU *²Ğèá:úm“;<%s‚ħ!- -âÉ8X›Í+p&4öj™äĥöO^ĵ1ħTpvD…^—ÄÄŒšÛ ôx$˜µí+flôäx’‘Ħĉ7ÁŻ=â1S6>rúM‡z 4àß0]˙ —£ÍX™…CĤŜËÜêÁ 2Ĉş_s˙5uDĴ^ú'?ß ŭjeqĝèÁúġ§ °ĵ(½ùӓÙQEuf%xÂè(m"B (brqYqu]ÎĞHgÇÙĤp7 “˘­:ħNÙQAdĵí†ĠĠY•ñïQk(|Â_÷S£/ÈË÷8a“VùÈ%'oÚv"U2Ž!Ĵì§kh5Q?óĦŞ)ĉŠ•g&JĦ$ÔË,àÇÛjS]&Ê1ìFqÌ*Èê*ÛÉXš*ŽiŞl‡òSfN”—{qZ Ż'@Çàdĝnl¸{ŭ"KÄDô˘˙Ċš Ö4tÛTY9š˙X}4heQ lÁ_7@”ZUÄİ/Acş*İAÁ\4;NÓ{´4˙íĦü5ġĴäÀLŻÁÙ=!V5. }rKáûq‚äS™*'Rú=ž€:ÉtF_}OV-î€ÙŭšF‘=ñâŽ;*ZŸğ„ŜÁ ŠGoŒe÷ -EŽ×D,A$ì Ïó˜Ôùêí…CĤĊ⚃I€9Ü: ŻFω·/%`,mгižìĉSàâs1—M>lóÍŬĉ£úZâĠŸì_tJĞqǙÁJôžĦ”kuÈBy²#+Ş°İ1HìLaëbÊLŽ ”ċ‰™šñƒġċĈ Wb°])Q×jfnËphċt­™;Î\ÜŒö8:ê,{ˆ²²=ŭJEƒ2[WDş{DĊ7Üğ9Áö'J€Ŝž÷ċû#1ôÏ1j—:Ñn+ġG˘,×ĊÏ,•ċlsŝ3ĵŬ‚FI˙THàH…`’öšvœ•ëİċ=%Ó.aĉyK†‰­yMBùn!½Sukyv"5ħÛDz -Ö§Ü'4É÷ß΄Q| &Ö¨şÈÀÓ·şRc3k&ÓĵÙJ   4mÎ ó[ĜÀ[“Èh|Î]œ5äßÌ -9JĥȍıÈġĠÖÓ -0­ĠŸgòäÁ_ -wnáż{éĵQA·n§İıGg“IH–Œ]E ù°ó‘oĊV˙·ċ€ĵ4:(‡Ë\T¤Ys<ż³ ¸à–Nı?à -MŸÈ í é'°Ê_ĥ-šT&mC\vpáĝŞ5ĥŻ™_ÖI ˙.uANˏ4Ñt@üèuš˘ĉ`YßÔÈğÊA˙á€ón£ÄqáĴÀGÌï¤7Ï,Ĵm²E§ê¸69>•Óü¨7H†A—Ġ½eÑô­{ ?VÓËN£,pPöT“ŜlΟ fgž;Iŝ½ßÁ•?˘"™ÛBÓÖÓDy² LìM> -EŬ,Ċ4cĤÖÁ|é -}‘ˆċ=úç°ĥÍxbKî2üîĵŠû^ċî^W÷UAV7xQ~e#îEJÌf/5R2§ j›ŜÇ´Ôn@FԚI&d|ş•+.á;b^†ÉşN¨(S ÚkġšĉĜ<׊„ƒ Ĵ€şš ĴqÑ/·’Ŝ3?׏Ĉš~żÖ¤s°ÄS}Vœ7+’ûúóvÏ8ä‡ŬkáÜİñ!ÈżŸÊí}x =7Zò}ƒǜ´éž]c–Ĥë!Öj~ލ?}&bX¤˜¸q×iE‹3x‘mŭΏùûZ6ĠĤEô7˘³Cċ+:K‘ÔꉓħáùŬ~FdNgŞ1GÎşĉ%ö’Íׁ¨”µìÛÏŜäĊۃ1yâ³ŜċЈ́w½ClíĉŞĴħžÌq1FÁQf 1àĊğ‹•9\•ïê@Âĵ›çÚċ(Ċˆĥ^ŒšE³ŭ%¸ħ( fJz‰Ì^ ›´'•³²· R ´2͏†a„ĵǃ˘îYֆZ¸ĦôŭZƒÓÑg…d U9Ó/|ĦôÓVϽT_Ŭ&$_›Ĵ…=1™ûzÎG×GáxÇè /‰"²ĥĤŻF÷ġo¨³<,*‘ŻĜöÙ#×Yño×:ßa&jCŬÈŻĊuíġK½`Ş°ËuŽÚÑ /öœuúwaEtžĵ #l!€}‚óĞ áŭžıŒü…jĜ‡†œˆ§'*eRhċ-.h¨;hMoĈĜĴcŻÏöĊxú(iÀŠw ¸ùN̸uâ•Ĝ öTîġ=¨ş6^ V™˜ŝ¤$²Œ[’fäÎíÖì–ú@[sÖk÷4kJğ@/SOŞÏnYJ\"mÈċîz{1Ħ³”µŝœċ*ˆJüKîْ|(˘nwCÖ¸ È4É&j_½GĴŜ.ŻYŽ­üb[ıJĉ8§•7*"&!€ÎΝĴĝ&$ñ{GùîĤ?`l½ŸŞ)ƒŒ;&|v†MşĝÀž\öžSSE£Lokè.ŭˆÄÑNž&@`ÒSšŒ9ġe£Ëġ´–ñ°†ÈÑϋ—ĥ•cœ›Ŭi½ž Çn ôŠ½î"*ġŝ¨z(N(žÎûŞ™`îš(ğŞÒj–>CŠ—1*Cɚ¨ßIbtûr‡jc—Wq÷t€?[Ii5ûáŝ‡Œ6ßĞAښIJ‹'{-Al²$h;ïm#­Q¸5dd0u3+ŞÖCcŞġZÓыÔ|1żBÄ];ĉĥá  Tˆ°şÑ}‹Ŭĵêó{*ôŸĥ!O^É5é ;ĤÀ6ßĈÔÄIˑŒ™m-Ĉx@óÓÛʏsÒ[ż2ĵ‰ ŒNCÙb–˜+£iĉğ›˘+ɌĝĞÚnu}àŸŒŒîjlĵ””Dµ=É_ž}‰ÙıÜ*1Š3?â9İÉr5ÒŻ“ä\Êħ†ÈB˘˙‰ß24É"ïF#¤ŜKœ­L˙E*BémİÜw ˘Ŭc,É°h,Ÿ<#fğx%ŝ+ßL54 •yûéżR#Ž—óSs¸Ž…+ôjŞ%½ĈÈáÖû×èrqċŸJ°ż²‚°ÁäÊ÷ċ÷H엁`ÜS|•ġ'a!7[öÖZ&€.BvK9ƒ4{~ÍŻ'E”läöĤßŬùB9 6gŠnS&}íÌFL›5r1}Xèğ?;ÏHÇŻßPO*E4%_Ó́Qy‰. +1½ƒÊ}Ŝġ;ÍÎ\S˜lKE@ĴÊ%Ċ¤Q"ÔäŜóí%VDó݉Ĵ‹Žş›†Òĉıyí!ˆ;0§j`.İ·•ê(ù9²Üâüd !§”0;–/[ċó>#qoâdŽ]O>À=z-)Ğ˙ĞĥdĝĤgWl|n€LĠ² ñFEHқ\~l'˙҄’ËıáñïÎċuû6UİeĤĊüîGBn·ÂKM̉üOûŒšeôüŬž€Ó‘ëV?hoR5y„?Ŭ™v Ä¸Zŝ@'´î+Àmy˜5ä@:pžÒĊéqğU`yÍ -2àĦŝ~&@Í´Nt;ƒŒ ŝĝ=ΰ ÚġoëÁżY+ŞKĈۛŠFĊt…zÄ/·zRk€ù]z,žl93Â&´ ^Ž Ѝ˙yûÄ&¸Ĵ\ -Ħ‡´v+£vXêşëuC2úI ì~Ÿôgƒ™’s=ĝ"(pċQĵ§ö "RQÀé§Sq1x‰ÌĤ,çé1fɈ[G‚]x&͕kŸ˜ş5Eü¨' üzŽFm—ú™]­‰ÜmT{ςh™1ÄZŠ‘˜(ĈŻŭvœtOÀ:Ħk˘›4oÁP˙~Ô˘ ĞèħŸl;â‹÷Ŭ³ŬŝË1È`³ôyI@šŠŽ!f·L†ô§E6£×<ƒÎ+Ŭwœ š/_+XNó†VÎLéÀTI?YÈĉœuk6Ĉràg¨şa”‡ tq=ùçM=Żŝ?úuç4~h7ajG˙İw֖†¤Ë£Ġ™°ŭb8Ĝ|7éèê_•ÄAòǵ2s>@írĜkŽ&$nċÔ·n­Ùż`û‹ÏĵdKDNf… Żä60Ĉ€4#ğ&6“ġ³49ßÌÓŝġÍàXGOU˙SŻVƒ9ݞ'š&FŒ#UÏá@VŒô½ÁrùeN)Ŝt§šÊXŞÍÌôžż{báġĉn³ÓĈà”Ì·Û|áC'Obŭ^ÏJóp$Ş·ŭâ:ˆ2‹}os£ré†Éeŭ ċÄ3ꁈş&³™vì³ÄĤˆ -§ƒ5ÏŻıáĞ8¨,żFş÷t˜wҒî ħĥŻW½—?"̲eoɌ,ġüĉ›eài6™ ĊıpX àSxòĈîè^êçŞ<ħnšmŽÉ~‰í\Óz]ŠĤyâĜH}™·íŝœ}HĥüÔËá³+΃BĞOITñÜ•d‚ZU2hŒ¤+u~fĞĝĝğ HùkÔŻ.ŞĤ4í*UúW…ğ$kI7ğŒü”3˙+Ĥt~h˙I§û ‰ž-âóĠ^‚څ] U5>€Œĉ•ċ…“dorĥÈ _È) Œ˘á×ìç›ĤƒÚ{NÉĈvïΕVcäıÁĤ•HYUvçÜ}”—´¨N÷Éo•Óŝİ#Ż#FäiÔ^èí,*h -c’TvaŒ:X =~|1¤63”%1§ ù+ ûÁĴ°p ¨2‘Ŝ¤ ħÙXr:ْˆ›$F.Qá]EK(§Ú`àöò ˆĠé8 Àd––ù5<9=Í9ç HĊzÒWï²jraÏdŻ22JÜ­£[ZÏÁi8ğ]·üĥŸ1âbbÌM*üN,Ïx£…g Ó*™ ­è­[ƒ2ıŸ5]ñ˜h:fúŝ·¤Ĝ“,ÑċJĵ”íg{ŞŸúhá&ëZïp•ċzżÉç OPÁûl˘2£²*F5™ cĤJ•ùdoÀ²XݞŸ^$° ò‹n zNżgQ ˆÒ\d|ı”< ÎZGÇpĉ,iÁüû.˜Š:{ -A8d~é{6˗O²Ó.ˆM_ĜżŞ ĵ9†P×èà–ƒŒdĵµšQuÜbEʽ½JÍ -•*Χo İŜ‹ëG ‰½4YĈìÚúeċ¤:dmvBÎÚ\)/­¤Y Ğ“‡C¸q0QÓB÷Š> -stream -%!PS-AdobeFont-1.0: CMSY10 003.002 -%%Title: CMSY10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMSY10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMSY10 known{/CMSY10 findfont dup/UniqueID known{dup -/UniqueID get 5096651 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /NSLWFJ+CMSY10 def -/FontBBox {-29 -960 1116 775 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSY10.) readonly def -/FullName (CMSY10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 78 /N put -dup 106 /bar put -dup 107 /bardbl put -dup 102 /braceleft put -dup 103 /braceright put -dup 15 /bullet put -dup 50 /element put -dup 17 /equivalence put -dup 98 /floorleft put -dup 99 /floorright put -dup 21 /greaterequal put -dup 0 /minus put -dup 54 /negationslash put -dup 26 /propersubset put -dup 27 /propersuperset put -dup 112 /radical put -dup 91 /union put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÍßቐYĊˆ5t&× {hLšGÒqB`d­˗PĜ݆ÑÖ|*îĝÎx\ÁœŜ–HŸtEĊB-ĦÉùóÁgedogÏ7—‰ï‘Q`[['“WÖü…7Â3çĉ¤ŭsçZ9ë m Ĥö!–tAžë‹Y!$átÊY\Žr[˜uTIUÏŭ‹iŽ÷BĵŒùy[Ž™ÊŬŬȜĈĊ—3ò˘KŻ6­†zJ!žË’Ç‘œJ·s&B5öCİ•"m†&Ŝ`7ŜûÓ˘Ĉğ‘Ç3uµgNC O~Ìĥu³o5Ö=žÂŜò_ä›Tù/ ¸’‰h,°—$B%ŻdöʘïŻ3lŸ ³Û˙MÓo§¨÷YLÚĥŒ~ƒ3^ĉĝ`š‘12]•=l8Çà£B6PlpËfWÚü<• %PIN!jáuË#,.ġ£ĊiĞX“nôè¸Èĵʇo$îҁX½šëÄꑷI5öÔV*E6tħK×oż_)žÓRŸžPğG;Z@9Ĝ"V3ĦT×TLç˜N Y:…A€ÓkîİÚĴ6Ì =‚¸=•8€0~ÛDQìħ QÂù^br/2^KŸZh`§N'Jt4iĥëüèBYҁ7ÖŜŸBŝU_¨~\ŸfûŽġçôµïŸXA³ˆZl‰”żÒ_£Ì½ZĈŽ˜Àì½'•çxHµúöbÊG:Ç"„lĞĥ5şCŬĈ‰U[ĈaLĵô¸rÂÌfĥôù 1[÷;4äp^èµNïpûŞqBD 'Ĝ…93­M€&9{ ˆVD ġ8 aµ‚2Ön.hfĥ -äl?KÚ˘ë[$‹¸Š³úGpöŬşħ/JÇzc÷‚F8ûvP3Üà/XO6ÈyAożħî~ëç]WqD‚MıˆY4ߧ󆸢YĠÌ˘XPELŭ2_2ı ­ıİoH•{ -1xÒÉê'żĵu|ğo ĝöúWNRšE”òĤí™ıÓôû&”˜lF˙\LRh1FžbñĤ­Ï}+‡l Cĝ] ĤÛÂ(„vfĠoƒ+fÏœMëí³}÷l?c*Ŝˆ"î­^RĴĉ]Şm†äÔi§„KŞOÉҎ!I Œ²Ó²ûçġRŝ_tÓW;™żÌñ˜Çu@(#Şt*̧Ó U œ{|ġġQ}a3ċF¨l•ó8xĴ¤Òt’HWA¨Â­â;³!ÚVŜŝ CşÊƒVo³—Ûvşžì’?³”;”œħ=ËÜ>,„Ĉ§Ğ\"Ğùĥ•šÑRívRC•ĜœQDh -Ó@_,žÇ˜½kbflçAIĝP^޳™wٚĤdIÉHzk(c÷3ƒxûŠÉìSÊUPI³f{KÎİÍs… îÍYŻĵĦí/ìvÁÏ[ĦıûĜ¸L%OĦ@ë™Hƒ†“<ŜP'ŽJ£ËÛv‘Ġ,Ĉ$´"hU§M?ô³ë?á“p*ք7v×=ÛP1s}G“@¤N’5^3•‰Tċ³8fş† yQĤ‡ƒıO)„´ Ĵ07ÓĉÒ%… „G ¤ú’Rz£óófé{‡^DhÜô<ä˘{™™âB•ËêÖ}úÀĈٞs2f'CóyŜâ°_ÇÓ@]c8“ħn7q'ƒĉKˆü4kO=íŝĞ@ÖU ’¨Ül,ŬPoE‹Ŝĉkԙ*7q[Ú!ì÷ú·ÎĜèÓ\oğ‚^×$·&Œċóò]8l•ä·sı&„„Á/ââ^)š!TċĀa óáĴîٳၽS"Ħ;è•üu^S‰ -A5ò™6B=Û˘vnۙT­™ħÏĵ"…Ñ÷İ]/Í-}{ˆÑĈÉ@ŸÓ–+‹šiŭİcaÎpnÉÛ´ÓàĠ{Ş Nİ‚ïh%sùŞéž ı×áN¤‚äċĴVÚäÎǃżaİš]ôè?Ġ, íòbtĦl“˜h6‘˙OˆvÂ_§Ré̳9S ^Pí!Qp÷ Á÷ır6÷ĵÁ;³Z–èżĈävĜ9k yŽµH’yp;DÉ× “jí1œ:R„]ĴŬ›bzGC?"%‚|eŬw!èħ–Í6ËRPè$ĉ·ı:˙½Ô)ɽŽE#Ĝèd'Ĵċż-ıĥ È2/Ċ %ñŽ}‡ÙżŒĜÜ m˅ŻZüĢL8ÏÀôٍcËóµÏoÙĴŠ›LHÔşKÜôóĥž)˜ġqž+×ÛcYy•ĊÍ🛠-_M̌ŭ`-@³0Vŭ'ôœÏħöİtS¨É¤d?ŬħX(ƒYƒ…Ä÷kNWµYÀíFĜ<èB}³–ék³ÛßRí(ÚĠÏ^2Ĝ%0Aüŭìm„ğŒÎél|mƒoÓÈìİ4Qċş­„Ħy|“Úvï+~¤ŸĔEµcŽÔ²Ù’MĈë×/­öëtĜ…üHeš†ÙPC´évNîç"G6} Ĥì ]µ1ĦAÀŒ”+|ç°(äıVĠñߊG¨Ĵl7‚KfWzŜrŸ_í=ûG"{'Ş4ˆXM Ĥ(ż•ħ†ïz/ܳĥÙzÒLZ„|ı‰DĈ4-ùá0EípĥŠZSú¸óAÇá‡Ĵˆ³ÈáĜ¸Aä”ıÁ½tlħÎHŭĦ[TxsÎM˘…P‰*´ eeݏĤfĤwkڇĝH1)7¨i"ï‚$0Ĝŝ´ĞV?iż‰zóç8ĈĊ|ż>d˙jyTšµVmÇĉ—áq§ÌgCÊ‘ó‘ïĜÀşš9zğċTˆCŜ/Ät~ş‘Ċ˜†§o*í—9ŒĈrÏĠI‹ĦojŻUíKöxjĦş. ,Íĝ+b1°Ö²ñ I›lDLïQZ3÷ĥP-noôĵò½'$ŝF zg!ˆ*£oşÓjŠÔ-NûíÍÍ­oò8ĊKwQgŬpœ*1^‚.֊ˆÎÂëħ LV‰~ôÈ˙üĝm laÎ ]%ì."Ĥ`ğİ_Q·iäpÀöĊŽÊs’5y.XƒÒÍ)ñĉ˘TĦíĤöd1KŸ˘kĞĞ̊jŬĞ˘n0zŞGáq‰·ëaİWQé%z„ÓJ²ıĜX¤˘Â3tIy0Ä£.Ó#‰Ċ[“#¤ƒD#EԂ’ppŻF*ШġħŜ˜vïrOÓdÎn7n ¤Òf9ƒ*ŻìX:ġç>Çĵš:*ÍŜLf͍9’&a’j;+{ğ0‡ )ÚA’g°K*êXKÂÛVĥ'zÙZóÌAÚ) nîöÏ ³ĠTĵ”™ÛLÎßJëïòé^Di¨ŭ[Ĥ:s<Ü¸2Â!ñŜU‡ú|›–#ù5V„ëfÑUŠêqP}÷üÒ|=˙ŒšğGÂ5O|Pèsš9ñ§Ž}äċ“* -+gpA€,°,Á=|jĞ25Cɂ7›ġĠ ’ï–Żµ—Ĝ.é/F¨ÉıË0˘–tRœáşŠ."we hżP€ eäÖmpòîJ‡o´@°ħ▁˙_êAÒ3§âQéżBVô~$9E˘şj= -‹]? Ğè{wŻ_53÷FîgÓż³4B™èä›ìA¨Ğá½q²ÏËßÀŜÑ4µŠ‡¤î1PfÔ Ĵó,ÖSĊŸ6ôĵ r¤§[‘ŬÁv`à ĵµħûôżx÷G$˙Ÿ„êÏ.}ĦıΠ̔·¨ÜÏF͙”c°ħš‘‚=­Áf!*˽Ş./çwĉR8ş(@Ùًšz c¸½@N&Im—žŬ£>X!Èm•eñÊ@ÎlW˙"ÒVCHèĝ8ÔkĠ‘Ċ¨ÍÀj]´nó3X>JĦz?ÙDí€=Nĝ…½bn {qbY(>"Ù8*è‹ÉÍk¨y3ĝoâŠĝÜ €ó‰H Dwâıĝ]¤€ ½ëd {E’ʋwÙá™.$Váçhtœözk$kk$]4ëŻcf¸ĦúŻğCW–@òËóû3ö—plQŻ “Qĉ™‰bá¨/póµó T“qFÑ8_ŝĠA’żnëQÔ˙˘mKŽ{&z;<Ġżžmò[i7Ìϴ뜣ñ'*ŭqX€Tnòt<ĠŒkò/?İ2m)žËÏfôıŻí•áâ˘ĝy#(Ż`%Ú{ާ!ĵQœ/0&sßxıôfçBĞ+ĴĠr‹ïEßï[tÑÚgOKQ£$ú$²=à‚ל?êd@3c)]3Ş–êĠĠ%*M}H™éž;Cd£á˜Érp½°1jŭŸFżˆc…st•íG'÷âC\–şp)­)öŝœ_š˘)ħĠ(ıú›µ MMş -µ³„ qĈv&ĥŻÊ÷Cßċ3NĥLZs³wTPu{‘sĵşÏ°ĝPž‹+-­İĦU‹—ħFġUĝP"ğKΆ†+ĞĵÒYe7?0Ğ(•öidšL´;gk9Á(YI-Œl`ġî;`ĠçĉAH:´ áYHb1“µâğHÇ{¸wƒÇR^Yњ, - $F¨Ô–HDÙòV?pòyїıPŜ%F=ğ‚ÂÇĈB‡öÙöĦGKĜPh³~N´[¸IÊ_ꈀCTzŜÒf ç <Ӗ”Œü`4|mƒE1ÖJ'ĵŭáŬ$`}R ‚Ú\¨€âN2kf˘aóouJ73ê´òváêżôKÛW{œMÓŜ3?׏İMò]ù:W;v…˜Xâ;„B’ ‰§X.PáI;?Ÿ!T¤ˆ . ·sìöU]䃒=ÑXŠŝ ŭ’5´ÀŠ€r€Mt>y=Ż†*bC~^ ½tĊArħĦl'ĥĝĊĤ•üó\ô÷ĜŸÉLëƒĦP“&7ttöuGz;Kg4Úóэ;·u)"é³;úÜS•–Âv½ËüġC~³?żJƒğ/’F"6U.°0>çô+ÜKQӄ0"ÊÓĞÑ=ëñséŜíƒxoJ]áת!Ìwü6OŬ.}‹ž€tëË5˘VâËݳ+Ĵ·Ĵ­Àü7Š³Us‚šÖİĈyçċÊēTŸŒC5üGrgâUÄ5Ì$‡—Œ&|°µżŠ~•ŬGŞäĜ8ž—ê ĦŻMvċß(jt§ƒß ñÏ˘nñí›]Î]ĊQÌW…OĜ‘ˆm.Œ£Ž­ R[˜oNngô IFç:?Ât”ĜSUOÎcĈj2Cm[àĞO7>kWúk˘İ½ËXŻ'ƒ²îĤœ ™#ñ–Ñt'X•d9+E7ħNä™dŒ8{Ċ]òŒmı/‡ Ĉñžğ׎dv‹Y†Y–öŝwopôé™!™EÄP7F?oÏÄjP9âò­"›Ág“BŠŒÎĊÙPîŽô;B^QOİ“3ùż*B 3³ƒunğ$·ßIĈê˙Ÿ_Oeŝ`Ô -˜$Àß`‚}-9Q/ÄċM³e€ž?ĜÁÇÉêÒ°µìhä]ŠĤbż ŭéğêĞ_ê2<Ñĝ͖Ĉ+ìtÂŞ°[ϜħˆJĦŝİO@¤%M‘I‚Ŝé tĤµĜvƒ†Ġ\ı/bÑòMVFÊ05˙Î+kIċ2W9>f–}İ· ĝÄĥô3t‡ĥĞ˙şĦjކĤ|"§´ĉôîÖ -ŸÇÉ[ÓLŠhŸŽY³)Ĝo57kßŝ“#%H’\,ĴxÎ|ôsŻsxíHžÍ†|ĥ;`Ċ vû%ĝÚŻT[ícÖ]ï‚eŠ"G—UjßĞ„yŠtvxĠ:udQ‘uZy_²Td"“Ş£b+çÁO†]ĜlŻxà'6wò6X²CżDKOÁ‡f›(g@w]fĤV™ËÂ[ê~ëŒ1Fùé^A3vĴ ÇâO›vÒŻĥ2v -zúċT¸ŜúË0ÙŬb#ö›[›zyϒĠ$e1ĴÛkĠ5—dRAì`(Ċ…@{=yW>żˆä>ú‘Żçy@ĉĊ˙ıUáú;”œħ=H;Çc{–Û3û0´ĵ£^Ġ”)Ġ™-{·Oı°OÖú2R¨Â´xÈèëˆQĊôwBg‘âĵŭSŭğž›"תl›böz;ıħ˜IyĠ\E×ÁËê‰pr¨kM ·@@Âe&À 3•˜lʉtS÷ĉÄ%í)è/pRÇĝŜÙÀŞ"2µu -˜Ee’5ĝ+ÄÙ°s§Zò'ħı§ġ˜àçbˆQ²ô°SlŸjĊö zvŜ€â~%.Kz\NĦŠ„çü÷Eê,eV2Ò=Mo)-JcÇVà¤:ÒUÙ2Ѹ>É1ˆ×ȓ"żQWş ƒOŭġё4*Ozûş.c¸ójc”ĞY&üßÜĜĜϏìê=ë7”Y™´öĝÈê,A5nÊIßFŠ•/œ?ü̊™á ]as.´N/ú ç,Mceû•wW³˘0Ò#¸]ÊÙŞĠü3wœ]ŠœŽ2“ĞÀ‘Öf˨ĝĊn'ä_ĵ MuH½ -OëM‹lC7Ŝh ?p|`e÷ġ‘š(“şÓ›·|*è{dgî²HĊPNDYLèQĞ´Ÿ›íŠô‡œê£sRÑd=İÁ҅ñ^\#ZHdŽ¤àġÑ; -ĥDŻĊ+Z†”ÊQbË7QÑÚÁħNı̧ŬP#?8 İĠ“F,ùÒ(ĵ÷韓Àv>Ô%˘Uú§ô9ÍĞÙĠN¤ŜDÔÄâÁ˙OžQkç‰O´L€?™ż{™(-ŬaÇ£úüUs§êљN·#·^&÷ԆŸ[üMJ˘B,ħ ÂVËÌásP÷eQ­OğħÇBĈ,s“%v6ù2ċ3}.D|`,;(`İtQÉ)l!TÀr+ìuì=Ù’[ŽÛÍéÏÒĵ4ß`hÇ-?àß2òD#e+%-ıt‘U>kx²ß£**ċóßĜ‚ĈÌXšŭ?Ç`ŞîÑ]!&dè)Bgzó·á‹ùúìFmÊwĵGV‚M\nŸIç{Œŭ`Ŭġ"S$OÙ05AğGXVېNêI]Şù9ì:ê$öƒjï1Cúa낛“¸hËı…. öĞ>Žù_\¨‚62˙ ·ôuŝ–°OóĉöT,OÉ.“î' ˆ÷ŝ9ĵ,ŭíñ½j(G6ÓQ3ñtgUKĈoçİ&nqPS{A Ĥı*ĴŝÄúEĴÑtI}ÚĝXH߅½ĝJsŒa_Ûk#ìò^Ż²s½³KÑŸ -êÍ|VÉTمí£eĠjŝj'ìß8Y°¤f/r*ÂÑJjáû‰Êœn ñz}jœ˘×+p8ô(,ŸĠùr,êeż÷Âém1„4˘Ëôèá&Ż¤„{ˆ„ıìÎŭ}Ž´>2ë^šfŸÈ}'Ü"½²eĜ½BCŭnF F,9¤p_kï²\njìQôp6è6;3“"NŝQ]ı[Q]Ŭk^Ğê0]¤–[šŭ:M~Hw¨q%ŝ Ğşƒh_˜ŒğgqzšˆVBDĦŠË¤ë`µ–êà!9 û‹šıúı|÷#KSċĈ [)"YÄYĈ°vOËÏ=3‡‹ĥÛ²OÌ{´`Sêħy^Ê'@ƒ#wuŻ{žÊrk3îy)1Îĉ·ğĊÏÏjż\§f„ÓgĈ\Ğ À3³í2|o×QB†²~Ĵ }pİΓ¤-Xà€½Š%˘­É4^ó3&İ”˘ĝW:´™ş t|Ğx€ñ„fÊÑ;ECêb€§Í½Œ‘q“Yö4>D‹§×a"hx,ž46&ëÙg˘]~7ÓpùyDŜŽċ·²N]Ä(ŻĦ¤p'Ŝîê’ĝʍ1›~ÚB×à䟖_ÚĤ…ôà\$^IÙġ0>„;#v<›ptiPĴİĜŠ¸K‡…k‹”Ú°R2Ô'…EŠ!neEî›W*Ĵê^ ­,½giqĈċĥP…ŠÀż¤qşISú9v”Ħ¨™Žê ĜàĜFsĞĤs*kÇìż ÂĴì>œ÷њ›m˘ôI²ğÂäĴ+Òċşnœ”ÁòáË×4!”DÉjéÌ?iÄu1n8íûDf$½ŝ-ksç÷ò<ÑDx¨Žus,맂'Üġµo•ÀÁŻ]'+ÁeÙı͛mòsh7Ï·UĉV‹(Ż<ħ‡³­š¤ÈÁÄ!ħ<] ‚wàÙÇd<Éàè@"bd&+{ôÈŻ…ñvÀEÉÉ û#[§ä@ëĈxĝ³sôúr/„³²ü²:ä‚÷@p4p2‚èoʝv½äöÎy@“ïɉ ˆŠJù·.†GS|Ù£Àm§xÊ:ġ–·Í€'¨Ùĉ˙Ĥ\İŞ_ïGÚü-–΂À?‰o˙͆8vh4bÖ&”gXÖPx“żž½ôXäk›„›:·oN hgd'§…h7i4Ë="E Q–5‡[׆ı°‚EŸ_ú˘Ï5@Ŝœó:Ĵŝ7Y§RÊyµñ.ıwÑż†áj˘‹2„Ğ;ĦprLöċ9 ŝPÙ`LÑĥ.|Ûoœƒ$&@*ùÉ/÷âv_œĥ$ħqóOħä H{1–ş˘W5\H<ħ²ĈöNé”àëè8‡Ò¸…&½Œ'm“ áÒsàĴdT¸›éÊ5Ükîl~e·ƒmÀDÁġşyòá@LÛbüiğÜÊ?„²`>ôÊ*|˘‰éę́­lxàÁ bsħË!QƒÒÔüĵÊŝùpÍnéáÀôŝ)R[š"‡ -› aŻŻÑté£7ĝÛĤ/Ê˘ÚĥT'B wF*Kg£T|pòÑ r‹ŬHÒî=OÚàwòŝžc?¤$żÛ²TKÁäaî™.èn'ğ4áŭÁİSÒaû‰ôR“jy‹QÖx:ŸÔSFrÖĉUB÷k7'^İë)vïÀ"à`<ö„×S=›s­x}YŻílpŽ+)+/˜iÀCġ9Êİ> ´ÉèŞ5‰Ġt̄nîNğ:w½¤żĜmv2”|J³ŻŝŭVšÑċ gˆj=@*€$lJ­éœÓ¨’a:é!lş/“ -h§XÑÙh˘ 5? ÖĉÒ]eÌ!,ĝu””EÉYUZ„kÜwpj[]ÄOYòòÑì’ŭ8ċWŬш c†ċitEPİ”ƒµ)QŞJĊ%ċƒ.Fim.8$Uà€ĞÔ ğ2.É y·+Ğ4Q”èqéz -y] I'·ŝ,dìI—ĊŒké‚È_sŭĉ7TNïïimPs† -Îà“‹ÖóI< -endstream -endobj -690 0 obj -<< -/Length1 1438 -/Length2 6345 -/Length3 0 -/Length 7783 ->> -stream -%!PS-AdobeFont-1.0: CMSY8 003.002 -%%Title: CMSY8 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMSY8. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMSY8 known{/CMSY8 findfont dup/UniqueID known{dup -/UniqueID get 5096649 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /JHSYKM+CMSY8 def -/FontBBox {-30 -955 1185 779 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSY8.) readonly def -/FullName (CMSY8) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 49 /infinity put -dup 0 /minus put -dup 2 /multiply put -dup 54 /negationslash put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÍßቐYĊˆ5t&× {hLšGÒqB`d­˗PĜ݆ÑÖ|*îĝÎx\ÁœŜ–HŸtEĊB-ĦÉùóÁgedogÏ7—‰ï‘Q`[['“WÖü…7Â3çĉ¤ŭsçZ9ë m Ĥö!–tAžë‹Y!$átÊY\Žr[˜uTIUÏŭ‹iŽ÷BĵŒùy[Ž™ÊŬŬȜĈĊ—3ò˘KŻ6­†zJ!žË’Ç‘œJ·s&B5öCİ•"m†&ŜaĊÙ[9ıÀétaœï‘ôF·F!@[ĜÒJ-d}bĊ²ŬO k1ĵíˆĦc’úŬïJé(µċ@ -6Ž|É4M¤Žĵóà4fV‘>ÇC Ħ;ÚÌıxğÁjR½Agdˆ@-#Ş:Ğɭ܎›‰zA÷vxħġ°†‹?RXeT†Ż˘&ğĠaחĴÙżjħÌy;ġZ.NôxµĞ–V‡L<8î/­2ġÒÊşH óCËħßÉ_³÷鳆ċ§î.ÊUÉ+În§Ó…#›tŽÙùEëİ[unĦnòVhJ94œ }ŭ†™p’&’G(ìmŠĉ7œÙ[‚m!^=”Œ>ëc´Š -"‚=" ÚĠpĈ€ĜçHüŭ?r? ^~‹•_[Ż½ż™ƒDz›Áv -›½SíU]´‚nV,'VaÉĦ0ƒñh’¤Ċ3];ğh³wġŝd轍ùmš5‰z§ˆkPΤ4:á”ö7φ6ġ.‚ïB6½QԈÎüف<ûqáÁŠ'Ž÷ám²€l7y0g$³ê;HUÈ.ùlÉ*%–04Ò+›1['BwY8g3 ]^`Ô Î—€ÊpH?$yƒ³ġQP€Ä3güdrž„ìP:6šM˙šż9…ĠCÄVCßZŽ0.hrjI5olB€Ÿ–È{ ö‚“ÄmԚä|˘Ĵˆ7éÈqa{ydeÓ^h÷M5÷nGsc´#T§ĥ.“Ĥ|ó[–PŬóƒçğVGĈ‚˘JÚħ‰i[gU@hÌ5e.\ıà -‘KùQ§R6r Z܊#üÇËëzĈúTô!<‡*y]BĜĦĥxûË0¨Xĵq$ZÍĝžcôÛ§¨´¤áİv H€š1*Árċŭ‡Ŝ„'‚á^½6ÖÏWËÎż•í \YmñYR?yğš!G 5d%Ħ’ìKÛġbÖ˙§ġµ²[H:ÎG´~ ]üÄ€ż­Lš ôŞcžNÓµŒç Z¤z 1[÷;4äp^èµNïpûŞqBD 'Ĝ‰ĝÛ'‡Ŝ͛X’ùčk´|¤ĉGQ•ĈP´€éÚŭ°ÄE4ˆż^½èıј‹à=˙|%ŬZÓ)`Š>c‰¤|˜Jè½)_lw‡$[ċïĦV‘TŻĝ6ˆf -¸Ċ=ܟü*âċ ip­LEr -ÄR?‚äq”vt½” rS÷šTó#ƒğ×Ĵù½0ä•Ìŭg¤´M]ċ%{g¨˜YŸĠ†Şa3â›Wœ¸ËÇßòD İ×,&²h!Ĉك݉ŒĜíq˙^ ħ -µKû A~7VËÔÔĊ–B•x÷‚ÒÉMD26Ñûä¤y°o™¸:ž…Î!‡Œ"D ;m#òóšÂ'ğ™WC -\ys&kÌ}ZŞAGó‹ıjÜùäìäà†—RöŻ¸m&²²Ĉ]ë‡ĤnWƒ‚Çc£ä5&ĵ6"ŭ˙בéöD×öû0Ĥ÷ĜÑħYñŸ$ĈĜÉ۞òD>wÙRüÇ€Z‡aşžċ8ÄÁPs¨Û:)ĝŒ" E6Í6#¸w¨gĵ~ĝž$}Û6üIs¨ mĊ8TÀK„Ä$)’àÒƒ(ŝ Yw@â3h[ÄU”Ĉı½ #†żô„ö bc™· -)!.àğèĠÑW…·`áŠcÎɗAŜ‚$w§?A -£$úİĴŽ­Oµ@çc>ҐE2ÛÖI›]ĥRäÇż+ȐL˜f: ˘1s O5iW LŬÉŭf1vP&2l¤Šòp2IKŭĦB'ÛwGƒĈ‡`·r”I•ĉô[ûîŞóLjĠ(èîybe–PÂÑmĈ(ï²ğ—;eĵ]t8œĉ!U$‡éˆÁaoC|ûƒr†?j5½hm2Ï8OuµdĞmvħ_—ñ¨Ŝ1Ĉĥ³aE™²b× ħs,²÷c7”†yĜPĜ÷™aXàQ–OŸ(‹ËŝĦxö‹kÁqdQ7ùcvñ -¨‘ô]ĵ{¸’­<ĉÏ |gèëKXo¨p…í׊£°Ôcz›Ù{W [:‚R§!•J˘ô0Ĉpc1˘cBÄVKV!›T­ÂĉlƒÄ…YĥĤIû‹ˆlĥêy*‰2 ÓĥÑJÜe†dĵë6CŜ(’Z÷úáL9Ó_@Yq> xÄ/ž•è˘—OÜ8œŻŞ">šâúô€ĴŞSf-²O€'&MY›RüÊdWü³ġ!žì@ö/î!ˆ~Ĉq~#¨XĊ-uGıÒtߟïiñ,Ái&oX´9ñ+a>s\1öQ† ŒĦÓNŬíê4ąÎe•0Hµâĝt›Èà싒ż`çH -ö;ŻÏ`˙œ­Ĵ†Ec!û—Ĵߑ6PëÙöÍM#Ħ8™~ÏWÁr´żÀĝguuCEdÏîT(>E˜ú.6äëhŽŜ3ŬĴLo#['ıÁb=èS>ŞpĜ‚E¤Š4’ÚÔĵ_#*[;âçHÍ6Ŭüg­üĤTú¤}äÑí‡y̒lào‹’<⋷½Ià£Û=™Qoηİ|d¨EúÂì'Œ*’Ĵ]g`Ë}@ P0€ŞTƒ •­¨8gŭ: ġŽäµÖ²-DŬ7˘ùÒÍħÙK'!êÖ`ò€żùM—‡\ç·£8o鄍/ÁŝĵfGġh׈ħžQ€ĦŽ ŝÜz¤>üËĥ΄Hż’š¤ö[n‚“ğW³ÇÛ­£~sC.ҙ@°UúĵħMkÌĠ+ gó߇öj³ĉgQCµpnZۇ\ߨz°^oÏ·5Ñ]w^"­&˘Dz˘ŠĜlŞÖŭ$…dc$Ä'eĈ߀ĴaGyYA=qˆİXž7KTˆ?á)^ÙĞ|O÷(ä42×nXk9pñE²=Oià/µy5+8çœ6KW^ˆ6vŞAsâĉ֖/Ğıȧ˜´RxɅPk@îD:~ĠK_ 6žL„eىԏQ ĦBzÉ$Lˆİq}GUŠ—gnÈü -á·ûèġßETí<ïËvû=BŸnĜôr§}" -†ĉP<şŜ™á÷œu?„ŬÉó)Pö]ËèĤb›¸½náˆċŽÒġß×ĊĊŞôTBpÓì -2osyR75DÑġKO8ú%íM\bĈŜèĵÚĊ,š·ĝeè !uvĞs–{Şs÷–‹ÙYXĈÁİ+Gĉ€£ghD—Î%µ³AF’“2"Ġ+0µœ ù„>™¤×ĝRçä<wÒĵŸ|"vÇRŭTíÏ -ŝ˙—mŝğF—ŸıÍıŻHüÖ÷›³DDܳĊ?¸˜§´ v$ğÄġ[§ĜäßHÒY\zP˙†.i·ƒ’(·•û‚ÔÔaĵš7ħXĊìâß3˙û3ħĦATÖaŻ^y—:foyU+wÊ;яĉĤ †Ár†T‚[úğ™4÷_#iúŭvYBX;ÖìNjžvĊk :…TÛˤ˙Š:Q\È|Û ˆÚUƒ3ŻÌ˘Qi| †àJˆ˘EIǵaŜgı…Ña)ż%ë/óĉċD?}ÏZ ´ö>Ċ–uĦ_‚ĵ6¸g, ııMUpĊË-ħ.Ú§…m£8m£²ŝ29:ûaî{ÓħĴôwÏïYHĦ°à…´’‚Ŝ–Ħ3#5ğL„okU#WŽÏc”½‚@O‘$rŸÜħŻżÉ-#pïĈÌì—JŞ çE!³û+Ĝ˙4Y˜ÚÏ'-4\^?Ŭf–Œé ÷j#‘”ğlw{•İPÏWoµzœĦƒe&ġ@Ĉ,£ "Âöŭ‰ Ïrí -dşrIrKğċ”Ĉñ3/ûΑ¨[&½38.˜&EĈ–°ĵ~Zŝ€S€.bìıħí@ -B6Ôx8=µ"üĦ’’Ĝ€Ì|984VşòLЍ‰¤q…uùû·ġ_2RŝüË`iğÛ; àû0@Âgĝ(0*ĈĤ鿢úŠ„ŭö\sW4^ƒUÊ:׏-™AcŠ†°–ëážA~K’NSeÎOéc‚[*@˜éƒĴ)à}´v^{š -£ĊÂżž·`aÑxç>eeY…뜆 {Á%OVE÷†èpġ,on6ˆË>}Ğ^óqpVĥŭU -Ç ŽÇÈSEËrÀîêSo †5šJĊô)–Kĝ7‹9I-Ĉµ*lüÄ$˘TİŒŝa³Ïtk#ñô%ó5mBMdÎٕú9Ĵ6c'—Vé;-˙­ÔǕù-i<^ÂçbOHÇ°‚£¸[ÇÏSĉ¨Zâˆë@nkŞd£Fò?Äü4•×ž:gñĝ>‰î=°ŝšìmà˘£Ì˒É-6Ğ7dŜħû&·KaœÄ[ĊO%5è†hΆżÖÌRí+J:. Û]÷‹*dEŞàˆ‚È´’3/œCgö{?ktĝĴ‘Ŭ’‹ïċtÁô“ĵÚ$6¸Ú÷Zï‹B½9YiÔ×ó1 LÎs&ÖÓÀ·ŭä;‡yÔʌ]ÀY†' 7ġÈ-ÀvpOQ÷" -\ayĞÚÎíÇ]è“B­Ì—;F‰ŭBö°ş_WĠŠ˘4^$ëŜİ"ħ훭BĵBR!Óc ˜c‚çÙGqËĦ÷v£ƒ]Ô~³Ä“H*Ì9 -–ż]ÇC‰ĊÖ˘-—ÜÔİRÎj[Ġkk~Ĵ!”/"éԒĝ1ˆp ŒŒŭô‰ÉV%òĞ -ù×_O3äġ×0H*D‘â§ôÊ.6z#sj*Û!(ÈÒ}­Œ€ĵ#HĵûvŽ‚óz}ŽŻÓ£°H•VÍôŝ€çùtĊÊÑ,.!+lĜœRÑÈÜ .o/T8€—é‡Q˙ûe>z[!\“`˜8kTCĤ’€ì^~.Äĵ³Ħöì÷§r.°c‡$蕉IĦ%ÈüÖ¨jŭAŒšU•ğ$£!@,}R"{żŬ{,kĈ…L2ğ´ïJöVMW2 JäAf|:ĤIÄBÌ*ĜGsĦDÒŬ,\~.ò9×D Ż[Ä–cĥ$À+*ùó&Ö ~wÌ*_.LuZÀŻÒIÓ,ĦÒDÇŞœìĵˆ„<Ŝ -ƒ×›µÂžÌiÒXĤĦĉ‡ŻÂ/]ùàË|×Qsí·)o”}™äĦO+Üw]·Ù uŻĴ ¨´/˘ -<@ZĴÈŬíABÏïFÍ´Ìst¤çAÎ}Èê”9¤:ĝŜ ˙dŜŞŻú ŽÇÂŭVò×ï@w2c.ÒĥVKSxXÎUħµ -Lğ˙wÄÙß}şaíšÊoĠïK˜ÊhÀĝ,úıÔLTë 6^ÍCşÉô(çe…Ç™b#t•Êéİ?'m˘'etlE3wĊżL˜‹73ƒdLżKk'uóÖâvñı6¨ôúL]´”k9~?"}ĵ%°7 -Żö9Aa4Ñĝ£Ĝ‚}y=ûW=Ĵàu˙ċú˘×ùÌ#gçœÛ&żus¨YIsˆÂ5r(Sî#/cTC­ÛĥÏÉ=ġ8Á°O_ˆ—YxƒÓv5”$§ ô˜ -uAˆ/üé>̨Ċaria^LŜZ˘NôIµ>§^ĈĴ€é˜+ˆŝ†ħ ġ,|¤Ğ>)ĉÁÎbVÂş´êILÄuGì:’y.˘4>+ -ÖŝĊĠ}›”zµîĵL=ŝŠîw” €PŬïébAĵ󵧙 @ƒX½"o{ħ´²ÀûĈ3SPWàĜġ9VjÂŬ[àEô˜³a8ÀYú“Ñ Ĥ8·J<ñ{ÂúĈ3ĦàTŭ"5ì„cĜAêfWµÄsPy˘’§ÁbŬ£ÓBg)’KÎ.‚:IçÑ]QŒ;'ƒċsÒ"£#°kxĞ<ĥ µÛ×O_ÚĠ*Ŭvĥd´íĉÊîÍǤéâÇî‰*$107N}E`ùB@$6ÖWöÓ¸„ĥâĉñrF;Zċ:RE­vd1Ğ˘}I¸P†x|È˘gùtm²ÂéıĊÇRUÜUÀµÀv.LĤŻ÷ÔĦ5ZB“fġò ½É‡Ĝoêµ $#KŬd BpŒŽĤ³µ‘tŬ„sŝžqĝ×c i Ŝ˜˘Bm;5×n7·Xĝı|‰–oÄŬ™kúôcĤuDQlġ½(Vƒò€µÏ'ÜP“ ù„FÑHL}ûÌ\AuА<;\…-›üz)d­ˆzÒ°­G)xxڞ‘ŒU[,y‹„'[½ûämĊËıÛ°ħ|ßXPE‡{b§oQx3ƒÀ’ÇŬYöCĝ˘çò ò=6TmċÌpbӗMH‚Ħx…°|òJ­jıÓèòżžç è[ŻùĴ uóĞ~^Ò¤!çß: N0ôŝjZ/È 0M˜×\ps(>é[àPÌSFĵöĤG[A’OżĤ4ó˙x$W‹ MäF†ĝgâŞ?×ó)Šı–ŒwÏŞP*'ĤğÔ #ıL^³¨ÇÛĝİm3w:ĴÔ'żòQAĈgTßğ5ŻvG+.¤ĝùèğhŒİ´żQ|Û {Á@ĉßʊDV/JtÚrË+½í7=ĞĴĠaB+Ñ£ši#ÄÍŭÍZ&7Òƒ¸ùCzÂöéÇH×ëÇ6Ò dpOœÁžXŜó/>ŸôCĦ²tŬ’mRd‹Y…] ˆöÎ?Ô$G´œr?żXa’NħOöfŠÍ4'0µ ìûz"ǁô3ŽġY|á½şeAe$íüa9 áù¨k<ÍĠ·½ĝ/1ĥ3{::qEċêÀÂKÙY:[[‡ĤRS×=ş`Ò"ğùîUǚ —ˆA#–Í[J6p_gì4]]ó… úŒ4HzRĜúí@ä:U[Şù.,D”\ħÀsŻĜ(¸N"#`Ù~éƒsİŭž’Y>³û¤ -sLÈċäAÄbĝċîJIw`dúĵûĈԁ%ÓĜġ‰ 0’ȳá§_h‹ĵĊúiaÙ wÀŭ“[Yò˘Iu£Àhh ĤĴzÁ×f)"ŞDfSíǞ… Qġq|yPž–@ Ûµê,ŠĈÑXòRÒĠŸ~aEˆ–~o|nŻî\ùP+7\!R~%jt]>ï'4Anr í2vğlŭ@P²Ü?ÔCĦ+7ÒÁ;u÷×ħ^`ıŠIAä‹sÛ(\ák^ž0P?šĞ=Ëĵ{‹ŝ䘜›.ċ~´4ëş,.}ùNm*LŽ%ë~˘ĉ Wĉ/q>Í*:ğCşÂĴ^oÄŞcµĠÊOÁ=|,ñŠîÁĈ7Ül0ѳq Ą-@Mĵ÷bǜ²Ûá7÷iFCAlLı‹( ÑóPĉG­I–çŬ—œöêkˆ -endstream -endobj -692 0 obj -<< -/Length1 2278 -/Length2 19476 -/Length3 0 -/Length 21754 ->> -stream -%!PS-AdobeFont-1.0: CMTI10 003.002 -%%Title: CMTI10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMTI10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMTI10 known{/CMTI10 findfont dup/UniqueID known{dup -/UniqueID get 5000828 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /FPIMLF+CMTI10 def -/FontBBox {-35 -250 1124 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMTI10.) readonly def -/FullName (CMTI10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 70 /F put -dup 71 /G put -dup 73 /I put -dup 75 /K put -dup 76 /L put -dup 77 /M put -dup 78 /N put -dup 79 /O put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 84 /T put -dup 85 /U put -dup 86 /V put -dup 97 /a put -dup 98 /b put -dup 99 /c put -dup 58 /colon put -dup 44 /comma put -dup 100 /d put -dup 101 /e put -dup 56 /eight put -dup 102 /f put -dup 11 /ff put -dup 12 /fi put -dup 53 /five put -dup 52 /four put -dup 103 /g put -dup 104 /h put -dup 45 /hyphen put -dup 105 /i put -dup 106 /j put -dup 107 /k put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 57 /nine put -dup 111 /o put -dup 49 /one put -dup 112 /p put -dup 46 /period put -dup 113 /q put -dup 39 /quoteright put -dup 114 /r put -dup 115 /s put -dup 116 /t put -dup 51 /three put -dup 50 /two put -dup 117 /u put -dup 118 /v put -dup 119 /w put -dup 120 /x put -dup 121 /y put -dup 122 /z put -dup 48 /zero put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ24 ĈòŠôWäEvçQ‚C<ùó3£‹ĜAÀÔĉ‹ùàë2¨˙·kX0k^ß|™‹:Ù´ĵfb,|=úësLu2ĉKżżZ`3ndgï¸RÈwô@Ó),qñċĠœéG<&¸÷­hï'ĥì. ΍‹883 „½Aœ½BħAÓÔI$sò@Îí“Féù™ĊË25âĈÚŞ,iá™êê pKôœê>˜èÂ6K` Ó%äÂEû(‚ôĵ„(bsÌS?#;IäòHòäIRg¸HÇàĊ—Cà"à AŸxb'â^;*żD¨şŠÙ•Tz35'ŞÂĞĞG=F ÄĜ FÑ섲.ŸK|LħÉђ^Ts•Ó™,˛ĥPSó{×1Ñc ˋƒrŽi,B½Rƒžj×l_Ŭ‚ÏtħU¤ĵH %!Šñûë#‚V¤|6ÏîÌG9iĦ—Ìû/ĵ'/ıÈ’/ëħîÇdú oÖ1óĈÄWˋ_GˆÄÖ -‰žħa vL"paSú–-¨§˘gçĥ‡}tòğá@{&•İYÓġ`‰I -ƒ|Û˘sÑifÓŭıˇ]˙„³<ˆzüħìi˙›–lW—˙…UħÌf‘Š Ğ}ÏĦq^c,…@Ĵ•{ˆ³Ë6Â~ïß?ŠJSż²ŞÄ³vġ$”³ôi³"$ñ²OŒ -˘šŸVÙQ‘?ëŬè2òĞĴ36Şu¤¨ËÎ`}²u~£²ĵâ­£–9ġżċħ#ÍM=¨f.bòÓÈĞğ GÓ ·ëİìäĦÔ"K£ÚúŸŞ™ aI™\N³*èQ Ûí*;ÄG40Z($ÎéĠXv*WŒsëPŝÙn hXŝU;.Ċa7XÇÒ5{~M™zçHĈ żTá•ġjĤ•?€Äûáš^ -ĠLh­ĤûIt}eÑ&ç,APĥĝRġìNy< €9MáçèCfŠQx"c<Œ“Úß~Nh­Š%0ï`ڇD­ċà+‡ŽqîñÚn ;‘/ñöXµ ¨œMş wZd°i3ïÂV‹™ĉ"+$(5Ġ|.”R÷îŽ`ĜG[ĞxÏĜM9s&ĥÇ7q%*=×ĥô%“ŭŸz’£J3FA%ë@k ŽÒàóÒd/€Ğ]žgóā‚2ËöÇĤ<\û‰%ߓnÏW(ƒ5uIß&ÒŜd£I ¤fW°ĵtĞ]—ù]ê32ġbòéݞVµÑS~€Oġݵ è&”`ŭéhàXsGA"³%ç‘Ĉ͗"Ñhîğ<˙µŽV77h# •#™TÏϊĦt LCgÔşRRŭ3˘Û}Mc}`Âò–‘¤ŭ™GİŻ\/hÑnr]Öx³9#ij}‘Ċ$ùŸäÄ ÇżödİVá]ĥİ£Y¨>*§Œ’4ΛËh`:gQgš¤çatNà–È9"ı#D*ñ$ÇŞĵœâyy\Ħ ¨9O¤E{y"QAwô/ñÑĤi ,֗şš£ĥ665:Ž?S€r#2·ġ… Ž+ó]íĊÊvĴ†²ŒßëĜÄÁŝV=] U8~ÌÎä፠Ûòĝ4‡"€5ç;óżı;jĜJƒŝ+ĝĜıo!‹çާ)y’.^<ÑêŸ˙Ô^gNlV:ñê„H Üú(¤úÑj$.ù‘CÛÉ>ÒĝdräÀYĦzÂ3”ÍD^"(ûŬŞy’İ?ŞŻÛúsІsD„t45KĝĝÔüqc˘§V˜·ë}ŜÇÄPÛËI'ŝREhÜşÇûğ€n!pî£}iğżŒlqH'¤’>Š2úġ–ż²ÚAOÏl“„2Ğ Ż¤#“ú [ğ˚sÀo˘ şûDtòûéaäK€Î—:}Ù½9/MÙ]fíğXÙlfò£-úFÎ|Ĝ Y A1ò†QĈ•°/2ŝ8 Séšċğİê/^—ÓdVB [aɤJz³¸H”0uä€ħS·ÛoŒ/Y`'g)5ÊŞé:\°‚hŸY”rG½!•ıy 9ħĠrhcè´aµgzŞßoϘ$@ˆ]8 ˘ĴŸRçĥEôPô´ñWh´ÄĜͽz]FIĜĦżzÛ³èĉLÎ|"CE°w}BĉœĊ½é03&póv…4Q:uÇK˜w½ô+nCÔ~vżöÖtož³‚:—a³, y‚\Y8î½L sċ²ÁÏÏŻ~dËÀƒĵ‘ÂpĤ=nÊ?D(ñ ‘ä=>ÀéÑm‰€ÙzĦN5üˆ ¤ Òó,Ë$2/"íóf§Ÿ6Ħ%)R%ÊbŬ8Ùjİ ƒ6’mqËEQ-C Ís–K·Ô˙D­òµ\Ĵ‚=R3Éúd>!YÛΎë9ğMˆQ²Ε/VĠd³áŬÂ+ŝBçÜŻùW&ƒIñï‚ÜIġpAġ§h*ıİ ,W°èòö_¤°Uk¨W2ÖG&ċtkĤ+hV<$İ_Tg§LëĜĥuŭôcz9?ï^´Óyüħ(;ĴĦ2ħÜíêôÌ-Ĝĝ~7­Ċ]ġÍêr­§&Q•×0[›ÑAM]žfĠXĉ?ĥx]‹iıĝ™ĉnU>úï˘Ü%ʸŭ(ÑÀT?‘ƒ™Í. a1L.´wĥÌia†…ŜH­Ğŝé÷#C-`g=fŬ) -T“²EG†û‡e›IuEƒo?Fg Ó5™Ás9Ş‘´!€ôGYr‚$ÖĦĉ ïŸóLäÀĊĝ½8“h:ëji œDċc‡8k.ĝîlíŻÂ|l|‘ ݳ/Ğĝܚ;'™(2P]< án÷ÓħÔĝ -l\ÄCüĜ€à:£•áŒœ'|-Ós‚y…Ö5eËD§”eûE‰ÏͲ3ڗĤ˘•ĝÄ0˘5•nşİ€v­>*!d üpĥ+2Ì~àïÏżrÉ);J;ıšÑˆàJ2µêÒy].1ù'e˘Œ'0çç\¨êM½t:gÀßĈĈèF+m‚êr”3Ö²İ*ttXKuRL Öë‚˨ĊBÔ4ċŽÌPmÄh‰eläŝż[­b9ʸŜùNRİr„ğ%0KàïÇ.ĵŽìb8ÄT˘™C{Š,Puí9 %" -Ĉ›1ÍÄĜşô^‚KUIÛzı¨ŸÙäfùá²sçż'İ™FiwG&2ÊbDX—4†òĊÔ&á"t]vU3òÉqĦıekàZ’b2ùımHj‰1}qŭğĞ_P2|Ŭa8ìÉ~ˆËÌk²Páö4oùĤ_ëç‡ìâ==ċ ó™v›Ô‘‡óóĞÉßÛÍ8ĝU5[ı_Óê ÁÑ)éôe=mÊáúʂ:˙ŭ¸1ԍb· DĤ9ŭ}ËF`‡Öż­0÷cç·än˘R܃ÀIöˆp´yiS?Ìz5qe“³Sdqò˙eôiŠ˙ QJV6Žá¤™>otü5&2ññë˘ĵ·ZWÏ$ŝżMQ:PÏĵÌÀ\îÀÎwĤöğ/óv@j¸=Î˙à_L•@†÷ŞwNÒ¸„}FÜdX;ı‘ÊŠîw‹ÇĉïÎ%şaM¨c ë/˘îñbbK+››2qŜĞffQ‚Ž„Á`" -nèL×o/Š†'wç Ĵ^*W˘”a²¨œˆ‰oĥñûŠá•”lî2)´&eúƒ+Ĝ´…÷gŝ£›ˆ ŭ˙„ê!²g´ €'f?q³wğ‰tלK˘ZĠût÷ġ&Ñ ,<#ŭ)âY˜,z˜ùĊz‹żĉĤŻ%1!•¤Ç ĥ°³†W"puÏü ”môaRr1¨ßrüü°@C‡( ^· tĥá˙R^0Ĥ†‹ÍKtï{ĠżgB³û"Ġߧ÷ïDfĝ!àß=|‹’İQ× -:üñ“(ż [Š~¨Gsvj™Ê“kĞP g/³=Öóö_]U ĥÁ•zê“ Tï,$VİÑ9jÍîÛZßµô˙˙5âß·§t„ĠËQqÌíٙÒGkcÎöáî{¤ |§RşùŭL èĈ]vCAhè$Ĉ(5Ħy9>8ëA88oê1Ëĝ¤°ŞÈ‰‰ĦSÊOÈ Av??‹—” ßğĠı‘Vks=lvbŜÏ£8É|²È\½_%{Ò¨³>&&zIœġ°WúV½SúiUAïV£+ŬӒ$ÈD}’ ĵġGġüèe=fL|Ĉ +í)ào‹^E`ö·Ş·éÜIv’äî7ï€fKĵ³+sğĦDz 2sñĊ¨ŝĥê4+Áé‰ċ:>AnpúT/ÖÙ¸&X˙ŽÔÉŬĦÛTŽ,@Tƒ…;wĞ ŝ÷İÔŸî°ŞzÈĵÓ§àÏêzeĠ÷Ŭk’c=zÇġaäùH`Ġ`$–ö4Äú -ϋàHÙG^œ/'tW˙WŭÑÊüçÎu5*bĊ9üNâɍ´&ÔŻ}Ú·#*Ü -Ö7ú†=ç‡/|úµCX2œ€ÔËWÀ!wA—ìkÈÉ'TM<@Sт„½kP8fĞı>?Ğèó­…Ì ċT2€K/µáçżKż\ >ߍ$—ÔÙɊ×ĜíħLSN 5ÂF=Ŝ)‰Ĉ!#×8e|ÉĜ͓Ôgħ•_NÖQ¸ġÜ:Ħ¨§œ“Û\UAüżŽd<@_Ê´Ŭ -áV„;M ŜÎ5ztŝMmiĈŝ½Jˆ×Ĝħ]ëwimÁèL˧ĦöácĤM·Ñ k>’HI­ §s_Żħ_ûêY/¤ÜH%HÏf‰“]_ "…áÖ5+9EÒ2TÄ̸ÈĉC´ŽOı[†³ĠÓĝ òÒgù=‡<@à³2L4Ĉ^żĠ§n^8à3…ÀИâöĤÜr‚AëĝB…zS·iêܗ…yġƒUO ZÄ G?mÑĴLÇî˙ç×ñlPmŻĥïÛŞp@n,yÂ4ÖÍs§Ê:ĊxN›µéƒKXa2#ú -Žutw(ĥüĜ ™7‡Ċ²´Ìè×â>ğĈچĝ,FŜnóy]fH_ŭ^;NyHU’/Ŭ#")Ġ˙t¸ï.İˀİÀ!ϛiw‰xž”{ê yCôŬ Cb|‹­ ·ğ™;ħ•7kÁ“”¤ä˙KëS1ò½˜äJa9µzŬWÀs£Ë”ÏdD°XHúœ\d۝’j)3xÜ%nŭ'l KO§úŻmR\ŬI5piO~5>g@YÛ5ä•+ÑÂ9ŭâ¸×·“0É´³k8@ü‰ŻÉ …ö°,q–AÉ“ÜDë‰ıé4NBŞuòÀytz]pĴıȧ”"Ž–.?ÂÌ’ÑŻÔ/ÜlÜ[lŬ&œç‰R~WwB!£ô’÷ûn]Ĉ8+I5wY]Hvܲ½;U"ǘôƒàŒNÁÜı4ò›†ÏŬ*ŬÄġ={ZìU6o+L%ÍŬ=ŭ°ĝ ž&ğ³vɃu}Ğqs°‚À¨,Qâ°FŻ?RGmaœżĝÜiàċž?y yüëbƒxfULWQ÷¤@†UÜ-6eÛéÙış+I³Ĉ•t!WfwĈî·mANÌĵ€LáôıŭZĠYÑLÛOñĤ¤÷yJĴQ“)ÀP2$b?‚²IĴ’O…4o ŜôâOJ¨÷¤ö³ŝçr—ÔÓD‰:†Ç8kıŝ2?‡T™î,úQĤYç Iıû鄳BEéJ&rĵZb Ê°OSĈ;Ô~qF9cÈ#ĝĤĞcc—şÖ™dLǤb0Ĉ–Ëż‹šŜhĊZײRƒJ§Ç >*ÔGŞ FÙ{;C'elIcXm ,œĜ‡6˘Ö™&â˘Em—ón.RG˙ÍA†e²Ş„ÇĊ¤é2™W| -K;—ħİÑ >x´û!ù˘ŽÇ MÍAġ™Ô;Ż÷ĜNJ}b˙3 ˘/2ۏˆs))^¨Üöiöİ–Ŝ‹œ1RĊĜġ (ÏĊ–ĈǏ‘¸èg4Ѳ4l/ÁĊXR+|Ifb„{ĦhÎ EĦˆ‚]5ƒ[n,›|8]ŻC ,ĵBĠVÉ"*N‚ZÔ·Çɗg”ŻŜ*`´?üېP†ŠC C„ğžòó)LĠEDÚÂÜÒïSSÎotOb‰ Ş\šT=/Ùûôû€sÈÑĊġĊÀ‹öĥtĞ?CĤ³PfF§öšË Ü.aí–(C!ĜßDbÁġ̛EİxÙj%í¸ÑYíĊÂïKWŭ’1ò›Ŝ–çĦ/Ykt@ .95òùwHÓêFcÄÚNDCŜÖiés“Ñ„ĥ•²ˆÏŻZ8A6””KZMh–mE÷GpXžÔ ö _;ğäu/t_&ż ĵ²\‚— >œ˙›“ŝfŞwb]>|`˙üšÌÉFsçG÷ĥDÚԝ{äz ĵôŝE b…fÉ\){`ğµTfĊŬö(lž…žÏ‰tƒBî?³êÇBżÒ<Ħükğúú#M™§Û¤b۝û¨8—† ïµéIë’]ŝ1 ˜êÀpWıü=ÎïğĴozŠmÓUÎ#÷{ù Ĝ†ríÂb˘Mĉ€Ò;™-uDyÍ6—)vAší E)é´šRàĠDöĊ!Ÿi{ò¤Ŭš×@èÎS:(À£żŠQS~ú-Ž ótG+\{µ rc˙§„JÏĴċžÚ”Óğ%›(á,"Zeħ…<ĦżT²5‘Á°ZÏ=F•+I£|é=×;icĞ÷ĴJó˙íŻû ˆŝŝĵ§ı¨ˆKSAŭ'ĥ&½7&Ûħe£€bÎ&Ġú¸€çqżÔA™ <”ŻsêċLèâÑÄ-sàŞ2+(v—‡ -sC#­›àĝô"úp$ĤԞK -•ú’`ì{ƒWżĊè/ĠħÊ+‰Ŝr3àž#Ŝ"ŽÁ@Ż²½1aW3!+NL˘ÒUT‚YZûŝCéUÚ8w×Úïŭpd>(Ó?}°˜_ -<.7‘‰6í3ŬšŭZ0Ï×(ñˆY/ -‚ Á m˙ êëCԈW…ÔÑ}Ŭ7<µzB&p¤ġŽğĝŠ5t§)™‹€PoLVĜbçNÑd+‘{dâ–Ôâ£YyScJ”ŻNïùµé#T2+Us§êљN´›Ü^ÑvSß÷¨È<‚j”Ĉêù]é‰G×/ڔ ¨Ò´÷DòXĉÌĵdX7ıwĊ‹”fÁï'i—ô?ŭd‡Éġyló[‹û6Ëòĉ×0CDÂ˙GopH,¨Ó!ĝœĝIOÁıt!ŝMX{_2ĵñ°Â˙â`ĝB„žĴööùÀt áBŒĝĥ›Ü+˘›ù‹3+{;Bˆ.î˘G²˘‡ĝÓÄĴˆ¤çŽ6_WħX{2Oġem$àÚ&ÎvŸ?ġeÇœ…Ŭ˜4°XfùŭÚVÎRšj¸şî·YPùo+£BlwöĞ{ž*<׉<ß*/ûYJ›pŽÚ - 1‰LšwÌi3tPpy⇀ëïmXÈá²VÛyı@@uo£PĤPui -Ħ'U†:ˆ^RäɧQŻ”PXĝ–ċrž+[£îjۋ‡Ĝ½V%:ŠcÚNΚë~Ŭè{µê? -ĴžèÑÂ&ó>†VPĵh<ĜĞE ›YÍÈÙ ŻÎ{ĉ§YÉğѸ¸ˆ ŝ t>§’ÎZ‘İĥĴh -ˆšz;{ 3ì)²jàĵÏúŬÁğî·â²Dï‘ŭ:‰(ÍétÖ2íw‹İê2YĞ  óĦ°žyb -Îw”A*֔ší—Ü…áiF#‘˘ €ƒP|5.MƒĦi#ô­ I8•'“À-Ì\ÊşÇŠGoùŸÜ½­œ†'阠W+ÀËş0öŽÛşHêçñ‚Şĥ&·yNYöÚ ÛZô -šuòáy‘›’“v™Ä•1^ÀU< YP¤ÛIügVnËJËċÚEÙ µ€%“aLۆµŽ4GAQtM4ö|²rdujXËUsÜĴòKfCżÀ)‰“n„f³ĦöĊb=igÂe‰E&.µD‰7ĠòğÊ,0Bò-ëq5Ğ‘ßí÷§­1î9ĝ³Ià;Ğ˘*8Ob1x%ëgÈ:f IÙËJó™kŝ:7Kg’A%ì›ò?<Ĥ<-´Ç_Ž›Vğ{ÈúŬ—Ş…@NŬLKàûˆ8iüÏ{LÀ‡Ê›ŠxíWSù'à:ĜŞ1˘?„ĝµú‹[‰oëĵîÒ¤êŝr_dŽàçê£˘z·ùÚÍŭ_Gbm—hˆœ8á/Ĉd`:CèИzÚéàڔ ż²VÄvûúÑ·\"´Ŭ‰DEŬsÑ4tĵ/t§ó_“H[ /ÓĦ(VËJ‚İ=żÔ ½kùâ -ÎöÈ <ú÷ü˜ß9˧?ĴĊABŜ)~BĦ’QMV_ Ñ):΄…*ó ċKôPĜ2“ŸBžŭ‹@RÜ8¨Ù5Š¸š.Lw‘ÉC³W$Ôs³ÂÜ!hş:ÇI/ëm\é}g=ò }CíZÂcùÔSJĊġó™T>ŽżŬ\çHŠŜOŒÙi‡Ĝ|×´ipàżñŠ%iö{ĝŒì=_•E,ÄEoó0ÒT êjé“&˘7ŒâáO úHqˆ•‰İ˜:üGwĈ˘ĵyyĠ .ò?öŸ5VêÙj$zƒ'Xït*<0lGZ‰ -ÔÑDüž £ĦUb½Mqħġ–hI'd +täÇĠ(şVóïsKùĤRš7fĊvuEh Ħ4ÌĝS1ÓÒùIÒí2sgž5ûĝ\÷&ħ@ó³ĵ&˜ôÊHÑÊŭĈqœ‚£¤4 ìŻÏŻ ƒêEMĥ+ÔuËöüŽnŠŒĤé̎bDKqqŜhqcUüê)hAœŻâċéäh²w\™ۖ5HÏSÍ–ŝʐN@ğ ŸEìltì'6éúzĠ z§ÌE@„T|‰Ú#Ĵ· ŬÍ"ŒùXíŝqĴs -$„Ž,ÉÒQÀ‚ÊJ\İ„ ŜltŜĉ‚ûbt·É -dÊ)ԇCYü˜ë¨^8sv2yĉîĜ8Ñok ĥZĴ$ÒĊ_‘êÊ;Óô†…ziXƒU×ġŻBBqeŸê9fP³ëƒÛ—Ìplŭd6£Ç¸i€¸ôĦĝĈ$ĆdħmißÛö  ;W&™ÓÏÂĝâÜì0ëŒH´I„ †Q eáÛ;µÁŜ•íûUŽk„ítĴDiJğžż„/ÌXĝY"½hċÌ$³ÇĤŬ2µ'i6ĉú#@ÙîL:³Ô)]l}g¸„ğxäN<ĝeâ̌6ĦşeĴšö5;¸%D<ò}÷Zè€F{YsXÙöIÏ!²ħÓ*óÇĊĦQƒÜ‡È µ+ÀÊ „¨zĈÇP:-Z4.Ìfĉ‹˜>jŜÖC¨ŞMÄf§Áç~6ÖOS tPvЈ}>.ufbyšá9ÚY‰;ΣsNŻ`ĝiĴ­İŠ˜¤9ÛmS„PRIqêÛÑǂ”qÒÔŝÎĥòì²z]xOAjmg>˜×ĉ -™.ÁıÈ_Zyynr˙jĵ¤ÀÀ•bZ‡ġx_äß³'9$3˘‘,6£)§ûš ša†‡ŝ^(T–*Hj!„4üĉÛ&‘Ÿ§0,ñœâĞZ|"]cä@§1O9óIOoú„Útp½R ”L9!ħÒd×ÁĉX']Xĵ -ßĖmĞż†xÔÑomÇ#[‘Şh¸nŒcÑqğlTĞŻ™j’£ÍN€S׿„ġË ­P=_tkŭKOYY(i]O?šĊ}J\I÷M‚…-ôeKvżó­pž’Ĝàü²ŜšH˜1ïI˜Ŝ“€ì¤µüŬHz§ħHİ<)‰‘GT€äÖOŒd~é5’†ŭŒ½NïêákwÑzG'O%ğıĤ³D˜“Œ‡Bä df—Öz£Á´/–׋ÖR]‘½š-ÍDCƒ_3ëŠC9‹=ÍN ¤^ğšFBĉ­§éÇÔiÙÑ` Ln§"n}?Z,…ו1#°9,E&ÍĊˆŞsQŸ2çì<4{­ŸâÓè\_XP[h…oóéÖÛÒ˘Ž`,¤Ï_`?â_ñÊòˆŸˆ²/êCw8j]U§ñ %ħ½µwĴĜ•ŸûNçZˆ{9QŻFŸ_g°ÁĴSÙ8é’&ÇşġŭTS;IRF’lúŠAӛòü4âys…!Íg%î1M3dr¤¤ÍeIħ‚2ƒĠ[÷†Eċ¨ T…ċ,‹]ˆğ>ÔÈùDĠ³7G{Ĥµ†L²"˙ëĊ„ÈüHlĦş_& ™)|• ž*èġ+äAÌï|¤‹ĝjTèh¤]…`Tà†+S˙pxÌúè È'Vı9r’QÚ(Œn8MŠsiž'ـ!V\qn.Ğ›FEq·çŒ@ö^׏§–‹)ĦĊcĤ9€ŜT˙ÛStvĴâ„LÁҔpD;2ıı{U£#/_ —Â7•£™Ĉb$ -.> |ċ!丙–xLżä"í·)Šğ`'éچT^J(÷2FCoĞĉ"•vIĵw)éÜħ6Š(2돁› Gáˆĉ´ ]Í?ô 4 )Ò†=Ŭ’4uÛĥd˙p(xŠ|ò^U›âgˆFŽ ž?ıŸèêxÚV+³ûJµ˜î›*ÔLU`˘ĞP‰áċėÍ’,…. >‘ƒù3Îï%Ŝ‚“oñ´ÈE‰ß§I%7V‹,VĝZÔUAĊy— „ôWÉlq߯Şß -†Ü -èŻğR×˙ -ކE—Êġĥú”yaèìšĤg$gh IškK¸Z…‘ÔĦšÀRÁk î˘)°Qìġ5[âò”ċżÂá7—sÒ:İ$' šYc² Xñ\ïŬÍL‹ÇJMĥ…†g[ĥŸÑ„µ/çŭò‚2ù'o$JL)fQdǔQúCKç†[ %Da˜†äš˙’İċ‚·Òğɖĝ†|'ŞÇ0M¤H(œ@ĉي½Á -5Ğ[*Ԅ_Neg™(À4Rû6µÀ7eĴÀŻÀ.‡˙ -5˜šxù˘ĵ95‘Ú¨ƒTc/DÉSv/5:úŒî9Äe0sOŜżû=ҞL2†ˆjÈııËŜW…—MBĦÚ<4ĈTšÉµ ) RÂú‘G8LlĝèÎñċ@uN³OyÙ*ckIMĞĞĦ„á½úÖš§V âE^†I%eÂ*³˙ |rzQ‰}i‚ü£?âgñûëĊ†ĵ¸rĉr+8CôI@´Ĉ.Ĉwd* -ôŝ˙­Kċ,ax×9sôw„(]Ïò¨Ċ•ĦŜo{gM‡]$-<÷ÊLGżO“°}STœİPçĴ¨M;c|ŞœW 4ż%/£ŝg€i_œ„Óì7Wy„atKˆ™ÂkŒpû(!!^9ígĴóŭƒÑż ĠIô SoŻ‚†‘j¨Ġ·Ġ“ò˙ÓĴŽ6@ä%PĈ‰„Ԑ²ŝÉ<*U¸˘áşÉ„Ž:”fkaSä¨S´²:|òĞ+Ñ ÌĤ -„ĥ´$Àşëkö Ú>Ĝd6Ë`<öA¨ùLHşV]ğ; ˘UR4ÊŬJnë%{ûŜéÎİQzQ”Sà(RPŝäˆ6ĦI9ĝ1Ĥrż„äŝKCSĞrLğPûjŠH‰(²Żvùc“ŝ$ï·Ċ -ÓÂaµ•µ6ü_:c×u§­2e‰~Ë˙ğ›*6gtšŻo|m裏4 GtêM)ÁĜ,Ĝ'ö $3ĉÌ|v˙oT΄Î`Èöú^‘W8-y•‘œjÄÁÊâ¨{£ÌŝŜż5=–‘Ú&ĥ÷äœj[;:ÄG‹AÛ ]@ œYèp‚ΓÀĜlB3*qŒn‡y}=ˆÑ@Pğ“RVey³ü‘ˆ^‰1FûÜş„t÷ë%C2îÙ3ì&íëC0µ#Z†ċwTH•gmIğŽAĠ~ë÷š|×Ô2.9FÚ [·ï҉¤EÑE›˙ kéĥ<‡Û§ĦJ­¸ÚHj¸ÑÍöڒŝ*Vħ% D¨.@Bßcżíl蔨˙ÉûÂ&^`ĥwyІûâë+–½ħpf‘Âċ™‡;Ü*â5$Úb*ûjoç4"[Ëé°¤üÀr„t_(*IíaaÇÔÈ“4gé$Cäq! Ïşµ–³ĤôL -eÓúxDUĝŝÀ½•ıŸ _VQ)úÔ0RCK èmç"ëAPv›ÓÀ†GUŠ4ñNÈAzÚöV‘ĵÙX[ N­ŭC+…bgÇò²(SX”#Ó §Úùô!ñĜíU\ìç‰ÁÇ>9}Ġf4LûI,êÎna{dĥÖbo\'2 䕕šÚ\ĞWäz…c–G\ÙptS²y =À-ÒHX•ĝš+^ Hâu9úL4žŸ$ĦKıŭ!oÁù‰ ĦšKÁ°c÷†Qŝaċp|ó‚ħ'„ĦCŠq¨‹CÇħìĥÊċwX€˘‰‡T 2Ĥ[§M|#?!5MÂĊúĦHÊê­Î8Ÿ5”ˆ¤żV½·€ĝŭ°Ġġ?­Z ²kGn/Üĵ@&ÏÀÀħ,áÁéÂD–m(ó¤¤PbìRġFÖêë$£Gf)òµn)[â´_ÛÌù‡xÂDÜĦ:m¤ámš‹€ ĞŝNyŞĠĴ,îŬAòJzÙuûŬïBMÒîufċTv)ÔWÏyq½œé9›dD"‡ŭ$/Êï]kŬÛĊğP÷j°ßU´‘â6“ ˘bF M}ï1ÛY#IÂÙUîYÄ Ĝ‚ÂÙ ˆ9ÈcèżË˘˜Z&dôeĉx2Ŭ#p‚dQz ¸öÑŬl.´ ZCÂĝ\£œ£+\ xùP‹míx'W×\îµñ #!-ÀƒàoŬéèÈ×Ĝlŝo>ìR´ÜĈ'ŭÄËÎtrnġÓVU‘0ĞE›ó¤Ì˙kġ„)GFŜ\|”Ÿ_òÀ‡Î¤A£ô/Ùw\­èĤċ‚ŭż†ŝ¸ùÔP›’üиĉ@,˘ñgĈ]Wŝ0Ìħ­áTf€Ĵ3°,…ןÍȋÂA¤ċ)‹ù: \7Ê,G'›ÔڏÉIAÊ>¨ŭß2pŭwàÌgñ@6§9'0ïh†¸Í+Ž^ȵG;"9ÊÊ µ@ù£âƒLŜ˜ò+n´RMlt &AĊyEÏ6‹ “ƒW£” xGúĉ4ĉkĵ+ŜJħÛ`€S_Ìĥˆàš{=.Œ6û%”:–ú³MÚŒ—ÁdŒ$˜m'çÓĴ_iߔ/‡s0ĞÈÈêĝ• E\—cVjAGhÊ,Ş–Ú“ŸŬÌü ŭj}´è²Œï“ĤAÊ9ÚĠÏlċğ&ħĴZ0ÛLRŒ \ş -WX•@š§ìċÛ]ħ˜‡§í‚½ µ_4†–ÄĜóŽÏĤ‚ŸÑ÷˘x $!ò¨„ùr‰a!H'gw¤Û#N8+B÷?fÂġ÷@ì ĝ3%Oš}pċg‹]pĴÀ×:Ï8ò=8‚^öÁxîšŭ*̍m›"Öĵ[•ù9ÙúUI‘֛e´Ï`@˘Nj•yâêÍA™ˆ‘T†g\¸îB{pˆ@áAÄŜ2ìúŜ–Ï%İŬŞÀhÚùĵq÷”F~FÏ{×;VÚħµFIÄ+ĥž[ RċY0†ĉe&£géµ½Qĥ•*Ħż?ÈàècŻ–Ñ;Qmôà+:µâÒıä…úùVäu>C͍Şî|ÖÙaòadÚñ*)ÒÑ6mjġÛZ?ȀÜÙʄÏv02â%ĈÑEf,Ê2Àpċbӑ–›ó;eÏ[£5í#Â_…2d¤]ˆ„‰Ödd:UË ı -ûĦ‚íô|½r4ÔUq›!hÈ,ú†°‘.Ҋ”_pAĠ`%'b'µ§+áyûlH£r,ŒD8φĉ¤ Rı[ùġüì‡Qxˆ ÜÓĈDd. r§+Ŝq7Fl Epm|OA’ËıJ"}Żdñİîï'˘Àö5(ZĜƒ_ÔFgĉRi´‹+áÙlqĥÉó\'&O£WA  ^ˆìA§ùì†Ä#RÔT³ĈĤdܝFÖèëa­Ußb²ôIàÙوڸ˙ún7'äĥGOKHÚóÉĵÎ+›ŽFsî¸A;CïüU·/^,l ! ­£è] ‡¸‰—œkà<íÄáRJLî¸"W‹Ö×°)c=ĵĜÍ2ġ[ŭH‰¨|hġ0Aú_ı?)ŸOhÏ×c˘Fĝw§Ĵ…Ig~ÜBE…i\´f“xꄰc4`‚Jl CƒÌ%Ž-hĊ˜ÊWÍŭ‰ÒBż'pú$â LgXtê*˘B“1ÍÄħ!0x0ä!7pó›LdèwħF ínüáT@lgĊŬĦ{ĝmLŻô&yšRҗSׅ\FóċàpĜ53Ĵ Ş‹mè??ŻäS•’Ÿk²ò)¤ŭÉĊ1•OŒzƒLŽÇ5G4 ŜCħ -ĉ3GİÜm `X<j¨Ç%·Ü6ĥRÉÛĤ‰óGŜÁ{ŸR’ c+<Á°@ˆ;qà—ÂBïsğ -­j }Ž*–ÖTÑXOŠ1r6ħ—ÛqßĈS¸ŭc -*=ê–ĵpıœÚÄ%ñk0փË*ÎċWK„Û‹8SiÙ+ç ïK›L’WwĤVΓÌ·†R"ĤRĠ@–F%{½İHo)^‘‡ĠTŻ­WĠÎùâLtŬF6W1ÄÓ~c@2‹ÖÔ̟4>Zv^ ÖWs˜‘[8ìèïvÛoF´l>˜@ŭd ÙUU`Ù=ü<a_şâî7k|Ĉ0l³ÓRVâ1”2 -P„Çuİ#ıáħ‡°DjċUV žÄ2hÈvġš/à{çĊ ޽-‚T`›2ħ––`‘WğŜ$Bn˜#÷ÜĈ@Á°ÓkĈE“ -F(~,&4‚|ı ù3lĉÚ¤ìòé%%żK÷MŸŸÛy/mîddĴ†Ûw>K÷ÊÛj£żĊ}î¨g÷ó0-èƒÒĴg¤ô‡Ó£ĴŬ—Ġ3Âïș}rÏMyş=wż&á=/ġ–uü{ĞÄ6Éjş $"£Ĉ!íúÖÄw&A< ċı˘ËOFàcÇ&çTÌ„rŒ‹ĦAż„q?ôVÁ –ÔFN RîŝÍ—÷ş9Ż¨žğ1Ĉ5*qċE@ŞWÜZJÄN7Ç3—îh€ÇÌ|hŽşôŝ!à_Ê,{E™™²:ì$òN|ÔH4ˆ6[jıëŞ?O'Şncó0|M†ĦhiĈ•~Ŝóñt²Àzş’=ˆ7zc­ËP°:ŝi3§QFqíyµşLQS/#âĠ7V¨ܧDu;3¤dfêÖÛbHfPöÛҊ·ÄD³f1ż“e'ö% ¤BĈv Óküg·ÙÜşE¸l]q % @ÊıŬĈs1->:Ìw'r#FBÊ(ĉi#·:ek(^„K* ;eO`ʁÀÈ÷Ï7nÚİàhï‚ôW LJ%m‰½ƒFê S‚µŜ-wÜeNv,™~A„³ ġHĵGUR|ŸÔà(—²"èĵ³™8\°xĦ‚.e/Ŭ? ÑË1%JŻvd’žê+@Ügp•:1pcÍ0ŝħâĵÒ9~”­="#4|âT - -cJŽ[$*ò 1Ĥ$êzğʽoJ2]V³0ì,_TÄWî^ÙS;ĥÂ֍:ókÚ}ÜÏêF!èĵIËI÷i§ĵ\]î=^͜À4B{$úÜ+óSׇ)a‹Ż^’ğž˜ùGŭ˘Ò„X—³öBİĠ^Óħ>|WÌE…Iuá?Û jç^Ĉ¨#b;ë½C,*ŭÊċzÁ¸ŬQ„$Beä´ÉĴa“SZz´$Š…ȸ¸ÈY2­Ç£Ú^쇘ż*ŻJ#wOÙÁzŞċŠ"ÂGZÀ÷é:jĠı4Ŭ½RrUé0‚3u3žRÏ´ˆ~AKZC@cÍÄĥx‚ËPl…a½ûĦ„39Ì£X…°$$Mg‹í÷ĝ˘µì]UgéP_³nz3+}ÔöjX³êÁ—ŸC]0É7˘PXĥ}ÊÙ{ …Ġ½Ï#dN„D -ùփUÙm×&!˙5}h””ì -vÀoö-]cú›!ŭљï}ÌÖ}ÑĥȁU´áó añŻ‰LŞ|Y¤€áC QòTĜkœ Ú{jcÒKWsÑhü%Óşż”\ oQÌ%;GĦûN@lEÑïÀ;½ÔoaÔÎĥmX²ĵ6Ż´DĤĦíU§öĦSÍ3wGpä„Ye -R,Efä.°¨½ ‰Ĝ\XĞFÂżİÖô–# WÇġŒ">î=1(êÒĤ´ó_iċ1'Ü;ÇĦàá‰Y)>ĞrĦÂFL[6·C<˘;uñTRCĠÉÍиċĵž^Ÿ3\¸§ĤuàN`.;… S9?ħ…¸ÈċŞÄ"İyc|²ÎkñĈ{âoßÒßÚqyb#:J4ŭ›E Ċêè—rkDNë~çZ·\’ĈŠ…h£=ï 2˘Z°Ñ‹Ĉ‰;Mq TJWwìñe£–ÉĵÏ.rÛ˙u(GÌÊ^^üڛ'd-Y]XíJĵ K~ïÀûJB°<ğĴ2ñŜîdĉxÉÔĊ·—˘]”R³ş–´ıVVħd6M’I{óx´!ÖtçZ6h¸N0ĝ+)íNö_zŭ™(u­Ğ;_½˘X“öŠDˆ+ÔmˆÙ­]ôĝquqxÉq_:Ûٍ Q"Ĝ#àĝ|ĉGÈñ ’'™ŝñJ@wv…m6ÖĈ‚zûGĠ_Ŝ2êŸÂĞ’vœĉö{P›„ëv<ì>뀠[U Zŭ o;ç@q*!7=Ş}ä˜ŭo(Ts“Hµĵhˆôt8è!"&ġ‚•7xO_|>Á“0Ÿàä)R…„Ñğ²÷)Í_9C˙v—gIĥ-qżÔ„ÉíäöO³¨LjPòĠĉ“[éÙèw"Ŭ¨e>÷uŬáüš^ŝ7Ö'Kƒ§İƒT&CÒe;½GÚĞŻ[?C G Ğ54¨nQÄs‰vqÜĞ:ıÎXâ!ĊĤž*Re3Ù*Ozf T*È3אX06ŽR¨'ú*“3­#ĉY‘`²¸ŭr°8ŻPı”eOÔċ…Ŝ°h3Ŭvı$‹—ÙĠ Ş2ۍ9™ˆ,ĤŬZ,*>Jpú]Léġš0糸•·Ġá÷üäˆ/°Éœ(qğƒ– ŽÜ Aä ¤ìî‡v'ċE^÷ÙTëïl[ĝoššĥQQhñ?)é–'͊|ĊèPOUg;—ÂfcŬH´fqa7}ñ‡V•İ„i4B–qрyÔŜ&ÀŻ½xxœ˘vMVV–ò÷Ċ’ÌZ˜ŭĵcŸœà3ħIŠ“VzbZFÈLîëş'–ï`²r:v(ò[ìkiqÍ`Ñ%Wħ2CóÇÇ ĜÈ0·›s‘ŠRSZħ¸áD5żĦ‡½ovğüÙÏÔA­ŜkV‚I(0´áM·÷bäÜM*^0.NĜĤó5XX Gw‹9nKÉABzPé觭Œ™£*­=;×&jü´ßc/$Ñ7Š×› TO -ꅂGú/-á9JŒ=ĥ1kXUn`=…‰ğ?/Ú˘Û2ßĞ1”z>y ÙáR+²ÒŻ'ĠIŜüWŸ3ÉÚ÷Á-Xf£cfÀ́ìžӎ‚‰é×­i§"†x­Ĵ¨KKр8\²ĝö¸=×~ĉlĴ°ßż´+hxwÚ"zšÂŜ³˜(ˆ;Mó : Ü+*%f5… Ì)çvcµÌŬèÔäê=K=kożbÂá<™ô½…jR4ĥÜäé•z×÷X\¸œìÙ²Ôĉ,ż((.ĵ*`ìÇ>İ8ĤĞȉџĵ’˜S€EĦZ,?í:ÙY†ġ‰&ĉf‡ÂĊY!0ÛKî–ÇRMF*Ŭ9C(X%I4X³JŭĊúsÒÂĝ’y}ró§ŞĈ`–şÊÒ³„˘ΗLO` ß8½|Ìí„…¸“Wx%ڀÔìvÒOP)U ‡€Ìĥ)]‡,gì|@†V=´ ˆÏ¤1HÂÔ(4óN;P]BlF4µôiQi²‡ ™FŻ:ñïéÜW;ÂßiŒ ž~·Ŝ·l(V$‚ÂX!DàL#rŽÍ›”nzu5ˆäò›… hĤD½gÚ)î˘/ËGÛz˜B¨„Uw·)ìí'¸ˆJ^êè ‘ħşU™ŠÔODh†–ƒÄû}òġ)NW•oO.0.=°˜—ÄA²'âĥ֏ 5ĈŭÏc‰™)Öê#$%ÌÀVô5qĞ "r% Ë+̆NË{p; ·ÀôbîZû Úhğ?`ž½ X02]cZTâm6k?*? ,*ç.ó,½ŸĞġëĠ*C*Nà^hW†'y6ìKûJĴŬ(!m­l,MŸ³Éĝ›IV֙S~~4w<ï¤ó˘dµ™ŝv ġ’ 81îd̎FYñġ:0ʵ­—”6)°2§­żhĦıJWç]AD~ˑ̅4Wġ—‡äi¨µ§WvïÇç‰ Y7ŭĴBY|ŝ·Ê”-™ƒa¤‹äšaĤ,drCĤŬÓù“C˘2[ìî@Ñp³Œg„6í;XÒb<ŭ x;—Ĵu¸´’1U= çT‹™c§CġŞ:k´ĜË kV‘un³ĥĞ™ĵ]ÂÙ÷ŠzFWîǟEIgŝ΅ˆ*ĉnEƒRÛP=2NĜN#B8|„ az˘t˙ Ü8y­\3SXìvúS5QŬÎŜ &%•l.Ĝa>%ĠÌnf}D‰ŭĈé˘[°m0|Â`zˆ¸iÓLb´;İqWÂ(vëÔ-*)¤T…]µ"Ħ?SŻyXşT–E!ñ{B“ĵe -`8pşş›cx‹?ŸÄLûÊ|w˜eF=Psó½GHàÉg‚ĦmWîڏI=,' °Á6˙{oŭğß(‹Yöޘr›s5y>”ËnWȈà‡ş¤ŭúÎM˘·lŽàĵ^‹f.İ+:3ÁqéŠ]‰]HĝÇ%ŭċYŜó)÷òO1Z‚§Ċ:ç=ŭ“ż‰>$· èI£›fĵên‘pjù½#m “}MLrS£ĉÛA‡Q^Óhvŝt´[2y³ZĤ8äxî33”kÛY|TòÎOó3‰÷„ëĴĈC9™ĠHİ~vŭe3Üúğïž ÓIĤ„ÇèhCCFC1µE0³ŻĊ·Ĉ´Ô°Ĵüg yj™hğ^ÙJ 2À€6] ċ|1ÓJvÛsTŸŽôk3Rä'ÇĤHêğfŞĈ3„’ëÉ_ġeoŸżŬAɨœöµlĦÓ’¸ħW‡ Zʞ4ĎL̏'"˙Â,FïѲ˘ħ£üŞUj7”‹Ŝ·Ş}p1öÎĠX<³jUşr‚ù8+)ÄH7(,>aÎÙ°ĝîĵf瞒ßĵÇĤÒ"‘ş„éPP8…iŸ%9äyÏĵ7Ê…éĴÂ/żžġíθEƒ2´ôHñç\ÔMSVáĠ“ċÙ9ʗ ħ2#eQâkïε -ʒmâcŜŸ£ş˘ZSÀĝÇÂ#çŠËıKBÑŻ†ÍĜµŝí,FŻÂ\ŻUù¤ŭRüŝYp)/kòú aU2êċ`ċ°hç— ĤhòŽúâG'9Ò?VÚœĝ™‚í0PÖÌô' ìMñVĵx<Ž¨˘­9)™DcžG‚C)A‰b aú£Ï\vsĈGĥ£ĦĤÇŻ×6`†ĞĜ…MĤi›I…ŜÍ -u 0&3·I -€FAş·Ä˙<İ—{´2„+%xr˜ó…¨Ħ!A8ÍE!ç ~òÏJ§g+ ôKLp²íZl¸z”›€UïÜ/yÖĜ‰ 9ÄS†&‹aAĠ Ŝ_Ó8֖•<=ĦiÉ|ëN)‚xa5Ìâú/²‡˜r*XË\İŞ)Ĉ˜ĊsDĥĝo—Œ&Ċ€‹]ĊÎQ8HxHĵ,ó/A‹¨ê³AfOfµ]=;>w1íâiĠ³ċ‡`+^LuëÙ˘Äİiko +îÀxğ™qˆñ!%ħTIm„ï+ìĝKs¤f™—VGeÒÉV²˙oĊ,úG+Ó1@úI í0íÙ2ë ZC³è\”Çeۖş@ٛìŝĞ eWn–o½HäVÇŜÑÈ^p÷‹ÔÔùdEŽĤ>“Q0lE’È_†âç0jĜ[ÉDq‘–ΝyÌ™ iaò%lŸeè9ċŻĜ˘Ĵ—ĵ|LnĴÀI'‰¸p•ĉ=s˘L[O=”Ù͜ġµ+Ĉc.0‰ê×Ħ@ËyQ›_cw'ËTĈ†ŝN8ĤÄcgCRWcƒĴxK.ë×=]wĥÛĦ]'1ƒÊù>dOê4š8—„‡N2稧jìßáŭR8ÉkmFû7™MòE ?ċM¤‰Îƒ§V)gÉ:qÊçUäÒVÁĴZ -tĜµöŬtèŜĵցê%Dµ£Òò l_TEâ’/ċÓû+5ûÏ#çX﷑ĜQZk’X†–j…§C#ö†JFky•iv1ÚW>£ô~ÇĠ•—ĞvÛG` -X,ˆ& -–ó0°<ğô(?ˆ<ˆzْâMûù *0V -&UĦËħLwL>“5Š-“×}} jF‘˙ĂcğP‡¨ûQ˜DĴÂ$8Q˘²š'a ïÍ!i`ĦĤ pg ˘$’ƒ;ñt/´…Ĉ—Ĵ8 œş%ğÊĦÄñœÓêSÇ4o‰Î(G6"6y8XÒÀıċÉì×üŻ ÖöYJóĝI@y˘Rׁv?‰2]&6gĝ׏„QôĞ[öÀ5V =Oì -ZPQbšè˜6>FY/ñèĝc>MPU̧è“U‰Ï™ä_¤–ŸÜíżI$˜Â‡Ù™Ċe¸….ñ–@ÁÍÌöܔu…Ùú]ŒZ2B}†x|8–ïö1‹˜ëH¤DhZÖö4N²HóχvÁ·ÄÂò¨`)­ƒÚ™hÂ:½à•³=5ĞĈeéȝ×&)ÍÇĞȌ¤Ô2öîpİ´§&żkssómÛÏ=ƒÁy~ŽÏDÖ1ĉ˙öċġ+îWÚ¤˜ÎìßĞŒħ–öǤžPœ(A6 N ìĵ;žġŝîb}ٝ¨O(ġfşq#ŝ¨VÁĦÒ\f3`4˜,Y˨ÂëĞ2‰°ÀѤAœYL[‘Ó¸ŭ¸(˜cgâ›×òX•WrˆO8Ŭ9úuA)/U/1ÉÉé(~ô‘uġ½5˙euŜ€÷hvQ›]GAħĠıÁ!²“*5é`™Í§äĝĝ8"bÇôC€ú˙ĥ!y‚CóĥajrƒÑ@͍ĥ`‘<ĵBŭÍVMӂġúáS [sı2ÑMmİs£—Ż™Žçx"ó„%~o°lû²\}Ĥĝ‹€Ħ’+²@#Ü°µZcż 쟄Ĝô:ĝ@67şâ3ú"êÓ4‰ À‹€ŝ߯(d/Ğq6ÂÖêCĊÈ /˜R°šĜ#Êg\ĵF#°ŽĤq$%ş,&Ú+ôı–RTr‘>6Q*léÙéež˘ıŬÀg,Û[Ÿ•ĞşëàŠŻéòż{%ô 1 Ë9ĊíQ%˜ÒۃeL˙&D2²2Ğú%½ĉ,•–÷ìu‹d™,“0 ÔO.zwcPÉ˙y°U…Oşû0Ġ3{r`Wƒ-S9?m,û¤ÔE*f˙[\ċ”-‡³3­¸ƒġÁ6œ:­ò:ıÜhħL şú†Ï4‚Qĵ§v•1Jç•4?Ó^Ŝ•áíH{Ö µ˜fiÓ?ÓŻPïús#:—û×jêóï äI}•Dì ¸ơ̂*üQçf0îìÑġŻòĈ¸üàCç˜îÂZ7DÙò|1spî‰wÓ792òĊHΏĜċñâÈ:ÄgÄĵáXƒd‚û+{ -ÄıÄï´œúöġ’=]°üaGï=Ó=^+’ž÷§AG$鞏vȆ#Ô¸}Ԇo³vÊ7ëhô†÷Ĝlò }è|¤RÄM8ÂÇáö³ÙSĤŝ—wmċ;EĵjÓ MSUÏkžŻÏÌğ²“lŝ6F[xM/§bÚ³Cá|ˆĤdzù\Kž—Ħ£.cvì9}Œdà˘RT4Ġ-žbi ŽéÓÌÓŞŸCjİÓÓ5$ĴïħL èşiñ°N^ċç³ô^ˆĜği¸]ĥÔÇ -Ĉ½ -§óĦ§ŠÒHĴòòâ‘$>Zd%ĵvO”c8ÈğωµŭÂҔ“*ñ½C×óçÖ:G -\¸ ™rÌó2dˆŬqw´.Û”˘ÁpdŻ½;ĉ`¨h•˘Èġñö"џËüù>H H+-`Mq…ù¸fpÁ”÷Ÿ˘™‘à•iĞwê/e20Nĉ³ó"A”Q…˙qŜv8ġätuTçµ.WZÏc;}F/×vwôN$×;ߋĤódôeÁ~`üĦ…ħŻÂY8­ŽYl/àIS1Ġa6†ċ€ùÒH^ÂŜ°}4M6(óà(Ĉ·Şi€ËKB!š‘_¤u‘Ù3_üağL´ŒtwÚ29b£W£S×çM5šBrŒ 9ŝé¨ċĴ\•;µ})ܢe7İÊP ô”Ŝí²éë2 6Ö²£ïŭÛ>Už“ŸÔÁÚAÈë1oB9ónx> hĉK Ì6ûËĵ* -endstream -endobj -694 0 obj -<< -/Length1 1786 -/Length2 11772 -/Length3 0 -/Length 13558 ->> -stream -%!PS-AdobeFont-1.0: CMTI12 003.002 -%%Title: CMTI12 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMTI12. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMTI12 known{/CMTI12 findfont dup/UniqueID known{dup -/UniqueID get 5000829 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /YRQLNB+CMTI12 def -/FontBBox {-36 -251 1103 750 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMTI12.) readonly def -/FullName (CMTI12) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 68 /D put -dup 76 /L put -dup 77 /M put -dup 80 /P put -dup 83 /S put -dup 84 /T put -dup 97 /a put -dup 98 /b put -dup 99 /c put -dup 100 /d put -dup 101 /e put -dup 102 /f put -dup 103 /g put -dup 104 /h put -dup 105 /i put -dup 107 /k put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 111 /o put -dup 112 /p put -dup 114 /r put -dup 115 /s put -dup 116 /t put -dup 117 /u put -dup 118 /v put -dup 121 /y put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ24 ĈòŠôWäEvçQ‚C<ùó3£‹ĜAÀÔĉ‹ùàë2¨˙·kX0k^ß|™‹:Ù´ĵfb,|=úësLu2ĉKżżZ`3ndgï¸RÈwô@Ó),qñċĠœéG<&¸÷­hï'ĥì. ΍‹883 „½Aœ½BħAÓÔI$sò@Îí“Féù™ĊË25âĈÚŞ,iá™êê pKôœê>˜èÂ6K` Ó%äÂEû(‚ôĵ„(bsÌS<¸RR.L“dğêw~äI‚pH38+Œç—ñ’ĝ[ƒÛaCâΠ)Ż5pô<1Òù'y“²Ò˘ZM!êó›gĞKÖ°h™œ·ëâsé,,*HÚ¸„N6Ş›½„÷/NıŜ?×ŜlÈԏ:ÁñA˙uŬï·mé( —‰ê8żµc˘öDíS6)‡ŻFñ8ż[„e6˘g żÒ§Ä!˘Dš€ç‹š[:–ĠÛTl, ċBq¤FàäŠk˜C£I­SÒ?h˜s™Ğ–•ùèhÎéÚ; ˘´TH½ìOV4ŠÜ{Óm@!ĤĜ£J…$êA "R>D;ĉĉèUĤѓµ""°:!ƒûcQĴMq:(MÒOÖ)·|$~İx!ŒÇA7ux(Çğ­IŭS„êG|˘IóQԏïÍYŞ=žŸ9"àÂÒi‚ñÜ1ĝ½BŜ”Ħğü/?ñx’şI84HérèĤÜÎñ›ÜxF‰-}S?ŝgeâXh·÷bê'N'™68^o€í ߑŸƒTŬ„j£"÷_Ĝ´ u°3S¨[¨žċŻ3^GŒ{½½W‹ĵĤˆùsh"N›ìƒÉäWîħùk´#IQġ†9žÙdİxàp¨ÉY Jğ“•JşOû¤ĥËö(çëUM€aKD×pĥ§P=|#fÙĉÀLäV<ŭJ#oò)Zêġ.À$UŞ‚(¨X¤=‡ıG-<ÔL^s .Üä?#riyXÓšR8Ŭġ*şp£Î òĉıR¤CuĤ'jà?ÜI—ìħµDa’1%Ÿ4’&Ë$ĵînR/œĠĊÙAŻ~iÂ&-İĴgÜÇ€_§\Ô?_Ż·‘Ğ €½lrôy×ÉE]1;1]’—ц·MhÏ^ Ê¤ÀŸܙÛSşçû´#? +c@„fċŽ×ÀMÀ´d['!%eü·ÌXŭ…JUû?²‚ŭf9Fe7%$‹ Üĵí΂ȉnb :–ĞDëĝ8˘M EDċ4^0ü54˘ƒ4·q¨Í¤IDŽ]­´;ŸZ[‹Á˜ĥ¤ŬĉIm ²{ÙÔ[νÊlq<*HĊùÖ"fŻJcu˙` ›Ĵ8 -çсœ˙Ó‚É^lpĈ¤ŜŠğBċÍ]‡ - bn=ĥ—‘£Ž˙Š5}ƒ‹Ô+Ż @ˆ5‚,ċ[ŭbaĦ´x½ĝ >Jkç°ċ%_H¨GòM %4†ß´à -ôDŒQj§YÛÓ1=¤šêKˆƒÊ§HZĊ̛wOȃ£D™Ù„6™C“!8‹]êĥg,cAÙÂœoà?îҞğjÁù?;´IĴ AG¨âYPżKKɧÙ˙ıèBòs_ä€ÑW9żA‡ŻD2IEßìŭWöKNŸħ*3iA%t‚‚İ  Ğı.ox á#È&SşhD"óĞ5{…nĈ‹ö¨‰%;{.=:‰ÙŻ}]A“„éú·­Ui ĝ=‡öŭ¤.:âÖwvï˙6 <‰nù~?VÓ+€êɈŒ—ĴÚ8‘ô°R rŻmsri–4Ì0X“gJÏ~ĥû˙˜Œ”9ĴH²‰)ŞGÌ3TAÏ3c<;ká \ü"›Ĉş -²"9† ĠğWB7Ş{YZu„>µ]Ĉ=•hÛĥ‚µŻ#żÜ×µ’ËïN¨ôÇ=Î8gkıòS^èZ΂Íd ²xĵ瀎Zóê ÁĦ>BÓ/ngš´Hİ$1'F%!q\¨˙´ûsġ™g ,YÎġÎKŭXáò×]goRw~‘IÉip¨ĵX4_ -öAë6)Ā_ħ‘ċŬB&m²VUġ²Û=J§šŠ9ızkt 7Œ×ôn‰/N+u'ábƒr$TĠ47Ż.ÛÔ\I0Jh>Ŝ)šQƒÔ°[‘]"ħÈû Ĝ ÚM§CƒÏĊ•çÛ͆”ġ³ïUìûpüÎġÎuĈË şkÀĠ{Şn͈èN'ghhs §}N–“ĝgü*ŝ³tĵŸ×\§/‡j4êpĥ‰'À°Í2ġŸü/Z{ÓĠÜ{5k°ÒŬŸúó…İpĴ˙†ŭŬžP% ?CÌö˜ 9ŬÁAVôpzŸóáÉGI€%ZXcJ -ë­rxĈîûgYNĦürf´cwä~—­½ƒBŞ?BĦ¨&&tÑĜn^¸ĞŸ‹pÒúë´¤DŭF&IÔÌòxÍeúš%ìcÍiï -â…Ğ5у”<÷™Â˘C0CŻġ'š–ñ†À–\ÉFĞÖĦŝäzğĈ[ÚRĞá Û4]…=ƒ†Ü)èE`˘•ÎË͞獨YI!J÷fn:W£]ĠĊ—kÎnI#‹j"éŠB†BvvÙÚĵuF÷GN;-ÔlÌK΀•i(sÓl}˘HGĥo1äÊLzċǝ|äS+xb‚s*e3 >:Ì× ŒFN½Ĉ‰U˘ĥ†m -³˙ġŻC'ì]üÜÉ&Óó`™Š‡W‚ ÇV’ òóËkĴm&àŠĉ€·BŒ@ €ÎϛÍ&ÖWϑ/4 Y^Oû‹ż `n¤>nR–E_l6Fì÷Yn³n·r%p7Óò•Ü}½%|ÀUDä¤û”rZĠ/é,Ğ„#NĤ1ÜHÂۏ.‡CŽ×M‡n)¤ößîƒ7²Q7!f‡óŞrɘk×dfNîÖë÷ĥ\÷oË-–6äżIʨô#Rw\CǛêâqïúdáû÷†*~)Ğ]ïZ°9“³T’ĊŞĜÚ;ĦŸD àše‚ƒ=Š#RĈĴ4WĤóżÎ>£L†]üƒÚĊôóÏ -\Šµ’égĝçê$2™ $ĜûmèÀ ‚ -qĥï¸Ŭ£Aqdƒ£uĊç™Ë5BñíĊÀ爜ÍÇĞJaÑ)Òżß =ä['…f İR}ĉ]ĝ†<Nâ½ zĠ×)#í0q·Ëğ‰G32‹È'j† „g&gÚŭ½eġÖÛÂöAŒúŻnaĦ>Iû—\R޵ʣ›Ç8ùŒôß­“›uš„à4'tż‹À ²$qi"—ûgġÔE;IàÌĥŸ(˙ÁœáĈ­8‰p} ˆ²Ïʳ½)^"rê¨ÒíÊúÑtS_V3Kh9•"œì$ĤŠĦa”'m§½.ï}Ʌ9úYħ¤éۖÏ~˜-iBüúŠ”ġ*+ëdခXR„ËI Zò‚Œ§Ê3FF§NèŝpC)1*ùìRV§² -jm#X‡ö³Iz93&;ÎvNT‰ÉÒipĜ q×s+;2"ĜcżÈYĥ>›'ŻN9sÇgÍĠ§Ñ¤VKĈċ… “j_ÁĊEĝڍ…Ĝ˜ •t$¸/ÓÓêÇîLڒÔb1€ĥğžö˘pUG&%î³Yw–ħĉŻž|¸³3Ĵ L[Ù˙NáÍF½LÏ]eE…ž|ŻŭşeAz„M˘ĠĥTâÓŜZ<:˘É,Ş.Ħ$çSñt=¨SjFĜ_pEâĉzÏŜr‚}B÷oÇóN¸Ç, y^`òĜ*3M”ğeiĤ™x £gB„ÏpC @m ĝ½Ġۂ;;’äuéċ­0-ĵQq3ğC?"ÇËŻsPĊBv…ñÛßeŸb^úġ„~ÖĞ)™–ŸZeÛù–,˒[ -y*Ż?ÏŬ³’EҞµ/_ÉZNçĥd“ĤEc"‹œé{İşáu3JnïÑï˘–ô5ŒÂkuġíL¤;[~™d("pMÏK¨ĤK•j‰˜›uôËÊAbJ6¤­ó´Ëvït-Ŝû‰*fŻĥuġ&é%¸ä‘XR5‰KìŜÔİ˙~½ÀŠƒqB˘ŽœŒ×­´¤Á(E:‚&ú -OĥÊġŭÏì‘ĉ.ûVX“@OcÖÛ` ˘¨&‘Ĉ_B­tüž‹OgRŝn‘-ñb’sê),+É{èUmځ'˜nĤC)‰là,ÄŻ&ĴLŠŸ UH˘u™ŽLUÁ'Jl6t:hş]ÀĵŠA>aRı[т8ËżĵÜN{ï’ù”f?£ âe‡=Yñ/ê÷„wîĜĞ#Ç·ïÓÑwì÷€;ŽŽòǝo6QlEs52€™p[żĦ cï$ìbލPͳĊ‹¤3sù9ìŜ1Ôí}$òq"áP҉Îè›b—o+ĠÍŝFŒsv-Ó@ê\4Û˙­NmP)Xçö°ßŬ˘żğ}Í_4hohF 9“C]X'ˆp€4|ÈËĜòŞ:aB7#K7ŠË²nä÷ê•"ë8³€ÈË1Ÿžè‡Ü-{ Nò–;td ³*a"Œïzj2aMŝOâħ)BL# ¸ {ÛjBTŽ3²9UŽœë­tşhµ3”~GRb¸8`7.–A olT"·D+,K8NJ§ÄòÑŝS덠ĴMÈ`'MX·ÈèN4°£v‚ŝj"é'ÒLO)³›CìÄÏD)9{;IJ=i}ÔġÔħRoœFú·Šŝ81×~ùÁ’Sٔô&E;9ѧ+áÍŬ“,£6JñS³{2ñŝŠH×ÚWzşIpWè.u7…p9ş2Q•™Ŭ޲‘P²–2¤˘ĵ^AÎëwrÍÍ£NĦšÔġEŒÉŜyÔĝĜ×ñ|âĉÛògq•¤mWUËıs—* f6.LK] 3‹>…MoUġÜs´ J77ĈŝÂbŬġÏ,ó”ĉ$÷ÔúÜîy…Öà~é +ô †‚†³“,¤hϖ½qzĠêtD‘•ŜFkïtŝQò!ÉQëBl(ĵÊ4“ċ>Ŝ:ƒhŬv­qúÁ÷IŜĈÀD*ü7W¨Ûä5z§G£ÚòsİĜñq˙ċ\X7vm£m–)NkŸ°Hêġê7Ì:úT\ô·Fná8ùĠĈàˆëżŒ!ˆƒÇ÷J„ ->ONZ ˆ - -§a8Ĵ™"è5n ZÛÙJd!á‘àÛèÇübŒ6`=ÇԎ -Ím:3ùڑY–K)yhf³gÍhÛ÷PA‚ŬÛc'ĵSU-‘|—G³Á8ȓ|/Ĉ"ğÀMK­kÁI ”™Àri^€Ñ{jD<Ŭ;p‚´ĥ…zŝjAÉ#‘x§°;êè|­#`‰Ċ'ħu䝈˘AEG™²žn 4ċy„h…ß ÎÍ}4Ôj¤iċ׈)BAlÂíó@7Bĝ§hy‹oBĊbfĈâı\ĉê8—GSž3’Áœ­ËŒ€‰öNŜµdX,´{4@ƒ&Uİ.İÇ1l&žP½K ÛÖĴQ{m×'ü‡cĝ‚Żá%usr6Ïş#°ó!Ÿ˘‚ĠUv -.é-@‹ğW…ñͲEdqş]VĤ—hR­.fdŬħŽogr3xlیü‹÷ú·ŽìqsĊĥàÜ#ayé•úŞiíĜ4ħmwLD‚­&YÌÔ4@ċ1Žïw*ĊOŝÜÒżĊ,=ş+ĵÜuʁUàÙù]£Š2hv‹~L•1-Ž -œ·èQ}fâë`gEk`Tk%猲3²*’œ‰àЏ‘J]I\Ó·7Ñ0´ĤaFÖÁğŭ‰jĦĴ’“½&lyz˜Ìb&wçGĠ]ˆâpßs4nvı¨_$2^š”Ĉĉ ċħ½§ŭjQĵŻ)&#èßq˙„öˆ)ż›Âbħ˙„÷ĥ~îè„9ŭéìĥšĉ°Mƒh`8şJVşħġ߅˘EäÌêBbĦ|ÌİıU´’aÒÍ_|›Á Ùë8 L~­Ò·VExîwŠµwĊĵkif£8gÀ„xm(‘ÁÂŸ ->½ -=İM€ÛlßT¸?ËÚyĜÒûĥ=áFáĴ .?èˆ$W!Ñ ™3ZñŬEŬIW~òàèQŝúijœğIo¤=uB\aÈÏì|>ĵ 2Ĥ ôÜH›9Ç<ۚu‚û£Rò–wÍ9ˆli·Yı˘TVž'żÏg9Şj3e"ħĤÄoëb’ -3yĊgžŒñÔ7{6×›„—™PZ9m TÊ$/ œÀ/í_`ġɗ}‚pü6áV ŭ‰à AËH\éÀ Ü0pĊwĜ8L)R ³éÈ<ìb³^Ñ8ĵ9ž89à3.ÉorX|ĦIJĦ ²:ri}fÀ  ¸”x-b' PqvŒŒßϝ4!ğ‰6zj½I$èŸP8Œ!û_ mĞĦiši1Ĉžm;ş(àÀ×üŬú?3ˆ=óJÓŭĴ&yżß6T˜Ô1·ú,Ù•c[¨*Qì£F›ïµÍˆ[Â˙ŝlƒc-àğÍ­•é´áj˜4,EÖ5* çŻŝ<ŻŞnJÖ Ùħö!RÎaŻŻÉ·wûËÑsb9<ú;É@⭃ħR b‰'a“½zħ|÷d€3ÍŬ_C˙öÁċ4…J'45™]ñ04CԉfÚu°¤2·’M EûÑH‚ g­]x,—Î$}şŸ#cßɧİîqġ—sLÓĉsS‚<ĝG7ĴA%ŭ<>1kävu-ŠyŬbÁş€™ˆzŒ #N\§ˆ‘m¤Fl˜Ÿ5 „$(wÉfš$žùçĤ0™ŽŽ! âZa„Zd‚ŻÑb1£áÑuœ„ı?߂8Ŝ?n/ŽWıħù0b¸;Z÷ĝ:‹yúèuúè%mŭÖ'†€%Iĝxp}ÎĴÇëM†°ġĵ a:„ŻÇĜçÄÓò½œylfß²eĥtÍÄÁ¤²XTwâğ~~"TuÓl) íì´-Ĵ$RKŻ  &kë—½PAèß³$â-äĥ•4÷ÎĦÌċ}ŒòÖCíp½¨j4álĉêâşùÛNŒMp ïkĵ=İJ’#f8Ú$o 1w`ut[72+üöZ­+ÛiúPùfWÏ\Ç_ĝż³rh$Ż)ŭH€ÁĝWDB-7mgò]Ğ CÎWǑUŭ ’5É5BöċÔKáä áÑ óĠÀSö+]ZA}˙‰Q‹öâĦ‚H1ÖY;d%•{zÇ ĞÛù‰÷]l Ĥ=e1 Že÷²mnŬWbGh"¨šŻZı3HÜÑé%φN‚%J\–ûéöU` PHQ”²âUÀ}A} -šRWé2 ´ ŝáĵwġU…|IzÌtßô:şƒ`i/VĥÓ{Èô!f?̗ĞÉq§òŬಠ- ֑&€™xÔfÀġ&üĥùĈ'ĵÚç‚ÎPY;Ż.,8ÎrÁ#ûŜ¨HBÁzZħΓîĊ֜’bÏ1ħúÔğYú~mŜÁWzÉÌegİûÇó?IplF0:ò5w;ì¸>>GkÇzÒۀb 1èċÎNż‡Ĥ4Ê~‡_Í;~ĴYÎAŸ_+)Gd–żñ=îƒ)C>Ó:~´lcj ´“×ĠFù({îE€p#Ċ˙Ħš+;Q.Išb}̀YÇÊV!ê–…kċBà™Â2* NàÓ sğ&²hžĠʕ™×2ûI†Š‹L˜Ŭcġôëz.Á\'lçÌïIžÌ÷Y÷Ó[…QŠsìÉĜ£ĥĊhçäŬù Ċ~.™QPdÙÎ;qêY‡™“¨„ä ꅕ÷Dż˙İjıôgúE§H,O{ÂÑ?ĥPFšގ½°ìXĈ1Í@; -Ù×E¨_ÁO·Ë\KêÒ !ïr™"†…½pĞd+ğšXA˙‡’Cúۅ û,­úë:ĠĦŝEz|tpħ×Lú ·q o‰ġ)ĜÏ.B²Zĉ¸’aĈSpĜ|¤nêlžT‚vW „úÉ&½ìç3˘O‚³=íŬh†h.¨qî2w:üŽ²‹_ñTrdñŬ\ANníĉK£‡×&öêu<ƒ_Iys\-CBĵ§0*b½3÷ÑPġ˜ġúµßlĝbŻuÀ1Ŝw"I~ŝ&ÜV|nF?B:i§×œ/z‡!¸”‡Sès‚/IµÜtÄÍí!-mĤ~”a|NëŽÜkİ€#‘‘Œ–…÷kŜ5_›p­Wŭ+bÓËNS✠ñµ†ÁÊ9ZS ÒGİ˘^†ßÇ -OĊĥ=pdúNZ/ ~òùÚë Y/6Y|~žĈvèÓ&ђ˜k{à·İ×ŭ°dBKv² -v&™żİmä“?W‹ù‡ĦE÷•*ğçxêƒVċd|˙uUŸSÓ{Ó>xh_wÍn(ùH‰Î (#4é ³tòaEħ‚éփ½¨´ĉċ5b:w*ÚÎÙ[JjċL‡–>Ñıܟòki8À­p,ÎܸŻW”ŝPUċ(ñ°â‡Ĵl#7S;y)ħŭÉ÷TÒMMŞÀO3]‡܎İyĦé=s§ĥ‹Âîŝcò–L;·KĦÉÊíPkÇG|Ħ2Bc{lA÷ŠàVÄt0L›K‘ÁeÂóċ5‡dD¸ äşĉ›’´Ë•´.K{/& -ŻG?ü²í…‘§Ö£­êÑöĠôm¸ħĦĝórş$>‘£GÜ'Mxô™ş[Ĵ{²4ż“™ŝĞ°YŽŭ¤Ŭ ñu ŝJߨgœĈ7gĈĈ  ˙c1ñŝ! ûŞ*œïÒ=Yŭ:,+ċĈšëŽDlRTâĝFğż,`cşcà = ĤÙñDחı„MÔ¸Ž­Ç;Ÿ9tI†÷›Bö,c^*üĈê)ËŬglï/’™Ğàuû˙9³„‰È’™†&ì.ìÇdc%şòғZû ÓïġŞá‹ev>² …’hË“ĞŻtŜ³TğÓ?pJÇ·qšk­S7ƒ[ĵĈ¨_Ó ğž -żiġĤÜ -f}3¸È.ëKQó§† -ÙQ$­˙?ڝ–Ûœ9AZÙ>Ĵènd ›>m’Ì s{6%sWßXYTҌDL$°ıjdXôÔÔġz.ö„]€XĴíw‹ÂLééÊVŞŞ&FşX‚áS¨NcWÏr2ŝJC(Ġ?Bßµóg ìĝ•›Ë“ùµxóQlٗ¤ĵíäiB,•~ò‹f­ĞĦ5ġp(}Ġ#pħï -'àġùÏ\ÜX]ıŽ\)dµħüBĴ˙„´uC9ŭUŝ>ï6ŝeëʍwà<ı5tn™J“Gĉ2ŝD6ü¸ùH‘VìĤĤatˆžwµLj- c!°j -P~OPŻ{H°ZçĦï•ö½XœÒW<ÌÍTjzdÎB?ߋùf–ı"ˆ^Ÿ°eÓ÷˜HW÷÷´@à#Ñï|2áÄ:]^1BR'ŭO+ ÏEHd0Y@›Œ4׃(aIÇšˆ™GyF€\<üürŸıy2xòNïTĝ8y5ɟ#é¨Ċ×]8%ICoQ!o ùmœ‚ -÷Qè!šÓG°/[Ġğ ìŠ;CÜq— ·Ġ¸‚¨+"+-‰Í<óİPïĵ$GÖßt‘I&`}µXÏ9-éÖıŠ1:èEpUŜŭòžŽÍŜ‹šĴ‘˙kÏ(4h³öGpAl ĞŸ}ÔÂFÒl…Pfƒf€ĝOÎŭ`C]Lu3ŝċ9ä)Ë£’weZġvP‘ì%Q΍·Â{żôëIƒ› ~,ùZ‘´‘^ŭoMÊĈ&Û=̜=Ì%- ĜԈŸDP…ĉ'ħVP0ókê²ïjwñkğÑ nÇà ܎ŝbĞœĦ×P2,rŬğa²Éà]"sÈ~ċž{ÑR‚Àdž×SSqVŻl²i›eÏıFdL Ü7Mĝï+êFŸĤO19ġ•e ĝ;‘ıî„m´V¤…:…cÉÛ·2_ŬX~<Ĉxt.&¨ì¸á}ß?êÚr`:5Ušó7˜aiÇû0êkYġÍ+ôĠ`˘>mÚûÏ:/37Aé=a1éJš -˙ ´Ŭ–M?m„1#€ĵ%7Şáê -ŸĈİšž…ëDJò‚kDĈ.Ngmˆ$ösp B2!"!MNeşúV”n}İkç%6À·äL4L+?J%èÒŜ³ÀImZġTe§}ċ;’³ œĊ_Wa}ŞÂQ5ĝ%ĵÌjŭ WJWĤj„ö܊ç)5sM”eXü9Ç^ŝbSuò°ïd]ô7â’R)›<}-ö'dmLrŻS Ô1WÜÙ8eŒr(ŠSŒï5›:@D…°n’pżÑòBO÷ì˙‹À]˙Rġb_ĥ£y÷1é'=I„0ö< ×xDa×=˳/AÍpÚDm/}l{§ŒÇğċUîğYˆ³6>½éËwš"Fŝż$Dçù3`ízSóß³|7Œ&ܑü‡nĈ‡"VĵÂá÷C”ämÔ‰—{OZfpŬe% }µ4QÜM„‘˘e.>ÒĽ[Á¤ğ‹z\Àäċ]Pû2Öu„:Xltû şĤ… s€”."ħr;yÀ5’”Üòƒ=_ü[²…Ü?‰K$;ĵú‚ ˘wëò2MJG:!Ż½µıƒNÁ\ YfšA5Î_ıħşç¸öxƒrÌññ{K€z‰Œ “< µ_ŠŠF‘ÛQıG_êV8êËeŽh,’xÄĠÛñَĉ´D.9k,uŽ’Ĝ:gÁ0ÒJ ¸D ‹d‘L×[ò8Ż*ˆiÊ5۟=\ŠÜ[œÑ*şó.³Ş zÖÓ21|¨rĊ ÈòŽŭ˜:ĵXU³ÌIi"0&ĠlÓĝĠìĵyñA„ëÀT3tyu}à)SJˆ… í0ûdĤɏżzBÀëÙÀb…Äfd~ŒI2ĦešÇˆb?ĈĉH ,w]ô„Šn½˘·@Şdî}~ĴĠ ½ìÌ|O<ÊI -ñBÛp¨lx[ĝB#ZááŞX.+ -Ġ !êS)ƒ™0!ìöĊ„ dHĥ h2Ĝo=ƒ„öS_ôIÑĦ>E³Ï•,>dÛ4Ï+§„×íü[F-şğoÏg1­ jü‚îĉ!` ĈĦ6żs{ĉ’T IžÛq34Т˙c˘“„ĵ0.8J0Ë8™SÀ+G¨ĝ?È'݇’8öëêPhŬĞe(ĠBëéó_ŽRĴ¨ÌmôP{8IjŜ -0Ĥ”9(@ü;rv6P™\šŜĝu‡3HÇ Äi6¤vDn4J6ü™!ÉÄ4]Ÿĵ—`ëĉ˜Êe„3ŜœŸp¸˜Ž-êÛŽ{ÜM´ÑA P@JÍ!eƒEoeÌÇ3t6ÒġÁ t‘C6´âH+Âò ›:~f*Äġ­.Îf›âÏ3f‘fò˙ÂfâÓxŞÈ*#2}³ì+Ħ⛠QpžİۚE°Œze=ĝ ~ƒ&ŝXDXé™]DŽ½ĤĉEŬ<ñğG*È=Ħ2ĝhÄĴŜá -‚\8×8|Čë× ™ù3,ş<™î=ê<Ŝ˜wzÌR†„,™¸tü ù˘ü?œĦÉGtDĝ€sĵó¸ŻoH‡jËÊĴ Â+ĠSĊû‡÷µ‡ ˆ+,²%.>Œo뚀w&ˆ4Ĝ…rĉ0Ï|eżP\…\š°˙ ż‰j½şKÜ#9{›ŞÍáTĴçr$IIKf A„/6ÔQ˙&Nb†½WġfäAB–CĜM*€`A¸,^ÒĴ,ܕ…,³§hĝ²ì t­ÈIT_qĜrÏ*ÀaÑÁNëžÉ3ŭèv#|&€Œ -fv”[\ÈßÎù?8^GX}C×9֔½ĥ$™Nr†Lúš³DTvV ×tœÓÎ9Ë8U Ħږ4Í[DB‘^Ò5‹—úiöĞ*œq-Eá@ï>×Ħl*ĴäNyρÂ~ İà{ç£Ĉ]hĊ Wj62C3Xëċ ŜżŞ‹'ĠIĤ×ĥÎ=óiûÛN: -àŻmfj÷—Ŭ[-⍃~oA—u›3í¨™9Qğ²:אb?°jjòNKÇĦÂm5 ħLFq÷Öñ˙LQşó…cˆqÄĞ€*,–w`1Sĝ҈wdP µ´ ôĜ³Ż fŽïşUôÌwù&”?☄ÄŬú#ùÀÇFĝ0§ċ佃~LNĜ !?žÁÑÏûî >evĘÊ*êü_V…ĞWöç\7Ċ„„ Óñqr µżAÛ;=ž§rm£ÁĴošğĥriĴ]ŭ%f;•Ĥ}!sŸïİîM#Ŭ=8H#Uĵv–ˆ|–|ôÀrEl,˙^3T:ô·EEoIHĠËçàÖy<&ûQİMáäܵòŽ$Ç0dJÓÖĊ_şó—şihRà€dİTġIží8;¨ËÏחڭ8lŬïÚµ"áû͓VjbwÜ£äPóVÎÄÒ^Í:jû­ߧ˜"Œfò`ġùĴfó×-w’ñhŻo‰ÀÉ5v›\P…ôS -endstream -endobj -696 0 obj -<< -/Length1 2769 -/Length2 19845 -/Length3 0 -/Length 22614 ->> -stream -%!PS-AdobeFont-1.0: CMTT10 003.002 -%%Title: CMTT10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMTT10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/CMTT10 known{/CMTT10 findfont dup/UniqueID known{dup -/UniqueID get 5000832 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /SBOMTR+CMTT10 def -/FontBBox {-4 -233 537 696 }readonly def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMTT10.) readonly def -/FullName (CMTT10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch true def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 65 /A put -dup 66 /B put -dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 70 /F put -dup 71 /G put -dup 72 /H put -dup 73 /I put -dup 74 /J put -dup 75 /K put -dup 76 /L put -dup 77 /M put -dup 78 /N put -dup 79 /O put -dup 80 /P put -dup 81 /Q put -dup 82 /R put -dup 83 /S put -dup 84 /T put -dup 85 /U put -dup 86 /V put -dup 87 /W put -dup 88 /X put -dup 89 /Y put -dup 90 /Z put -dup 97 /a put -dup 126 /asciitilde put -dup 42 /asterisk put -dup 98 /b put -dup 92 /backslash put -dup 91 /bracketleft put -dup 93 /bracketright put -dup 99 /c put -dup 58 /colon put -dup 44 /comma put -dup 100 /d put -dup 36 /dollar put -dup 101 /e put -dup 56 /eight put -dup 61 /equal put -dup 33 /exclam put -dup 102 /f put -dup 53 /five put -dup 52 /four put -dup 103 /g put -dup 62 /greater put -dup 104 /h put -dup 45 /hyphen put -dup 105 /i put -dup 106 /j put -dup 107 /k put -dup 108 /l put -dup 60 /less put -dup 109 /m put -dup 110 /n put -dup 57 /nine put -dup 111 /o put -dup 49 /one put -dup 112 /p put -dup 40 /parenleft put -dup 41 /parenright put -dup 37 /percent put -dup 46 /period put -dup 43 /plus put -dup 113 /q put -dup 34 /quotedbl put -dup 96 /quoteleft put -dup 39 /quoteright put -dup 114 /r put -dup 115 /s put -dup 59 /semicolon put -dup 55 /seven put -dup 54 /six put -dup 47 /slash put -dup 116 /t put -dup 51 /three put -dup 50 /two put -dup 117 /u put -dup 95 /underscore put -dup 118 /v put -dup 119 /w put -dup 120 /x put -dup 121 /y put -dup 122 /z put -dup 48 /zero put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ=Ó%ċW˜)-{Ùr½uú•)Żœ‚ßröA•ÉÂÜE(ġ@Úŭ{ëı´‡ş“Qğû|ü_‘RÑċğ -ĜĈϤëA³Ċ -T@ĉ|ŭq|VkıżJ% qu8P˘ĝwÄGx³ĊŞÛ̆ÖċQĉŻ6K üŞÒ-UŒ\§Ô%ĦbĠ"t-*xÔġöÓŸÏ˙J‘+ -}ì3{Zà2ŽùĠzŬĴT2sÀ$ZġÌÑ&{Bè–J×{¨ĤŒß=מ0).ßÌĊ|Ëż!í:[LI0lrÙ9GÌ$}ğ³/X œċS`p*²pë×+fwwFG˘O¸ĤÄ^ĉȇ ÷ˆr+dMvNy{ĉáÙġYëġKëí²Ï[zÊ[fâ -âÜ·BŬDŭ‡q}Môĉ8À|¤j›İ$ħ{jÏìpÓxĉxS½ĈĞEîu -¤•™¤šĥ7%ɑġħ4\ Ż9ğb \Á)[ÉÚFUÛ.qñĉŝ4íĦÌZ˜8Kûzwwµyl”ÏĤI5b·jc‘íZĴ™Š,“7Ÿ¤ÖÉŞKħ:ĝ#@JÛd@ÑğFìÍM‡ç÷Á_ŞĦûd#g+²úë=·è>ëŠÔZ‡a¸·—WŠNġŠH5Y/ÚìÜ .rċĴpf{0DÀ|6@ĞçŸé;]ê/Żh|Ï.ĝ§RAŜÉ°KÔmœlö^Ü&W܀‹ŬÇ{·˘ŭmFÄŬïН´—żÚĠ™É3FK~I†7@T7AÜMûOPŠ.;ŽŬŒHÊ+i†Xħž;}²’ĝžĉjĊYXġE×uĞĵ£5ÇğpېBIĵĤáĦŠS üİ 7pQ½40cH™ÔĠ4u[ì wY½–šžċ2ĵ[tÒÉʖڣŒ´œ?hô™Š¸bœáŝ*Ù$€ -dĈ`Š$ P… …›‰:"‚ ñİ)Žİ|UÑïĈİëŒfùĞDµ¤tĝÔd—§ =Ĵ›œ5Íóĵ+ĥ¤îj7Á%ëi@˙—âÈ)шËT/qˆUÜFéħ÷ı1”tEςҷŬ˘@ Ñ˘€1£²F^R?–-•òÂĤq„^œ!ûŒ*1gw÷ç2ÀĦ4/Ĥ Ÿ¸3ż@Ğâ\°7zÛazêÑ1é)‰·.à™ó‹Ex‚Y'şÈŞ÷ê5ˆFc=nj2â½ĠÖcèw1 üĝÌè3€bŸI]‡œŠÁy¸²:ŽÌä fÖĦİÜꋓċêñĤû¨fgì%żpĦûÑ^`´(•­Ó'm™ú K'KâÓ '>ŸœEàPN,:Mè{ŠS3G2R@6\Ÿà?-Ġ^X'€ÛèġF.qh˜÷YŸòûl‚aިwÌÙNUpͧ`­­ôâšM9ħä_JgÒbw!◠ÌĵsāÊTҔ­DÀb‚É:Wq!]iĈĦwğ“`˙è¤İŒ'ċÂ`àh^ TTIĞnH‰eläĥ˘½Í’òŽ÷ `Ŭöց˜€ö×Ŭ '¨pˆß(=ĞY1ıĉöЉ UżÑĴ¨/ìOúT -%`&ì{„(KĊ:.CìiÍK9˘żxHĊ-vâEüÔ4x_5ˆċ ÙşüŠšÄ,ôž§dâl5'bËbŬq,–Hö. O“°è8Ċá NNn÷ZÄGòquÍ·ÇħÖM”ôÁgûéÔd/.oí~*Ľ–áşÊżepĝ˵ -1î²}o€Kì(–ï{AsM`?  žµË}|òœ¨^ÒÚ§(ûÚ1żvŸMXüĜAj!Vóƒk5=êĈ&›YĦìiÙwó†Ë|¨†vCŻ‹PezFħŜé`FƒâJO!ÀĞŝzĈĦÇ£E.)8£Aœt`+—ÎoêÙê”­ €ƒz`ĉ!|ŝ­a*ÍdçU ).tIhq‘×ŝˆ*0 qħ€Ż>ç„NÇU Ċ3Ĉȏà7Ā9Otĥ[3|5r0óıpĈĜŝûĜ8ߕW˜qDLĊ½ĵŽ{Üí`²“Èdw”|ׄ GJ˙z/·œèH'Z$„‰Ù™ĜMΤ8¤àŽĈZ̈Ž¤<7ß{ŻLpŜ÷V)%áèkÊÜ3ƒ„ì™To¤üCn}4>·Z˙rÈ°{ğrÁUZ˙9EŞŸÖÔGáu‘49Ú>à`oqÍ/‚¤á~éx▏S…|œf9×Ĵ?ÀXñ.uÈBxfGbEü.wW;û…™o,À BLkkKµ{9fggü,lé|Ğ&ĵ€ÒMÈa*£Ô$ö‰żv#Üĥ>ì7UìcéÍĥĞ'·‡n¸N™Î1ŒšçĤWŜĈĞŝ¨Ù˙VÜ İ˜Nu+9˙Ú47‹yG(ÑÂŝßß ¨ ÂÀŠ"­zÊâoOÂ_”|ĴcZŝzB¤ĉƒ@·Z€AŬùà@a£ex–ċb?ç>"Ε˙ÉYÀ…ïîœÖ‰éTĤgB´lٍ9UŭFêJŻ?"[p] ÚÊpÎhŒĜÁ ÎÀ’¨ñ†U8€ÏĠ“zĦçŜL†?³€ú“ü:K‹;ġúĦW˙%ÌX”„ġ$Ĝ‡:bÉ9p´F^dšBÎÖJR(6[-T*í4!œÑyY`'Mµŭ( ­ŻíÊMĞPA#Ĉf‘€T"fŒ"?e÷—ŝX§&’RÄEÇë ]¨2L€ê†Ä6 ñ?h)8&Ì/Bafƒö–“!ş0ˆµt·M<Ċ‹X0z½1ß$6$·}ûW<ß1jċiâ76çŭ$4ħe°´³ çİLċ,vÎĦTuQèoı:Ŭò=ñ}µE´Ë¨(SÊËÍ0.“żŻŽ1Ŝ) dû‹ƒ#óÊIÍ;ğ€P]½ÉµñıRżŝ•üè•şI,”"È?›“öbBŸÏÎÈü×8|ÜÛGϞŜŬï\;şH -nĈác2ˆßŻxXΠ1!?:àáı–ċt#à?%ıÑ÷•g„ŠSże[zšŸeͅ} Êßh)—úDì j-ú…„ÄìO„6vġzu¤@bƒ ‹Ċ ix´cĈŬ`rÛ&rÀç IìꏏÚı_> 1SêSdôċY$î…`)¤Â­ġÑÄ×:Š] ĝR]FITkx›jgbžH“d.(: -ÁâïĞœ.Œ—%¤pqżŞô>Ĵ>^ézx,Ú{^’Íc]r›â6o·†µıġĦÈŜĴtH“TÜCŭÏ× •O;qâ]8ù$y¸·BˆoLr €{=fÀĥĴ$' FĝĊ}*ġƒ%ù*‹úŞútds˘›CNzcĥğš§û‚5G~ÍĜ¸že ê2‹ÔdĞŠ]bsz'żÈ:ċÏaWA´Ş™>4+ -ŭĤ5uß=JTòú­“Hˆ8¨Yá·n¸Ï{üħ-ĵĝúžt˙Ò}Püì”tĢ§Jx³•8×ÈÓRÛá.\{Ê`uŬ˙[ˆµ§ô%éı3Áˆü…7Â\Ġrn‚†NJµêŝ‹Ïò™ŭ F­kĴ² ³òOjż—½ßÚĉ+´WeĠsİMĠV—‹)Şĝ˜–óÁàŞJñYVñ˛8´ìÀ1Áŭd#JL1?M´È?"Ċ›b§ÌQÁïıfc·ÓŸr´½Ż arĵ4דĠ@ùdŞ—Á”çvŻ5³êşœ5eÄDfR+·c=Pi˙sĞÛX‘8ŝšÔmm‹€šÛ;E­ŻLêÄ]œH|­S“°ħ‡· #ġÈżż§ĝË´§ċç°ÀğĈŞlçġ²ù™ È÷¨ò„S6ùŠĉe¤îÁż!3€BYTg˜Úħ}TĦTa˜Îˆ‚ˆŸĞÏf›ÔgŸĤğÔŝXĤ_+t”1Ħ2)AÖ{ߨĝïcƒ×° ‘ШzP*QËİ—S×Rċd*çlNíĜbjɇİw½u_Ċ§0ß3_żm=/èßQñô³ufô⢠-ñ'I N˘ğâ?ÉqjŞñ™) -ʎëšÓ²+žĥĦAÇÑr˘âğİ6&H”C9Ömr|7r²óGù%:‡òJrŝĥ<Ŝ(ĞgG^ÂÄ´³~ŻxPé^€KâŜÔÁàYúY…D˓"ĝ¸”$?f·7—Úšß}ı’XËäoèˆç3üœ'â+T…e|7ġ~Ÿxĝ9F’Öʓ •u -Ìih -9Nt’…9‚ğuicĉsÍäJ€w -cZ|ĥÁ$CÈ[ÑiŠ×eƒ Ò"÷û²àĈ;3|A‘zFáY4öWĜSHʘJ᧞é)~˙%œ§b[żO?ñĊ;ŸRw‡ßıÇE­5£?"žWċ|€;ĠI6X'\dŠèKùôs}2Œ{QA)wJêtXàŽi3uŒR3T›q5‘b|~ëú’<é2ûÀ7bA}…Ÿ™LXÔO6çû/'`:ÏÔñ½´ż´‘¨şñ8gŒI$ġG,•˙ÌM`y}GêĤœÊ?)c’ÜŜó–š˙7áK !8BʽŽlÉ.Ü oġϵĠuˆv -K·„S?Í0Z<ŞĵòM^žoEáÖï” §´"1éĤí\­eÎĴIĥ SsÉBIT·ŒĠÔvòÙeèµĦ Rğkvl$|­i÷ì0qp½ -QxÑroHúQˆ³™vzñç›ĊƒeˆÙñ4`¨ÇÌeİb÷˜ş?ĞV'Żax Â*áÍ ÇĦğ~‹MċCCô˘‰”ġ0Ò"ršs›ÎSCĉ=ÂÒyÊ û[ÔûÔ^ŝĠ”Iî1‡d#œJ9î&™I…#ħ ÏĊgŽßĥc*ğB+¨­ÜFWnd†M}ÏRYu™bP·‚­všçc?_gMk5ZoÄoŬ䨟³ƒÒf †~ßíGÂ>ÔüĜµë͈,Ÿ Ĵ˜gkÉ]E8·?˜ŸĜ`aˆN/`p§çÎâé22i¨útË (/[Ä@|;CĤß]ar6ĠXġ „W¸,ĵC‹ŠOö‰Qì‰Y`¨ç`J_BŻàh§Ôqñé8 !;É.òÏÇż*ÄżLM÷ĴÇïç›bż”ĤMK—a{boK›IĉnÑU„o¸wĠgò3’ÁĠ|‘Rq?Ğ'úİĉSúÖoIÖV\ÄÛ]iÖTgȋ[_ßZµ_ìj†£ŝ”5¤Ż¨'N8wMˆ%+E:vŒ -ŠÊ"„¸ÓŞïİá“aĤx;ÏY Ž`³m ÷ħÎĈeòïïİ"bsàiq>,ÄZnʨ›3ĉŒeÌ(ħgĈĜoûĤĵ =$ìRù·˙ŸµŝÜĴúŻŸ'âJ:cjŞ3Ĥ‚f2 -N’µ:3CC;OÊv"<ȳA?9=żÔ‡a’ÓÈ{úúMËğŠĥö&}LĉnuĤ4۟V[Ìà+.˘_…bê¨$töА1ê.ĥ}ÉÖÇÓÁcÑüŻ{äĞ<<›vì÷ܸßÌzÖô‡<ú Íñ–È£Ŭ9ÌrŜµ"œb‚tĥ™Ê˜$yéŞÖĦVì ]W–ÂÖÒÔ>£Ŭ0žġP¤B’·W*ZCÉĈ›ŠOžêS€ ë0³é€Ġaş‚ÎÖÀşċS„ħ5Ε÷-}7‰‚ÔĈÙ-Á›*¸IC{1Èı†AŠ˜ßZĊ³ärO‘(G n˜6ĵ˘9i5ßbDŭN÷²'wL ċ,²j"•éWv³yMÎbfv›ı¤ù&,Ġ†H†ƒÑĥĵG[‚f…íÄ&“İPÀx¸´&Iš™˙뤏i=(˗ èz:‚[} š$êú>ÖÑ]´ĦçIlvyPôÙüdŒÓ[‚tşzÑwä;Ñhc9–ŻéX S8ì{‘ĠYĴJ4ksı'$r+›tšŭ‡ĉ7)„)ßm&‹LWÌQÔ L7“)­³gö€·†×ó‘Í‘ĥ".ˆÀĵ˙f ˆE›ŭ*â -°MÊö‚:7Żġjm›˜ Ş!µ'Ĥż3ıxÄ<[r îäĞënŬ^™sşÉ:Ÿ^—M{9E“Ċ·ÑÌ8ÑŬBt<ÚW#ë³WsÛ 3’}ĉ~]ÏNAŭÑ~ïŽÈûFğÀk˙ÑÑÌ3qĊˆ%Ó0{eŜs?úòµċ~DQF· ıžd“Vĵ°O!0z]ÍÊwĝƒ•*-”nÎÀŭ,JXcİğü?ŻGúNLN*[ƒ(f ó%GèJ - Á+Uì!ıÙ'E—;ĦDWBĤÀˆK Í÷™0֛`÷Së·rÂ8gëÑ; qTÑŻ›NÓêVIJSì€Ğér`HïŝŞcŬ2‹fô½jêĴ­KÒ­ŠU2ħ07È“A;tÂmĞ OÖ¤b´Ş¸SieĊŠv;T'|ùĥż½v<5†DP8„ˆéŭŻ&—Ú”ıŻ“ĞĦ>2“îûW°<<û#šœ,ĈC£ÄÜM|ĠşúÙOŬ­ÈXˆÜéGĊĜ.ÜÜ|Žù3q]Ùèú‡UĈ*äÙvôùi–EkÙ ”ĠžèzŬ‡…íTߔÙâ5˙·€“ŝ‡Ĵ#ŸVÌ:‡§e6ĥ- çÙ0†jÖm—Ï•-™ĥĞû1S–:úŒí··èXŻğŜ…Rħ~3,Yh!ş„ŞÛmP"„W Ĥn3Vŝߘ–ô eFİÙbÂ& qHdG1D*$sI‘ˆ0òxžBàd}cA2‰´ŞPd' äùĜnyĤ•òI™T 0ò‹XĉAoùĜ…Î –ĉGŬùSZ xŬ>P˙.Ì ¸ËŽNu5Ï|='ĦAû>Ĵİ'™R˙¸ŝQµÊİ…qMŜĴ8³¨İhWĥä]/7T™sħ½ímcĞCĝq%ğh€€v‚SŬs,+ĉfŞeDžÍ@aD„×/£÷w:0͟“"{ќ:xd)šàu­\‘÷—|žĞà×Ü;ëÖÙÙst2Ér°DNÑu?fí:›ž‚~ -XÛâsëÔĠ%pÔL7ŝGZ—ˆĦÜn;fäAÏÂx0(›ž§Šîıjĥ°ĵ5ËÉÒĈżDOéUšÔjqá„qà0×_„+v˜PґÉÙ,ƒe1ĵ#QúÜë"ĈöwÊGEȑ˙˜iÌ.ŝç†è‹[{ġGĊ$"Ù^I¤ôJİ£âşôoş0Ħ_34OCú“ĵäÓùä]ËéŠßRċ'Ě*9 #µ4ÈuÎqĠ[wŬu°²kŒ.÷§½ÖF‡Q°“”Ŭ“ŜŜû -+U:³?h7.+¨zeĝ”›‹h”ìÛßĵÈħ !Ëçµ·ż6ìž"€lÚÊ;Ĝ­àŠì(ĠÒĥOIhqçÑ÷u8kíÈ`QÖP-ÏAŻ+[ĥĤ.'ĠµĈ“÷6ÓĞLԅ6iĠPĞ”Z’_[Ç5fÙ´[g£ŠÉ‹. ÖQú{=ğ½jûiš—˜âXpíĊ*Ÿî?%iûÏz­ĉŸ“ò•éí÷‚qíEE°zĝĦËYżdì›ÇSqİ ωˆT€ÑÈziüŒ -vŞí–ŻÚŜ[ĤéâÂġZ]½£3’'} pfh6m:ËÊѽUx͎b,­ÙËğ—äÛMYg Jûaυ×Wä4¨˘™ˆĤœ~v×ĵÇrpĥŻy<Ñı³V¤Jr -Î2‡ ËĜof˘è%}‰} ÍëşŭšˆHZò4žlŞm”Żâ“sçE\L§S„şHlHT0_!H[°D'S2éĵÉ9İ8rÜ_pż‹·› 1Ŝ÷¤2OeúoïğŝÜ#D~„··â)Lˆigrd™!›ġ}F4ùn(AZÍğĉ†] O´T?"P -#–0JíSƒŻ‚î={<­Fdí< ŠÙO47ƒâόTDâĠ ›Ê%5\PŽ„>‚Eò#s@ÉAUlQ>Jµò‡ž+q##v(UuûwñҖ"¸â×&ëÜxòbËiv °GE8§‹ÁÏ #ĝıñ†·­ÏZ¸ÖşúQÇ[ò`Ït‰şËÁ:’"LdŬÈK“•½Ĵ#ïZ6† â9„@™ğ lE)7ħ§L2R^òìŞÇd‘“˜ÂRRÄâ”u| tE?D;y*P‰ŒaŻ£xž(áĥ0Ëß3—>;/>È% )öċXܞ"Ùp^Jçé Ù½Ô̅/S {ĵà°ĈĦ?ÚNaMĥ-°ËjrzŒíB%z'ü•âĠ~Ò%óaĵ†İ÷’i¸ÎRçÇí+%İğ]Ħ°kr e/hùzí&‰†·‰˙ġġòŭd뀚ĵ:}¸ !8,RÏŝáĴöŝqĝ˘ˆş=2Úé'ünŬ?Ó°y"”*‚ÈS8x„ µvħSi[§ĦċÎFâs{V*Úϛ³XPü–„°`–švKeV,ó9;uˆ"&tÁşpN)˘ë{LhŞcâ ê*àĴŠë°šÇ5” {–uÜ% 9TĉZ70:†Ù½îċSíÚ˙7yŻZ–°—'°ŝ‡g5f,ÛÇM@ǕlÌc‹14ËŻ$ó+N3AKŭMÎĞ+—ĥ 7‡˘ı…;nUrŒ›[dTOıçĵŸÏ;üï^;ÒÄŝ× ´?€=sjY7DI£½Ŭ|ġÁâ‘g>%íX7ŞpĐ×Jj[)'‰ċ0şÂ#}DED„ͧ5·VE";ÓV4֛ġ”4zöKEiûĵô-Mú*ҍR‹%…iX–?äMŻòGĜ -BδbO³0 Ĝµ%ċ÷ĠEùTÖ4#ÊeÖD[èVŻam[=/­­Q‡XYĜ]Ê _+ŻD¨b, -IÀjÛġ -BÌ1­]ód(ŽÛCìYëQ‰ĉóˆ‘şfêpżN¸°ùÜ‹ÔyŒ5^"ò<|È÷äfkY\dùZa˜pr eA@r·ê ×@p““Ÿ™™I‚Êċ'üÔÚ"•,ĞZdWij úvĵ6İ$œ}`܀d7½˜Œgq.ÉûwĤ§ŭ“ äĥŠĥÔYE#Äü‘r}`§FW´ħġ”V³V›>žo•ÄëĜÙCċ6Ünĝ˜tX`m߅Ĥ\ċè%v0ċ³3UòIí“Q;ˆ)ÙïüŞ8m -ŽĤ–,µë;Ĝ›˘"Τ‡gr—rO›ïô Slt¤k˙ŽÍl^À²(R³;w×oŒĵ°I#Š8Úò•WNÖ²ŸĴ*éöŸû-ŠBŭĵq˘-|˜-(ĞBšoħ½HMñdL§" 7j—jêĈ>¤´ċÇ€͏Óéñsf cèïè P§Ïĝ3 ÂòĉŜŽKâ6ilçe3›ƒ™Gáâ{¸.Ԁ^2½;#Âw÷Ôۃ[™qî;Û;*„wîŬ£Ĝš÷’ü5FE@ŜĴ1údËöĉÓìú?`^¸(ÌeZƒn&hi–&Ô6}܆qìHdùÜÌócD[|Ÿ­¤Ndš’‘§”çû°Œċ}KnóĠ%ÖI²“şü„›˘nә@ptR}x%Ŝùĵ?RÍËњÓÑ+x-íġR^”kmw§h,îÙYáĤMݐħœpĜ4ƒB°¤ĵvX•ĝ•½„ˆœ’7Òì>tmÏ{R(x{yK$Ÿı ooRhÎVé1Ìn‰:²ğ[ÀŬ‰u·û*{ô!£WfÔMú½8/Ž?)J…F*ün}È\!RÒomÖ%4'u…ÒóM%{ü×Ù= û†Š %È4›yÌÑh_ĊıcŒKq>­klj\ !²è&ö9(gÂCPÙ_ëa—׃'aEµ˙ú-­h9C*äĜ}>UœĤ5µCBTâşġY"uá -oĞ+*ÛöŠKÔ=MŽÄŝ떐R -/À'ĵ't—ĴÛ^ëäÛĉÀóÜòüJÑ¸É7frSf á8b€‡ĥ,+7è~$DßÔᜑî›a@`‡ž žâšÊ/ŞL’-–Œ½G–WÏm÷vâ-—§‹2ŸĞú,}@#Şj6Ÿ†ğ')„ü)”4c‰_2İ­I€“똣RHÖş}–¨*–ĉŭƒ”ĝŝÂhƒ9´³›{˙˙‡$(s­O˙GŠÈ÷iëĜ;3”ù’`g谔š&˙C¨˜ĥT1ġYêĊN”5,AİJàŝöSܳaİŸ_ÈDŽ,…u“oğÀf† #ċVĤ!Ğ˚ċF!.Şe> ċ£ğ°D‚ż5áósĠŞZÙÁ äeıhçBäà˜úµlèĝÑDrNS8Àĉ#F~“ɤ“ EòĠcŠZ½6³‚<°>£‹K^ÌÊ3=Íô<[é<ĉáÀžŸ“ıĥF„Nƒ:w‰ T›Q҆ƒ‹Iü7òĜÙĜî -GĠ+÷p jÚkÈ5  £ŽêtšÔ@K*‚?ei4˙ö€âÁo5üì˘˜™gĴÌ!rR3X•ş“Q]£¨[ş´fÔ:À%C+ĵŬyT5Ħ5á>âĦ'3G6 äġĝèû:•²•µjĠ‹z&o‡Uıĝ3‡áŻ†˜½ӅŜ4Ž¨C,i|QmJ'Ş_r”ö2İŭS"{͔ħÂ6ŠC>ÎN˜1̃ħ²sûUżú}â‡eÎ"2œmÈ ÛµĉüßÁ6¤³ _IˆFJÇ"jí™Ğ~>BĞğH˜ ?)a2òJ[2Àşöġ1Ú𝠤p âàuş]Ç…pÖVÄԟġP*RèC:¤ħ“ĉÀu÷=Kc-ϸ ͍üœ–ĴèhôÓzEG°L²Ż=Œ9MÛJù’˙M=û]‰ËěÉܖ¨'›£›ÚBÂW'kh{ ĈCĜ‡ TÏueLŠĴÑyQ‰‡ ĞJħV6³¸ *Hfù-ÜĴ2^@Ž`ù–“camŭkו„ŠqprŜ#G)ĥ¢İÑ&ĝäŝWċÜŬVäŽûÍ7ÛêêTŬ‹‘™Ĉ‰, •Lû(,:ƒŬħx¤^`Z] -”.Z˘ÉBKŠi§ä›à6³5Èa}şŬ ;—6<˜ğĴŝz`ëfĴù^ŭkK,ÌE ç°.]µZ°2fèUĊÙLp'˙5ĝ\ĉWÊËÌNĝŝy˜ž8&P)šî‰iñˆ;K]p~í)–Ú́Ġj’ċúZĴ°Ş;ÔÀb[Œót>§ N8ÙğIN*~ŽïG¨/ܜP+d™Q²˘°J8ĝäo€öÌ$::îĦÏò‰²U€tŠêd;,Éšä­ô~7s -6ŬHŻT•Âd뜽Â_…Ŝƒ”Ĥ;ñ,:ŻĦßqñĝ^§ŠhjFÎZ‚§,–áSÈ^qH@$%_ ~ċ’Hœˆˆĵ_a%Ċ"pŽ+"ì‚ÏYTîıWTĉwDÁn?<ŭès_\EvöïDËûfÀħ˘ċá;żjŽÀÑ̲Ö˙9îׯu_¨6ìc=G~Ñ0Ô\JÁŽíĵŽ>z¤ÊĵŽÚ#`6&Í+”-yw5{µ›#ÀĜ¤Ïn#ù$4:ĥDÊ:srt^Ñˇ)#Iƒ5XĤÚxѧâqħ<w^Šxwġĉ|+‰|Ùĉ£u×Înèù§Z<ÔĊÑĉ EĤ×Iv+Z¸°Aĝ^Š€öòLJ2ó8ä*œĴfԁRZVjl‘ĜRĠ¤yßÉZ{{ĝzŻ AĜ+GŒ~ûk‚JEĥ,ÙĴŠR­Î%îóÁšĠca˘8nşH_H@k½”ÍÊÔIĊóòöëO€š?TµH!I<ÙvH3áqċjĵǧŻ^df\£÷iÚĵ;s”áƒöâìƒUtòbĜÜ8Uš-_ÔÔ7À•étM’Ġy™W^ê‚T{œm:ƒ˜Z-Ħ)™r8~÷‡J_‰9œ {îùž…Q0”ÈŸ‰Ħ˙„È)ŝqLMÈ×cŬEU5\›{Ks›lžĦÙÎw°{ûı|ìZ¨o…€ĴİWV×-ë^#àÀá`ò -KBò?´ߖxîñ-TMġ¤Ħ`'p?ÏS;‰ÈÑùTdžá -ÏştUŽ÷l˙1Œî×џ%Y‘ëşì8i1ıPۚÎĤŒàŜuO|BÙ‚]Tg9ôE*Ċ$œżjżI–ĵQ_£Šö1$jo0éܟ€ â9ÛÔıQ3żHïôœaB*O!•³9ŻuŽXĊ›Àì-·„)AÚÏmÄŞâe˘Ċ‡v2h#§­ âŭ1ÊnµYs°µç¸•w?LíoħXŸá^ÛP ¤·Żà:Ġ…|ì´2Ÿßġn‘·ÒŸmËm/ez!fTೖgóŸú€ú˘zÒ3OQĉÁsŬ#RšÑĞ'}żN”Ÿï+ OB{Ş"TĊĝèŬ×ûö -=ÂG;ż1‹D?<<îĤš# èóíÉ֜lêúžTì aŻ‰ 83Ħ‡Èê½ÉŞ›ÖePèí!­nÉ:e]­ƒĈĉUhŝK[o,ħ醴.µS˙iŻĥ<ò“ŝdĞüEì0Ç"TF%ÇÒŝúg§§²û%áı*‘&6òÀwIµÛ…ojĊœXĤ]Ü*÷‡IœpFwàÓÁÌ{Œ0¸Ì*ÌmPé2ü½áIëwêÄ!ġEëşó…—ĵÉaÓB,¸njˆĞħċ×&) èKgšK-3üó̗Y–”§*9xk1  7°-Ÿvhè‚ĦƒÑ¸xíLĴ5íAHbÊË#mñ°ZPŽâŻşX6 Ì"÷à›Ġžù5ż2òdc.UÂPĊ’@!¤çí8÷öTÎżém°ĤU× {./CT‚½a7î…G8Ĉ^ Ùè½Áʤ€JéZÙRX|ħíÓ-™sC"Ö”,›<ë¸Ġór’,|Ž÷F֓mŝITb$RdÁFהñVĝµê#Ċ*ŭ5÷<‰˜q펧ŒıKPjy â|É?ġż;˘ŬŜĈı°}-}[ċl.çK8ŸR }ël^탚ŒTuĵ<Ÿ`£HÀcNû"OFÑT§™áCɞ½0ÍçR# ŜĊóaÙüM•ñg Ŝ˘rÓô6%Ì%oˆ'ñ=ŒBaŽÌeZm‰ ]ĞGŝÁGÔq)S„C†—lx(&ĞdçTÌ'f7½i^ù˜cuRL“ô°ñ˘ˆĝġŒ‰$…iñ;ÏïĵŬ³6rĤ)ŸÒTšïĉûçÊÏ[›9TĤ#^Ëԍ×÷FŸ‘ıw°èè7èl·×˙—ñ ”*ô…ĈQ'hçä6U3)h=Tïöoğñŭ=”€íğ6/5pĊ\‹½ç^Ÿá†˜}m琣d˜$2š -{ZûVXr/Ħ3ÛZŒl|8 ¨ÒEGĦ°ôA ,'X3LúôïC÷DžĊú†ÂGVġè?=Ĉğ²ĥ³“€_,—j‘Ô–ÓĥB’ô88eğaùŻż^áŝA×˙eŝ ġ4ŭ@ {Żór pS9èż8Ż„ 3⟚kUàsùŒg³}Xˆ…q[p¨ĈdÂĉ-ˆ"yh1ÁÁż4œİZ#P]‚Ô˘…×qyü3܏OT{o¸ĴÛNĝÑ$²3gÀE}ĞéÒE”§-‡H]"ÄrNuXcBèV”!{ë€âŒNVGaéşü¸{\Ä\µ'ş°~;—Ÿ…'šËpìü†ù%s Ü#`H“¤ĦL iö$òHMó[í÷‰WŞ6ĤÛ2úbÜÏ&ÔßTd,ÖNgÉĠ! £52÷Éo¸ĞD¸ŝuˆ@ÎD {% ‰àrFL4şq[ĉW'oÖÓP‘0£FŽ·+‡v‘ß-eW¤£qè˘,”BZ.!Aá†r'JĤ:F -›żëâÑä=E~;zĵŻj\,w_Ĝ‡#ž?=tdŻŜ*ùż=;çdĦĉĜô)2‹&ˆXÛ­àĞ€SżdÌÜä€ĉIò×}µQ’!˜ž^‘l wİ ˜a'‚ÜP€`Ĵ ˜ŽJ…7éǑ–Ç/úĉĥ#:fLa*ĝ~÷¤SŸ…í0û˙QSĤk˘ò×ègç3%51'‚vĉ­E>Ž`”hġü4UL¤.ŽáÎß{"SxŞż—gX‚ÑċK›§HꠂŭG!bܳ{fGšĞyƒL¨è=İë+“nħvŻĤ­f·œZ]}•=‚0/œÂċ}¸žÊç?˜à ÁúS–ôÎ*:€µ–yş"şßŝ"êŜg0ü,U¨ŬKÏgßÍ eâĠû6jLÖĈÏĴ×ĵZçİ}Ï÷/÷zôĴq}ñPPĠħC %›dmEŭ˙@@ ¤tí_¨›°û“áÄÄÚ>‰¤X');SĞüó$ŭ•·ƒÖ'[‹{Ĵa ‡‰ÈŻŜŸ$Ȟ ‡ò€Éœ™Œ×z…—…çI1Hä§Ħx‹áàn\ĴzĊİ OÏHĠ3dˆ„ŬÚYv³ SO×ñ?Ԝ*½p…W[d&¨/%&)2•wŻ5>‹–+çž 9 ĵĥ°hî‹ EBÏ š9{L›¤˙6ġĤJ`”ÎoÓñk‰ċçáË/Ċ~·!5%0îïpPNĞòĈ‘‘ŝÈJjeĤkî¸ò&ü"Ş İW)ĤPÉÜżÑBl1Ĝ+¨ = ?£E½ĉ“ŭ°ÖÈ+²&ĉ\á^™—;=}?€Ò7¸’µÖ1öŽÁÉ:‚ }ÜĊ¸N–9€ ÇéXäċgíšċ—…ggÏ'Çò”¸×àQ[½§:êŜÄDÎĝIùSh •>‘ŝ­çíż´­ƒîiài#àÍó.?K<€üAf'qĤ l˜âà>o0ëJê™i -rĞ|ħ·Żkž˙D—•ç }äÂçUkĵqĜΖġ¤dEÔU9k4‘ƒflµ0…ŝWı%ˢó.P1#ÓĊŽK³À]Ĵé;f…_HbB{ñ$[ŬıŞ· ¤jòċ­sÖ (?Żŝ ‘ŻF³^È×òüşä2•Xĝħ.ÇJғ8·üġ ™ÌTéÄS -žI]iòŭ1û}y˜ş´OŬM·4,$Ê(özĜşĤC$Ġ4âĊ…Ĝş€,ü94)éˆî‘¤ïTÎ K³¨_à³°GˆÁç”äTì­ġVUĠŒ/Hfí› žÌÖè'âÍRúĥêö"D/́ĊŻ×~=3Šw¨šMî`ɃêsFˍ “ûĞ83vIB`„ÙIVĦ@H‚FäsàÀ%î°s -GJxÄ-ƒPĞ$Ùş;0ŬÂ22iÀ…³Şo”PğÜY4BÛ­0vŸžĤİGĉ#Ŝ X´šMÌ -EÓqıµ²½4*.ŭ0ÇU£v 2kiš˘ŞPşĴ@_†Ż_ 4všn½Ò‘€ô9ÌĤ^?~ìrY!‹’ŝñÌW”­™ŝ\ŸüC“£ù ÍÛJ18ğ”tOêŠ9Ä1R€qġß[Ğ<ĥÀúÁüôÜäù}OPÁ°Żˆ%OŒpoëžz[í]ĵBoX`Ey Ċ^lĤ™Ĵ‡Z{]ĈŞc}ÑIlunô \-‰ê;Q9rżĈŭC'Ç>~yÉZÔ ŸzµŞĦ$ôî-‡kx­ÙXLw†9töâ9™&Ùñ³Û§í4’Wß.ûXJsHô°susÙwÜ6~Ĝŝô-„“!ìDž2*5­Ĵ6ûKl¤8ʲ]DŸ6Ĵŝx@Ġü A+IÄçËnĤц`×·„ä6˘-ÄÏtÙfaG׳eX7ÄD‘Ûêŝ|0bĜ‰K:´0g d¨ı9הTg¤‚:ÛġÔCÙQ’V0­8´›µr&Á÷nŽŜhËÁ$ÌÚ½ħ\öŽ1idÂßĝ'3·ħ/• 7Jçì8=ıpMíK -aĞ`b7Z˙Ê@V.0Ĵö…ğè*Ĝ…t#t0bvS îÎ;WêĠ›žüÛ7yWÖñ.Ż7ĥ75¸Ë./ì÷Wŝ}ôñÌ˘ “%OBï °n„=$‹Ġ^À ıx›–éş)ßà…Ëĝj‹.Ż5_⇠ƒƒ,·êèżxLħWË÷k˘.Žı"ô­•  ŽC›îFòĈ=q¨#A\5wdÛŬàùG§ÌeÉrYeúo@Ó°|“r0ĈK\bC§ çz-°‚£3F+S{8“ßçE4ĵ׸T*2îÉS´kˢğoôĤÂíó9öö$~U0 ŬtÇqJşĞâ -£fèQĝ”Ğ2c·zŽ#Ŝƒ4qÜĠ -9šm5¨E56ç1(„Órùĵ8Á@¨@ sŜe ı˙‹›À¸?^t¨ġVĵúçğT³İ ²l#V“̍Tx£x>PRDè˘0öĈù%ùÄr]„8*ɐ”‘‹Žìy VeÂhĴ>ĥ:(šÍ ĥ…eÔĥ -œoŸÒU âİaÒZÈĥ“ó`ŒĤQžžIΆÈèŬ -¸~Ż()ĤÁj0 şy‰cŬú;†ÄfÛÔİ g1L߸¤cïAœ5İhlG…¨ ZéVħ1mİ#Ôg–hh‡aˆŞĉ™FE²ĥ -´{!R -WŠ‰`'ô˘³)¤òíÄ[ÊA·z'ùJéħ’Ë˙ÑVÔ¨?Ż^ËpqŻ“³ÜXŞ.Żc·£ëĤ%ZÀû›0@Ż‡R‚9½"ƒ°uSnsé½.¸ĈgqmÔZ…Ġ%,ż'V]ÙÂx—˜oRAĞvż.ıĵÎħE–HPĵu#ÓÓŭ¸.BñKİĜw+‹Ùħ Ë:dĊ‘e ,0#ßĥt ˙ġĤŠFJĠêġKŒŝò­ê -ùĴî3V¨Ġĝŝ‰0÷ƒŻo³@!‘)Ëwbƒ”Mr“ÖûŽQ -$š\ pY—ġ<”µ@ÑÔÚüJÁ˘Šd3Š /üÔŭ9o§ÖX[ĈĝíĜÏÊCJ&ì"|yK<‚ÑWˆ Ô[7 —R ù]6Kċï(ıî,Jüߊ‡Ż‘ċĊÒ¤h÷•È §í•’:8&–›’^Úò'—Ê°@ż9/VT*H‚²HXŭ\Îd™I<*–Ë-^—şì^qeÄkH_cû„X§ê+"ĤŜ5î‚É&ċĤ܃V‹3&: şAdoĦfځċìh›zMó´`“'4ë'é ÓĊ(d‘²À#˙A§Â'ÛCó4vÚŬ9ħ³È ş ˙ĥl–û!ÒЇ…Qâ0Á¨fÇ{œ"[;gôôĈm(ü -Ŝ°IܙìÔ]Ĝ y—:Şsš™"b)‰ï:ŭö"ŝ(550İFjuĵ)1¸Jj‚E*!îì¤ |`x1köHÔeáâµ÷lrD]ttl)£¸ÑMİMÙe"Ú(ğzá˜ç+ĝ*8ÈŻŒŻÍvĵÁowċ"ŝhŜ‹rsx:’T[€{ƒĉĠ–Çé,ŽóRĠz8•¨O-ŻÇ½¸âƒ9ó(çĴŒÔ£á ÑvъìàT꧀S°mÄ<÷ʤĜqك4ĵ,Ĉ}rZş;ı3ÒŸ°£Ĵ5à§ANçi‚Ġ'CIv]€İ3 Ñu¨@-JO“)V=>ôDÏèĴ//ôcDœùŒ{­‚ġm€…bXĜ.3ïܐŞCMĥG4´Žx˜-_mi 9Ĝ˘ (¸&|÷jñ[€šİDr!EżwY&1ê]ı™.iòĥà]Y-§î O*‚z1ÀŒß5'ŠÌÄî×<ĵÍ­{uïĴ½ÑNÇOŻê&~lH9Z÷ö¸À˜Úq|âô IÖùnG’6n÷ŭ˘veSżmN‘+¨L|ä—éûárW‰°v43ó•ĵӀe˘.¨úï=`´{ùO)ĥ}*à­ħZ ?:™Íh‹×ÁFžžWì=ħgv{/Ġ0ÀÜıÁxÈv랍Iô­19X Í}t%ĞÓ!LtşOvKÓ}1ħ– Ħä*B›˜w-2Ÿhk…7~ /â Ûf ŜiĠĤIÚdĠmŒ×WéĴżh¤z¸­[Ġ“JkêÚĈe7äL@$ĉ  Qıü@Ah’;ħžDҔü×7·{²‰jïËŝ–e̖tŒÜe¨ğIS -hnĈfg™ì”’ÉĝÓ*ƒËrħöĵ’ğù48Ŝ ‡6eÓâH²‡+ž÷bmHNŒéÂÀhF."˙ı$ÒI-^žƒ ‰CWÁâ,{aN;%t-(’Ž­ŒÊ³ĉ,iZG]phthù×—eIǙšµfŠôŞÈuGëäç[Â>ƒ‹³ğÍJš¸żFŬêWL‰ŞtĈO!4ywô…ĝ˘{v…işŭîŞÂê&bùáċÖñwûûϒÁœn>töUQ3ġÚ9à‡ŒLùTm!íR/Eê“íÈċšÛŠOgĞMıF…d÷Š!˙§Ċâé‰Ò<âŻĞ§RĤÇrĞżŠ”4HFJdżĴxÑ{óûĥZ!bœÍEÎş€Ó¸½ĥVû„äg%É_äŽ!Ô"?ïKj•àZpd‘àBfK~ @ÎKÉĴV#•‚l2ü!àBRŸ['P­İ#ת,ŻPĜŒ<~ EĦùO2wïHZ‰è]âN¸êó€ ;›b3œáE{,vݧġ=òĥƒOu¤Ħ€íİĊ•ħ=Ê°ĉï7ĥQ†=gÏğ,)fëŠ }³·ı™A:pĦ&Yeûtó4ÔœÏ]öJM)zöĝĦj™ŬYÓGısÙ -ÈğĜ•ż(œ ò +8rt“Àġ7+sšTÈĝ˘󤤤›òÎ£Çġxlß}e V=o W6i÷…œ#‘7°Üŝò˙y m×gäÔSky75°b†ŻUî"Zâ/LkÁlrŞ`Òu+I?ĦGò  ÙM ÒX! Œ“Fñ7s!'¨ÑızÜl$÷|x‹•£]ĥżM_V>xóİBħƒ¸œâħ™"h9D -8ÖĈRüĉ`™l‹— —ċ -zsĜŽxɆJt à™IĤma{ŠïŸí!'š+qê™,µ˙—ĤoĴ‘°§ÏıÖxï~…Ż‰ù{0áLĝrиF=àxƒËÙŬÎapĴ­Ġ&‰Xŝ´r^“‘ƒdĞ‚cï[$2#݆û%Ê|ġQ†Ï³+í`Z'ƒJHI 90ÄĉĴ•ŝ+zu[g„¨6ĞĤzĞj…%ÇH˘şab€ÛM쉏ôŠÖ˘§7äÄĉ$‹k|Zg b9ÖG'€7@V<‘xàÂp2ĉšeX"2Í8.Á ŞŒí?”o³­ĞÂqQ;gÀ—CW£"`.Žâ†ğŝOÂùÎPe#òte²ŽEíI53y@ŭzÚ§şcÊé ħĉèĤŠ—r·Û3LŒğÊт˜^Ġ­4'5˜ŬÁ³1Êâ}÷ֈQšĉÀNyñ2 ô=&mcEÒ×pIÁ5OòtK…yp€jÛó]İï}8Ÿy0•N ´qÊîĤ \¨1 ıáôrĦÀÖĠCágĊ£TÒêäƒ*/Ġ7pĴl“Ş -ç×ĊjYϸ½n§ mÇt o£áı-dĝ;ĤĴNÙ°U UÜ -¨÷RjG³3Bµ‹µıŭÂnğéù÷'hĞà‘_w™Ş ë·äÖÈġT›K>~ĊžĤ”ìÊ°†­aáâËÙĉÖġ×ïUóläáH˜r‘R “X*f% ¤_°k“ÙAܛ~cÇÖz •ĉ§„xw³Ĝs¨Ç~´Z8ĴT(3ĦñûɁċêa|ˆQ䘭ÜNl²b3´˜ŝ3ħÌ#$²]>r.öÄĥœ–J Ìa„.NĴ)Díç2İu‹$Jċ÷òT›`™PÏpcàik—]Òĝ{9ġ”7$IĴĈw {7Th5Whu S} -ûgBN·£aÛA<ĊXĠɨuĥ L$ĥ Ĵ³ŠÈcIá4ñ½42tĠ28_„zF³;ÏĜÜ°Ò ÂPÌ;AÍdŻĉĴ‚„–żÎ}íâÜ\İGâĜ_·ÄÌ{P rMIHÜ.èċĊë %,+ŸU'7ċ—-,qĦ§qx"@éa”g­Ĵ"zL¤0;€ĤVV|ï<&@œ†Ù T5B^m5¨‹j|R=Z™ÇÑ0vİŒiġšŭ…ĞĜYÓQë6l jĉ[V’Eş -ŝÒ£P7°Ìije2Böù½xĠß*jĴ³ac›pŠäÖ[’Ì^r-Ïv:÷â4-d #‡œĥ ”œĜĈŬ3qqÊóÀßJ‹šhúGŒl$HúFô…•ììTĠOv!Ô&[ ¤dˆĞBPQêOçżŸÑqùö;˜İİ,!Ĥŝjyš1Ò‹<ĥ‘ß÷áPÔgӑmÚäyÁù;ıœ}8ö Z‘* îOށEä÷CĉŞĜÀ™Ü.D$üHÉaÇ$HŝíÑ~î¤Çñ0u–3è t…ùKğg~ĈW÷£-ÏaĞ<˙ż9Ùó/g…ËC“îċw•jÒfC'+?ŬóÎ^{À¨I'^11Vf1BQĵĦ6\sܢQ8ĤQá·ñ³)‰IZà²kú·ġVŻ˜’,‡ä,Pà½v9X$S ñGü'ɤ]lŽŞnuŸË“J%9ÁííÁC›9ĵß@ë³ò9´˘ıù”ûħtħœ&…‹y˙’XíÙŞCšßħ÷ċ?Jç[/ĴĥŝGqÍ;›żÌ#ƒ(ĵƒ†6eµÍ·â7'žĦhCóN˜ßĤ]ꕤˆhÏ`ċż"*Ŭ:|˙%2şîÂMiö*$ë €‰[°èÀ;ô²vîY(˘£@O&ĴrêôÍüĝ Q•Ú—w|°ŒV­}¸íşñ°Šè6(ġ$jñüeĦ1PÔ #",=ß [°AƒĦĊżĤƒä ŝ -pt²@°,·b÷í—=E÷PA"Ÿ–ÇȵÇ'yÑJ’\Âb·Sa‘µá×4œÍ¤DíS‡é¤iĉgŽ~êքy䕍:E(2O&„àOI¨Âچ˙ÁĤğf}=²Ò³Ĝü›tpıŠ²LTwVh -'Hw†píKWÔrèŠĉòQ–;{3o²U8ij͎P”Ħžړ·“³Ú6~ë Ó(V2Ö\,Ŝ c‹°‘tÒ?oŻÁ!NŠ´[²£;°QÒ떺!ĝJ·1DĠÖU ¨èĝ 'I· ô†& -ë[i)⨌Œĝ6Ó}ŭM_“~2–Òaˆwúáë{·%àbé^’>Ws,žm‡CWŭlŭÎ&ƒ“4D‘ĝŒyí\Ÿ~´„xż‘XџˆÏ~2¨Òê(¸ V­Â„ğ—OÖn \aİš{_Ĵ}˜“Üd4˙wqĵQ…—íWƒkDcAÈÏx5ĵ5ġAsĞûëZ›/&`´IĠQ0n²÷†´50éK}€UsÓ2š-­™ßz’š–HÈĝOPŸô(+nh$M¸şÌ5˙"ğ;m˘0S"ħœÒp:ü†dà˜Ÿ=y—TÄ5İïH‹\?ah²ù·Ê"‚“˘ĥ’”˜Dğ÷¤ÁwƒŸŒÁħ^”äµPŠ>3:Gó ܋?ÒÀżÓĤR󏟀ŠÑĉ; şVâN‘•—ҏĈş ’˘}šğˆöYŸ"ñF£|NN—ŭÏ·ŻFŭ(qPGŻ.²Ÿ^ê&WÁ|@Ç·ı8ïúA³ö -LrÌ8@MĴ 1#L˜lŻ6˙`³E˸µĤâJċÓq4ĤÑFl&áŞÑ*Bfc=ŭëkFaüĊ>g Ŝrâ°N]¸€:ɨÖÓN'şÏ -bVĦ5áÌkZF”ĵġP¸uÂħî’—Ĵ<(ۂNN*,·ü -wt´€Y˙D7·yÛ¤•¸Wg.Cه˸ì|ó“Ù)òy—dI”òÎÀX%›ÏVúŬ·C<Ĉ9ûB*ĥ…{‹~ÀŜ)€ç˙ğΣv9ŜHÛX<Ĝ%M‡7§sĜ`.C™ -endstream -endobj -698 0 obj -<< -/Length1 1306 -/Length2 1345 -/Length3 0 -/Length 2651 ->> -stream -%!PS-AdobeFont-1.0: MSBM10 003.002 -%%Title: MSBM10 -%Version: 003.002 -%%CreationDate: Mon Jul 13 16:17:00 2009 -%%Creator: David M. Jones -%Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name MSBM10. -% This Font Software is licensed under the SIL Open Font License, Version 1.1. -% This license is in the accompanying file OFL.txt, and is also -% available with a FAQ at: http://scripts.sil.org/OFL. -%%EndComments -FontDirectory/MSBM10 known{/MSBM10 findfont dup/UniqueID known{dup -/UniqueID get 5031982 eq exch/FontType get 1 eq and}{pop false}ifelse -{save true}{false}ifelse}{false}ifelse -11 dict begin -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /QDTWCG+MSBM10 def -/FontBBox {-55 -420 2343 920 }readonly def -/PaintType 0 def -/FontInfo 7 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name MSBM10.) readonly def -/FullName (MSBM10) readonly def -/FamilyName (Euler) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 82 /R put -readonly def -currentdict end -currentfile eexec -ÙÖoc;„j²„ĵĝ°Aw-ċÎ24 ĈòŠôWäEvçQ‚C<ùó3£‹ĜAÀÔĉ‹ùàë2¨˙·kX0k^ß|™‹:Ù´ĵfb,|=úësLu2ĉKżżZ`3ndgï¸RÈwô@Ó),qñċĠœéG<&¸÷­hï'ĥì. ΍‹883 „½Aœ½BħAÓÔI$sò@Îí“Féù™ĊË25âĈÚŞ,iá™êê pKôœê>˜èÂ6K` Ó%äÂEû(‚ôĵ„(bsÌS=Gîq³żèÙuĠúӁqbÙ¤ŝ‚ġYJ ­NN=>3qÓk'4ĜÛXj“Ş×ÒÌ´Î\4 İÜG`–v׎Co„.k×C1·b™›Ĵ›h¨‘³F˙Ŭ,ûĊ+™.‹5Pħ.F2E"÷R Ŝ˘ñ -ÇfÏ P“Zc†c*³‰ĵñw6Y_P-~×|íy,BÁŬk“ä¸[R”4kĜg0<Èé½AyÔyŠµ4}pċgeÁ*f\Y˜Ğ3]@Ìm¸ìä;²s{~ĉ‚ˆż¸˙ٚ.û‘"šĊTÌk/}ĞÒDúáJŝüÖÚUĈ2WŞG3²ĥĴKUë¸ġaˆÒ>u0Âğ[ŻykTÏ -8˘ƒ~qKçŝä.m·dL§šĠŬ<à*ÉË͛İL…ê}>Ž@!——ġvÎêRċ.Êlŝ}İ—…#qœĦ­8†2…Uç”óÀ]*ÛP·{aSÔ(³T³GáùĦ½póġïÚ| G^ħǟâEhĵ"\S> {€‡çxiR(ş‹8KTW!ÜםéìÔŞç“Ğùڂ}MܵptR´+^OEo͖i -€·jY˙ çÏrÜ["ÒNŠh ĦíÏĊ,KC"m`ù´Ö \3´½ĴúĦ3”8tĊ5(ƒ‰½;‰•½LrSÊ ¸UaĥÍ{ÓúĥPƒƒĴjèxÛ$ǔŻ(‰mRò£°çëîΠ֖Ĉ‡İ†žÎ ĴalC_-ŽŝûcIó#gÛì6R2ÄÑ·£ ¸²ħE0Ï9Vm4ĉ†w‚%ġ{‹-÷ŠOñċֆ@Ñ·oBœJG˙5… rg÷HÊ(ĵÏûtiJòÏÀôŒç&lR:UFİ,Œĥ/SĈ¤†žfôĠƒ:Ĵï P8áġó˜ÌAò£ƒ9íÓ¨ÌVq5Ç;úœÓœğΒ’z£¸ċAuuÈw$AÒŠ^Y ”Œú§M·Šş—½˜/ Üö^v"ñ ÉċÄ -endstream -endobj -640 0 obj -<< -/Type /ObjStm -/N 100 -/First 933 -/Length 20176 ->> -stream -403 0 349 54 248 108 299 162 301 216 278 270 636 324 642 443 644 557 279 611 -283 665 234 719 233 772 528 826 281 880 280 934 302 988 230 1042 367 1096 229 1150 -282 1204 228 1258 641 1312 646 1418 648 1532 346 1586 232 1640 645 1694 649 1787 650 2483 -651 2551 652 2855 653 2983 654 3337 655 3357 656 3729 657 4393 658 5036 659 5426 660 6018 -661 6646 662 7153 663 7798 664 8393 665 8677 667 9309 669 9666 671 10035 673 10372 675 10681 -677 11002 679 11225 681 11473 683 12020 685 12370 687 12596 689 12826 691 13198 693 13450 695 13838 -697 14111 699 14681 205 14893 148 15032 161 15171 379 15311 225 15449 365 15588 361 15726 160 15864 -150 16002 366 16140 364 16276 257 16412 363 16550 307 16686 149 16825 255 16964 362 17103 151 17241 -226 17353 314 17465 384 17577 457 17689 517 17801 550 17913 594 18025 631 18137 700 18241 701 18354 -702 18443 703 18508 140 18576 136 18648 132 18734 128 18820 124 18905 120 18979 116 19067 112 19155 -% 403 0 obj -<< -/D [637 0 R /XYZ 93.6 425.986 null] ->> -% 349 0 obj -<< -/D [637 0 R /XYZ 93.6 374.324 null] ->> -% 248 0 obj -<< -/D [637 0 R /XYZ 93.6 319.935 null] ->> -% 299 0 obj -<< -/D [637 0 R /XYZ 93.6 268.273 null] ->> -% 301 0 obj -<< -/D [637 0 R /XYZ 93.6 216.611 null] ->> -% 278 0 obj -<< -/D [637 0 R /XYZ 93.6 164.948 null] ->> -% 636 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F17 148 0 R /F18 307 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 642 0 obj -<< -/Type /Page -/Contents 643 0 R -/Resources 641 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 631 0 R ->> -% 644 0 obj -<< -/D [642 0 R /XYZ 85.4 752.957 null] ->> -% 279 0 obj -<< -/D [642 0 R /XYZ 86.4 715.095 null] ->> -% 283 0 obj -<< -/D [642 0 R /XYZ 86.4 668.665 null] ->> -% 234 0 obj -<< -/D [642 0 R /XYZ 86.4 617.03 null] ->> -% 233 0 obj -<< -/D [642 0 R /XYZ 86.4 565.394 null] ->> -% 528 0 obj -<< -/D [642 0 R /XYZ 86.4 513.455 null] ->> -% 281 0 obj -<< -/D [642 0 R /XYZ 86.4 463.638 null] ->> -% 280 0 obj -<< -/D [642 0 R /XYZ 86.4 409.578 null] ->> -% 302 0 obj -<< -/D [642 0 R /XYZ 86.4 357.034 null] ->> -% 230 0 obj -<< -/D [642 0 R /XYZ 86.4 305.095 null] ->> -% 367 0 obj -<< -/D [642 0 R /XYZ 86.4 266.706 null] ->> -% 229 0 obj -<< -/D [642 0 R /XYZ 86.4 241.865 null] ->> -% 282 0 obj -<< -/D [642 0 R /XYZ 86.4 192.654 null] ->> -% 228 0 obj -<< -/D [642 0 R /XYZ 86.4 152.144 null] ->> -% 641 0 obj -<< -/Font << /F15 160 0 R /F42 161 0 R /F18 307 0 R /F45 255 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 646 0 obj -<< -/Type /Page -/Contents 647 0 R -/Resources 645 0 R -/MediaBox [0 0 595.276 841.89] -/Parent 631 0 R ->> -% 648 0 obj -<< -/D [646 0 R /XYZ 92.6 752.957 null] ->> -% 346 0 obj -<< -/D [646 0 R /XYZ 93.6 715.095 null] ->> -% 232 0 obj -<< -/D [646 0 R /XYZ 93.6 670.434 null] ->> -% 645 0 obj -<< -/Font << /F42 161 0 R /F15 160 0 R /F18 307 0 R >> -/ProcSet [ /PDF /Text ] ->> -% 649 0 obj -[458.3 458.3 416.7 416.7 472.2 472.2 472.2 472.2 583.3 583.3 472.2 472.2 333.3 555.6 577.8 577.8 597.2 597.2 736.1 736.1 527.8 527.8 583.3 583.3 583.3 583.3 750 750 750 750 1044.4 1044.4 791.7 791.7 583.3 583.3 638.9 638.9 638.9 638.9 805.6 805.6 805.6 805.6 1277.8 1277.8 811.1 811.1 875 875 666.7 666.7 666.7 666.7 666.7 666.7 888.9 888.9 888.9 888.9 888.9 888.9 888.9 666.7 875 875 875 875 611.1 611.1 833.3 1111.1 472.2 555.6 1111.1 1511.1 1111.1 1511.1 1111.1 1511.1 1055.6 944.4 472.2 833.3 833.3 833.3 833.3 833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 1277.8 555.6 1000 1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 666.7 1000 1000] -% 650 0 obj -[935.2 351.8 416.7 351.8 611.1 611.1 611.1 611.1 611.1] -% 651 0 obj -[379.6 963 638.9 963 638.9 658.7 924.1 926.6 883.7 998.3 899.8 775 952.9 999.5 547.7 681.6 1025.7 846.3 1161.6 967.1 934.1 780 966.5 922.1 756.7 731.1 838.1 729.6 1150.9 1001.4 726.4 837.7 509.3 509.3 509.3 1222.2 1222.2 518.5 674.9 547.7 559.1 642.5 589 600.7 607.7 725.7 445.6 511.6 660.9] -% 652 0 obj -[826.4 295.1 354.2 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 295.1 826.4] -% 653 0 obj -[826.4 295.1 826.4 531.3 826.4 531.3 826.4 826.4 826.4 826.4 826.4 826.4 826.4 1062.5 531.3 531.3 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 1062.5 1062.5 826.4 826.4 1062.5 1062.5 531.3 531.3 1062.5 1062.5 1062.5 826.4 1062.5 1062.5 649.3 649.3 1062.5 1062.5 1062.5 826.4 288.2 1062.5 708.3 708.3 944.5 944.5 0] -% 654 0 obj -[722.2] -% 655 0 obj -[295.1 826.4 531.3 826.4 531.3 559.7 795.8 801.4 757.3 871.7 778.7 672.4 827.9 872.8 460.7 580.4 896 722.6 1020.4 843.3 806.2 673.6 835.7 800.2 646.2 618.6 718.8 618.8 1002.4 873.9 615.8 720 413.2 413.2 413.2 1062.5 1062.5 434 564.4 454.5 460.2 546.7 492.9 510.4 505.6 612.3 361.7 429.7 553.2 317.1 939.8 644.7 513.5 534.8 474.4 479.5 491.3 383.7 615.2 517.4] -% 656 0 obj -[613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 511.1 511.1 511.1 831.3 460 536.7 715.6 715.6 511.1 882.8 985 766.7 255.6 306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 306.7 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 306.7 306.7 306.7 766.7 511.1 511.1 766.7 743.3 703.9 715.6 755 678.3 652.8 773.6 743.3 385.6 525 768.9 627.2 896.7 743.3 766.7 678.3 766.7 729.4 562.2 715.6 743.3 743.3 998.9 743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 460 664.4 463.9 485.6 408.9] -% 657 0 obj -[777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 1000 777.8 777.8 1000 1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 762 689.7 1200.9 820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 500 500 611.1 500 277.8 833.3] -% 658 0 obj -[525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525] -% 659 0 obj -[469.4 353.9 576.2 583.3 602.5 494 437.5 570 517 571.4 437.2 540.3 595.8 625.7 651.4 622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 750 758.5 714.7 827.9 738.2 643.1 786.2 831.3 439.6 554.5 849.3 680.6 970.1 803.5 762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 298.4 878 600.2 484.7 503.1 446.4 451.2 468.7 361.1 572.5 484.7 715.9 571.5 490.3 465] -% 660 0 obj -[638.9 638.9 958.3 958.3 319.4 351.4 575 575 575 575 575 869.4 511.1 597.2 830.6 894.4 575 1041.7 1169.4 894.4 319.4 350 602.8 958.3 575 958.3 894.4 319.4 447.2 447.2 575 894.4 319.4 383.3 319.4 575 575 575 575 575 575 575 575 575 575 575 319.4 319.4 350 894.4 543.1 543.1 894.4 869.4 818.1 830.6 881.9 755.5 723.6 904.2 900 436.1 594.4 901.4 691.7 1091.7 900 863.9 786.1 863.9 862.5 638.9 800 884.7 869.4 1188.9 869.4 869.4 702.8 319.4 602.8 319.4 575 319.4 319.4 559 638.9 511.1 638.9 527.1 351.4 575 638.9 319.4 351.4 606.9 319.4 958.3 638.9 575 638.9 606.9 473.6 453.6 447.2 638.9 606.9 830.6 606.9 606.9 511.1] -% 661 0 obj -[319.4 436.1 436.1 552.8 844.4 319.4 377.8 319.4 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 319.4 319.4 844.4 844.4 844.4 523.6 844.4 813.9 770.8 786.1 829.2 741.7 712.5 851.4 813.9 405.6 566.7 843 683.3 988.9 813.9 844.4 741.7 844.4 800 611.1 786.1 813.9 813.9 1105.5 813.9 813.9 669.4 319.4 552.8 319.4 552.8 319.4 319.4 613.3 580 591.1 624.4 557.8 535.6 641.1 613.3 302.2 424.4 635.6 513.3 746.7 613.3 635.6 557.8 635.6 602.2 457.8 591.1 613.3 613.3 835.6 613.3 613.3] -% 662 0 obj -[722.2 583.3 555.6 555.6 833.3 833.3 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 277.8 277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 500 500] -% 663 0 obj -[544 544 816 816 272 299.2 489.6 489.6 489.6 489.6 489.6 734 435.2 489.6 707.2 761.6 489.6 883.8 992.6 761.6 272 272 489.6 816 489.6 816 761.6 272 380.8 380.8 489.6 761.6 272 326.4 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8] -% 664 0 obj -[726.9 688.4 700 738.4 663.4 638.4 756.7 726.9 376.9 513.4 751.9 613.4 876.9 726.9 750 663.4 750 713.4 550 700 726.9 726.9 976.9 726.9 726.9 600 300 500 300 500 300 300 500 450 450 500 450 300 450 500 300 300 450 250 800 550 500 500 450 412.5 400 325 525 450 650 450 475] -% 665 0 obj -[625 625 937.5 937.5 312.5 343.7 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 812.5 875 562.5 1018.5 1143.5 875 312.5 342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 875 531.2 531.2 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.7 562.5 625 312.5 343.7 593.7 312.5 937.5 625 562.5 625 593.7 459.5 443.8 437.5 625 593.7 812.5 593.7 593.7] -% 667 0 obj -<< -/Type /FontDescriptor -/FontName /WOELMG+CMBX10 -/Flags 4 -/FontBBox [-56 -250 1164 750] -/Ascent 694 -/CapHeight 686 -/Descent -194 -/ItalicAngle 0 -/StemV 114 -/XHeight 444 -/CharSet (/A/B/C/D/E/F/G/H/I/K/L/M/N/O/P/R/S/U/a/b/c/colon/d/e/eight/f/fi/five/four/g/h/i/j/k/l/m/n/nine/o/one/p/period/r/s/seven/six/t/three/two/u/v/w/z) -/FontFile 666 0 R ->> -% 669 0 obj -<< -/Type /FontDescriptor -/FontName /XCHSJH+CMBX12 -/Flags 4 -/FontBBox [-53 -251 1139 750] -/Ascent 694 -/CapHeight 686 -/Descent -194 -/ItalicAngle 0 -/StemV 109 -/XHeight 444 -/CharSet (/A/B/C/D/E/F/G/H/I/L/M/O/P/R/S/U/a/b/c/d/e/eight/f/fi/five/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/period/q/quoteright/r/s/seven/six/t/three/two/u/v/w/x/y) -/FontFile 668 0 R ->> -% 671 0 obj -<< -/Type /FontDescriptor -/FontName /EYIYGL+CMCSC10 -/Flags 4 -/FontBBox [14 -250 1077 750] -/Ascent 514 -/CapHeight 683 -/Descent 0 -/ItalicAngle 0 -/StemV 72 -/XHeight 431 -/CharSet (/A/B/C/D/E/G/I/L/M/O/P/R/S/U/a/b/c/d/e/eight/f/five/four/g/h/i/k/l/m/n/o/one/p/parenleft/quoteright/r/s/six/t/three/two/u/v/w/y) -/FontFile 670 0 R ->> -% 673 0 obj -<< -/Type /FontDescriptor -/FontName /YJJMFD+CMEX10 -/Flags 4 -/FontBBox [-24 -2960 1454 772] -/Ascent 40 -/CapHeight 0 -/Descent -600 -/ItalicAngle 0 -/StemV 47 -/XHeight 431 -/CharSet (/braceleftbigg/bracerightbigg/parenleftbig/parenrightbig/radicalBig/summationdisplay/summationtext) -/FontFile 672 0 R ->> -% 675 0 obj -<< -/Type /FontDescriptor -/FontName /VFYBNB+CMMI10 -/Flags 4 -/FontBBox [-32 -250 1048 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 72 -/XHeight 431 -/CharSet (/A/B/D/I/L/M/P/R/S/U/a/b/comma/e/greater/i/j/k/l/less/m/n/o/omega/p/period/r/rho/slash/t/theta/u/v/w/x/y/z) -/FontFile 674 0 R ->> -% 677 0 obj -<< -/Type /FontDescriptor -/FontName /PNUTJM+CMMI6 -/Flags 4 -/FontBBox [11 -250 1241 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 85 -/XHeight 431 -/CharSet (/comma/i/k) -/FontFile 676 0 R ->> -% 679 0 obj -<< -/Type /FontDescriptor -/FontName /TWBVYQ+CMMI8 -/Flags 4 -/FontBBox [-24 -250 1110 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 78 -/XHeight 431 -/CharSet (/A/C/F/S/T/comma/e/i/j/k/l/m/n/r/v) -/FontFile 678 0 R ->> -% 681 0 obj -<< -/Type /FontDescriptor -/FontName /DKEMOU+CMR10 -/Flags 4 -/FontBBox [-40 -250 1009 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle 0 -/StemV 69 -/XHeight 431 -/CharSet (/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/Omega/P/R/S/T/U/V/W/X/Y/a/b/bracketleft/bracketright/c/caron/colon/comma/d/dieresis/e/eight/endash/equal/f/ff/ffi/fi/five/fl/four/g/h/hyphen/i/j/k/l/m/macron/n/nine/o/one/p/parenleft/parenright/period/plus/q/quotedblleft/quotedblright/quoteright/r/s/semicolon/seven/six/slash/t/three/two/u/v/w/x/y/z/zero) -/FontFile 680 0 R ->> -% 683 0 obj -<< -/Type /FontDescriptor -/FontName /OIRSPO+CMR12 -/Flags 4 -/FontBBox [-34 -251 988 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle 0 -/StemV 65 -/XHeight 431 -/CharSet (/A/C/I/J/K/L/N/R/S/U/V/a/colon/comma/d/e/eight/f/fi/g/hyphen/i/l/m/n/o/one/p/period/quotedblleft/quotedblright/r/s/t/three/two/u/v/w/y/zero) -/FontFile 682 0 R ->> -% 685 0 obj -<< -/Type /FontDescriptor -/FontName /VROLGE+CMR6 -/Flags 4 -/FontBBox [-20 -250 1193 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle 0 -/StemV 83 -/XHeight 431 -/CharSet (/one/plus/three) -/FontFile 684 0 R ->> -% 687 0 obj -<< -/Type /FontDescriptor -/FontName /ABQBBP+CMR8 -/Flags 4 -/FontBBox [-36 -250 1070 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle 0 -/StemV 76 -/XHeight 431 -/CharSet (/equal/one/plus/two) -/FontFile 686 0 R ->> -% 689 0 obj -<< -/Type /FontDescriptor -/FontName /NSLWFJ+CMSY10 -/Flags 4 -/FontBBox [-29 -960 1116 775] -/Ascent 750 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 40 -/XHeight 431 -/CharSet (/N/bar/bardbl/braceleft/braceright/bullet/element/equivalence/floorleft/floorright/greaterequal/minus/negationslash/propersubset/propersuperset/radical/union) -/FontFile 688 0 R ->> -% 691 0 obj -<< -/Type /FontDescriptor -/FontName /JHSYKM+CMSY8 -/Flags 4 -/FontBBox [-30 -955 1185 779] -/Ascent 750 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 46 -/XHeight 431 -/CharSet (/infinity/minus/multiply/negationslash) -/FontFile 690 0 R ->> -% 693 0 obj -<< -/Type /FontDescriptor -/FontName /FPIMLF+CMTI10 -/Flags 4 -/FontBBox [-35 -250 1124 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 68 -/XHeight 431 -/CharSet (/A/B/C/D/E/F/G/I/K/L/M/N/O/P/R/S/T/U/V/a/b/c/colon/comma/d/e/eight/f/ff/fi/five/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/period/q/quoteright/r/s/t/three/two/u/v/w/x/y/z/zero) -/FontFile 692 0 R ->> -% 695 0 obj -<< -/Type /FontDescriptor -/FontName /YRQLNB+CMTI12 -/Flags 4 -/FontBBox [-36 -251 1103 750] -/Ascent 694 -/CapHeight 683 -/Descent -194 -/ItalicAngle -14 -/StemV 63 -/XHeight 431 -/CharSet (/A/B/D/L/M/P/S/T/a/b/c/d/e/f/g/h/i/k/l/m/n/o/p/r/s/t/u/v/y) -/FontFile 694 0 R ->> -% 697 0 obj -<< -/Type /FontDescriptor -/FontName /SBOMTR+CMTT10 -/Flags 4 -/FontBBox [-4 -233 537 696] -/Ascent 611 -/CapHeight 611 -/Descent -222 -/ItalicAngle 0 -/StemV 69 -/XHeight 431 -/CharSet (/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/a/asciitilde/asterisk/b/backslash/bracketleft/bracketright/c/colon/comma/d/dollar/e/eight/equal/exclam/f/five/four/g/greater/h/hyphen/i/j/k/l/less/m/n/nine/o/one/p/parenleft/parenright/percent/period/plus/q/quotedbl/quoteleft/quoteright/r/s/semicolon/seven/six/slash/t/three/two/u/underscore/v/w/x/y/z/zero) -/FontFile 696 0 R ->> -% 699 0 obj -<< -/Type /FontDescriptor -/FontName /QDTWCG+MSBM10 -/Flags 4 -/FontBBox [-55 -420 2343 920] -/Ascent 464 -/CapHeight 689 -/Descent 0 -/ItalicAngle 0 -/StemV 40 -/XHeight 463 -/CharSet (/R) -/FontFile 698 0 R ->> -% 205 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /WOELMG+CMBX10 -/FontDescriptor 667 0 R -/FirstChar 12 -/LastChar 122 -/Widths 660 0 R ->> -% 148 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /XCHSJH+CMBX12 -/FontDescriptor 669 0 R -/FirstChar 12 -/LastChar 121 -/Widths 665 0 R ->> -% 161 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /EYIYGL+CMCSC10 -/FontDescriptor 671 0 R -/FirstChar 39 -/LastChar 121 -/Widths 661 0 R ->> -% 379 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /YJJMFD+CMEX10 -/FontDescriptor 673 0 R -/FirstChar 0 -/LastChar 113 -/Widths 649 0 R ->> -% 225 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /VFYBNB+CMMI10 -/FontDescriptor 675 0 R -/FirstChar 18 -/LastChar 122 -/Widths 659 0 R ->> -% 365 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /PNUTJM+CMMI6 -/FontDescriptor 677 0 R -/FirstChar 59 -/LastChar 107 -/Widths 651 0 R ->> -% 361 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /TWBVYQ+CMMI8 -/FontDescriptor 679 0 R -/FirstChar 59 -/LastChar 118 -/Widths 655 0 R ->> -% 160 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /DKEMOU+CMR10 -/FontDescriptor 681 0 R -/FirstChar 10 -/LastChar 127 -/Widths 662 0 R ->> -% 150 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /OIRSPO+CMR12 -/FontDescriptor 683 0 R -/FirstChar 12 -/LastChar 121 -/Widths 663 0 R ->> -% 366 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /VROLGE+CMR6 -/FontDescriptor 685 0 R -/FirstChar 43 -/LastChar 51 -/Widths 650 0 R ->> -% 364 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /ABQBBP+CMR8 -/FontDescriptor 687 0 R -/FirstChar 43 -/LastChar 61 -/Widths 652 0 R ->> -% 257 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /NSLWFJ+CMSY10 -/FontDescriptor 689 0 R -/FirstChar 0 -/LastChar 112 -/Widths 657 0 R ->> -% 363 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /JHSYKM+CMSY8 -/FontDescriptor 691 0 R -/FirstChar 0 -/LastChar 54 -/Widths 653 0 R ->> -% 307 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /FPIMLF+CMTI10 -/FontDescriptor 693 0 R -/FirstChar 11 -/LastChar 122 -/Widths 656 0 R ->> -% 149 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /YRQLNB+CMTI12 -/FontDescriptor 695 0 R -/FirstChar 65 -/LastChar 121 -/Widths 664 0 R ->> -% 255 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /SBOMTR+CMTT10 -/FontDescriptor 697 0 R -/FirstChar 33 -/LastChar 126 -/Widths 658 0 R ->> -% 362 0 obj -<< -/Type /Font -/Subtype /Type1 -/BaseFont /QDTWCG+MSBM10 -/FontDescriptor 699 0 R -/FirstChar 82 -/LastChar 82 -/Widths 654 0 R ->> -% 151 0 obj -<< -/Type /Pages -/Count 6 -/Parent 700 0 R -/Kids [143 0 R 153 0 R 157 0 R 163 0 R 201 0 R 208 0 R] ->> -% 226 0 obj -<< -/Type /Pages -/Count 6 -/Parent 700 0 R -/Kids [222 0 R 246 0 R 252 0 R 272 0 R 294 0 R 304 0 R] ->> -% 314 0 obj -<< -/Type /Pages -/Count 6 -/Parent 700 0 R -/Kids [310 0 R 316 0 R 321 0 R 326 0 R 343 0 R 357 0 R] ->> -% 384 0 obj -<< -/Type /Pages -/Count 6 -/Parent 700 0 R -/Kids [376 0 R 391 0 R 400 0 R 413 0 R 432 0 R 445 0 R] ->> -% 457 0 obj -<< -/Type /Pages -/Count 6 -/Parent 700 0 R -/Kids [454 0 R 459 0 R 465 0 R 471 0 R 483 0 R 495 0 R] ->> -% 517 0 obj -<< -/Type /Pages -/Count 6 -/Parent 700 0 R -/Kids [514 0 R 519 0 R 524 0 R 530 0 R 536 0 R 540 0 R] ->> -% 550 0 obj -<< -/Type /Pages -/Count 6 -/Parent 701 0 R -/Kids [547 0 R 552 0 R 560 0 R 569 0 R 580 0 R 585 0 R] ->> -% 594 0 obj -<< -/Type /Pages -/Count 6 -/Parent 701 0 R -/Kids [591 0 R 599 0 R 606 0 R 611 0 R 618 0 R 622 0 R] ->> -% 631 0 obj -<< -/Type /Pages -/Count 5 -/Parent 701 0 R -/Kids [628 0 R 633 0 R 637 0 R 642 0 R 646 0 R] ->> -% 700 0 obj -<< -/Type /Pages -/Count 36 -/Parent 702 0 R -/Kids [151 0 R 226 0 R 314 0 R 384 0 R 457 0 R 517 0 R] ->> -% 701 0 obj -<< -/Type /Pages -/Count 17 -/Parent 702 0 R -/Kids [550 0 R 594 0 R 631 0 R] ->> -% 702 0 obj -<< -/Type /Pages -/Count 53 -/Kids [700 0 R 701 0 R] ->> -% 703 0 obj -<< -/Type /Outlines -/First 4 0 R -/Last 4 0 R -/Count 1 ->> -% 140 0 obj -<< -/Title 141 0 R -/A 138 0 R -/Parent 4 0 R -/Prev 136 0 R ->> -% 136 0 obj -<< -/Title 137 0 R -/A 134 0 R -/Parent 4 0 R -/Prev 132 0 R -/Next 140 0 R ->> -% 132 0 obj -<< -/Title 133 0 R -/A 130 0 R -/Parent 4 0 R -/Prev 128 0 R -/Next 136 0 R ->> -% 128 0 obj -<< -/Title 129 0 R -/A 126 0 R -/Parent 4 0 R -/Prev 68 0 R -/Next 132 0 R ->> -% 124 0 obj -<< -/Title 125 0 R -/A 122 0 R -/Parent 104 0 R -/Prev 120 0 R ->> -% 120 0 obj -<< -/Title 121 0 R -/A 118 0 R -/Parent 104 0 R -/Prev 116 0 R -/Next 124 0 R ->> -% 116 0 obj -<< -/Title 117 0 R -/A 114 0 R -/Parent 104 0 R -/Prev 112 0 R -/Next 120 0 R ->> -% 112 0 obj -<< -/Title 113 0 R -/A 110 0 R -/Parent 104 0 R -/Prev 108 0 R -/Next 116 0 R ->> - -endstream -endobj -738 0 obj -<< - /Title (MultiLevel Domain Decomposition Parallel Preconditioners Package based on PSBLAS, V. 2.2) /Subject (MultiLevel Domain Decomposition Parallel Preconditioners Package) /Keywords (Parallel Numerical Software, Algebraic Multilevel Preconditioners, Sparse Iterative Solvers, PSBLAS, MPI) /Creator (pdfLaTeX) /Producer ($Id: userguide.tex 2008-04-08 Pasqua D'Ambra, Daniela di Serafino, Salvatore Filippone$) /Author()/Title()/Subject()/Creator(LaTeX with hyperref package)/Producer(pdfTeX-1.40.19)/Keywords() -/CreationDate (D:20191218142733Z) -/ModDate (D:20191218142733Z) -/Trapped /False -/PTEX.Fullbanner (This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018) kpathsea version 6.3.0) ->> -endobj -704 0 obj -<< -/Type /ObjStm -/N 60 -/First 499 -/Length 8129 ->> -stream -108 0 104 74 100 186 96 271 92 354 88 436 84 518 80 600 76 682 72 764 -68 833 64 953 60 1009 56 1127 52 1196 48 1278 44 1347 40 1465 36 1534 32 1616 -28 1698 24 1780 20 1849 16 1967 12 2048 8 2128 4 2193 705 2285 706 2453 707 2610 -708 2810 709 3019 710 3238 711 3466 712 3666 713 3859 714 4027 715 4192 716 4356 717 4521 -718 4685 719 4850 720 5013 721 5174 722 5336 723 5518 724 5695 725 5910 726 6125 727 6341 -728 6578 729 6743 730 6834 731 6943 732 7050 733 7156 734 7262 735 7326 736 7424 737 7457 -% 108 0 obj -<< -/Title 109 0 R -/A 106 0 R -/Parent 104 0 R -/Next 112 0 R ->> -% 104 0 obj -<< -/Title 105 0 R -/A 102 0 R -/Parent 68 0 R -/Prev 100 0 R -/First 108 0 R -/Last 124 0 R -/Count -5 ->> -% 100 0 obj -<< -/Title 101 0 R -/A 98 0 R -/Parent 68 0 R -/Prev 96 0 R -/Next 104 0 R ->> -% 96 0 obj -<< -/Title 97 0 R -/A 94 0 R -/Parent 68 0 R -/Prev 92 0 R -/Next 100 0 R ->> -% 92 0 obj -<< -/Title 93 0 R -/A 90 0 R -/Parent 68 0 R -/Prev 88 0 R -/Next 96 0 R ->> -% 88 0 obj -<< -/Title 89 0 R -/A 86 0 R -/Parent 68 0 R -/Prev 84 0 R -/Next 92 0 R ->> -% 84 0 obj -<< -/Title 85 0 R -/A 82 0 R -/Parent 68 0 R -/Prev 80 0 R -/Next 88 0 R ->> -% 80 0 obj -<< -/Title 81 0 R -/A 78 0 R -/Parent 68 0 R -/Prev 76 0 R -/Next 84 0 R ->> -% 76 0 obj -<< -/Title 77 0 R -/A 74 0 R -/Parent 68 0 R -/Prev 72 0 R -/Next 80 0 R ->> -% 72 0 obj -<< -/Title 73 0 R -/A 70 0 R -/Parent 68 0 R -/Next 76 0 R ->> -% 68 0 obj -<< -/Title 69 0 R -/A 66 0 R -/Parent 4 0 R -/Prev 60 0 R -/Next 128 0 R -/First 72 0 R -/Last 104 0 R -/Count -9 ->> -% 64 0 obj -<< -/Title 65 0 R -/A 62 0 R -/Parent 60 0 R ->> -% 60 0 obj -<< -/Title 61 0 R -/A 58 0 R -/Parent 4 0 R -/Prev 44 0 R -/Next 68 0 R -/First 64 0 R -/Last 64 0 R -/Count -1 ->> -% 56 0 obj -<< -/Title 57 0 R -/A 54 0 R -/Parent 44 0 R -/Prev 52 0 R ->> -% 52 0 obj -<< -/Title 53 0 R -/A 50 0 R -/Parent 44 0 R -/Prev 48 0 R -/Next 56 0 R ->> -% 48 0 obj -<< -/Title 49 0 R -/A 46 0 R -/Parent 44 0 R -/Next 52 0 R ->> -% 44 0 obj -<< -/Title 45 0 R -/A 42 0 R -/Parent 4 0 R -/Prev 20 0 R -/Next 60 0 R -/First 48 0 R -/Last 56 0 R -/Count -3 ->> -% 40 0 obj -<< -/Title 41 0 R -/A 38 0 R -/Parent 20 0 R -/Prev 36 0 R ->> -% 36 0 obj -<< -/Title 37 0 R -/A 34 0 R -/Parent 20 0 R -/Prev 32 0 R -/Next 40 0 R ->> -% 32 0 obj -<< -/Title 33 0 R -/A 30 0 R -/Parent 20 0 R -/Prev 28 0 R -/Next 36 0 R ->> -% 28 0 obj -<< -/Title 29 0 R -/A 26 0 R -/Parent 20 0 R -/Prev 24 0 R -/Next 32 0 R ->> -% 24 0 obj -<< -/Title 25 0 R -/A 22 0 R -/Parent 20 0 R -/Next 28 0 R ->> -% 20 0 obj -<< -/Title 21 0 R -/A 18 0 R -/Parent 4 0 R -/Prev 16 0 R -/Next 44 0 R -/First 24 0 R -/Last 40 0 R -/Count -5 ->> -% 16 0 obj -<< -/Title 17 0 R -/A 14 0 R -/Parent 4 0 R -/Prev 12 0 R -/Next 20 0 R ->> -% 12 0 obj -<< -/Title 13 0 R -/A 10 0 R -/Parent 4 0 R -/Prev 8 0 R -/Next 16 0 R ->> -% 8 0 obj -<< -/Title 9 0 R -/A 6 0 R -/Parent 4 0 R -/Next 12 0 R ->> -% 4 0 obj -<< -/Title 5 0 R -/A 1 0 R -/Parent 703 0 R -/First 8 0 R -/Last 140 0 R -/Count -11 ->> -% 705 0 obj -<< -/Names [(Doc-Start) 147 0 R (Item.1) 380 0 R (Item.10) 498 0 R (Item.11) 499 0 R (Item.12) 500 0 R (Item.13) 501 0 R] -/Limits [(Doc-Start) (Item.13)] ->> -% 706 0 obj -<< -/Names [(Item.2) 381 0 R (Item.3) 382 0 R (Item.4) 416 0 R (Item.5) 417 0 R (Item.6) 418 0 R (Item.7) 419 0 R] -/Limits [(Item.2) (Item.7)] ->> -% 707 0 obj -<< -/Names [(Item.8) 420 0 R (Item.9) 421 0 R (appendix.A) 135 0 R (cite.BREZINA_VANEK) 231 0 R (cite.Briggs2000) 227 0 R (cite.CAI_SARKIS) 403 0 R] -/Limits [(Item.8) (cite.CAI_SARKIS)] ->> -% 708 0 obj -<< -/Names [(cite.GrHeJi:16) 528 0 R (cite.MLD2P4_TOMS) 248 0 R (cite.MPI1) 282 0 R (cite.MPI2) 281 0 R (cite.MUMPS) 300 0 R (cite.Notay2008) 230 0 R] -/Limits [(cite.GrHeJi:16) (cite.Notay2008)] ->> -% 709 0 obj -<< -/Names [(cite.PSBLAS3) 234 0 R (cite.PSBLASGUIDE) 283 0 R (cite.SUPERLU) 301 0 R (cite.SUPERLUDIST) 302 0 R (cite.Saad_book) 367 0 R (cite.Stuben_01) 228 0 R] -/Limits [(cite.PSBLAS3) (cite.Stuben_01)] ->> -% 710 0 obj -<< -/Names [(cite.TUMINARO_TONG) 346 0 R (cite.UMFPACK) 299 0 R (cite.VANEK_MANDEL_BREZINA) 232 0 R (cite.aaecc_07) 348 0 R (cite.apnum_07) 349 0 R (cite.blas1) 280 0 R] -/Limits [(cite.TUMINARO_TONG) (cite.blas1)] ->> -% 711 0 obj -<< -/Names [(cite.blas2) 279 0 R (cite.blas3) 278 0 R (cite.dd2_96) 229 0 R (cite.para_04) 347 0 R (cite.psblas_00) 233 0 R (equation.1.1) 224 0 R] -/Limits [(cite.blas2) (equation.1.1)] ->> -% 712 0 obj -<< -/Names [(equation.4.2) 360 0 R (equation.4.3) 383 0 R (equation.4.4) 394 0 R (equation.4.5) 395 0 R (figure.1) 368 0 R (figure.2) 448 0 R] -/Limits [(equation.4.2) (figure.2)] ->> -% 713 0 obj -<< -/Names [(figure.3) 449 0 R (figure.4) 450 0 R (figure.5) 451 0 R (page.1) 146 0 R (page.10) 328 0 R (page.11) 345 0 R] -/Limits [(figure.3) (page.11)] ->> -% 714 0 obj -<< -/Names [(page.12) 359 0 R (page.13) 378 0 R (page.14) 393 0 R (page.15) 402 0 R (page.16) 415 0 R (page.17) 434 0 R] -/Limits [(page.12) (page.17)] ->> -% 715 0 obj -<< -/Names [(page.18) 447 0 R (page.19) 456 0 R (page.2) 155 0 R (page.20) 461 0 R (page.21) 467 0 R (page.22) 473 0 R] -/Limits [(page.18) (page.22)] ->> -% 716 0 obj -<< -/Names [(page.23) 485 0 R (page.24) 497 0 R (page.25) 516 0 R (page.26) 521 0 R (page.27) 526 0 R (page.28) 532 0 R] -/Limits [(page.23) (page.28)] ->> -% 717 0 obj -<< -/Names [(page.29) 538 0 R (page.3) 254 0 R (page.30) 542 0 R (page.31) 549 0 R (page.32) 554 0 R (page.33) 562 0 R] -/Limits [(page.29) (page.33)] ->> -% 718 0 obj -<< -/Names [(page.34) 571 0 R (page.35) 582 0 R (page.36) 587 0 R (page.37) 593 0 R (page.38) 601 0 R (page.39) 608 0 R] -/Limits [(page.34) (page.39)] ->> -% 719 0 obj -<< -/Names [(page.4) 274 0 R (page.40) 613 0 R (page.41) 620 0 R (page.42) 624 0 R (page.43) 630 0 R (page.44) 635 0 R] -/Limits [(page.4) (page.44)] ->> -% 720 0 obj -<< -/Names [(page.45) 639 0 R (page.46) 644 0 R (page.47) 648 0 R (page.5) 296 0 R (page.6) 306 0 R (page.7) 312 0 R] -/Limits [(page.45) (page.7)] ->> -% 721 0 obj -<< -/Names [(page.8) 318 0 R (page.9) 323 0 R (page.i) 159 0 R (page.ii) 165 0 R (page.iii) 203 0 R (page.iv) 210 0 R] -/Limits [(page.8) (page.iv)] ->> -% 722 0 obj -<< -/Names [(section*.1) 7 0 R (section*.2) 204 0 R (section*.3) 256 0 R (section*.4) 139 0 R (section.1) 11 0 R (section.2) 15 0 R] -/Limits [(section*.1) (section.2)] ->> -% 723 0 obj -<< -/Names [(section.3) 19 0 R (section.4) 43 0 R (section.5) 59 0 R (section.6) 67 0 R (section.7) 127 0 R (section.8) 131 0 R] -/Limits [(section.3) (section.8)] ->> -% 724 0 obj -<< -/Names [(subsection.3.1) 23 0 R (subsection.3.2) 27 0 R (subsection.3.3) 31 0 R (subsection.3.4) 35 0 R (subsection.3.5) 39 0 R (subsection.4.1) 47 0 R] -/Limits [(subsection.3.1) (subsection.4.1)] ->> -% 725 0 obj -<< -/Names [(subsection.4.2) 51 0 R (subsection.4.3) 55 0 R (subsection.5.1) 63 0 R (subsection.6.1) 71 0 R (subsection.6.2) 75 0 R (subsection.6.3) 79 0 R] -/Limits [(subsection.4.2) (subsection.6.3)] ->> -% 726 0 obj -<< -/Names [(subsection.6.4) 83 0 R (subsection.6.5) 87 0 R (subsection.6.6) 91 0 R (subsection.6.7) 95 0 R (subsection.6.8) 99 0 R (subsection.6.9) 103 0 R] -/Limits [(subsection.6.4) (subsection.6.9)] ->> -% 727 0 obj -<< -/Names [(subsubsection.6.9.1) 107 0 R (subsubsection.6.9.2) 111 0 R (subsubsection.6.9.3) 115 0 R (subsubsection.6.9.4) 119 0 R (subsubsection.6.9.5) 123 0 R (table.1) 422 0 R] -/Limits [(subsubsection.6.9.1) (table.1)] ->> -% 728 0 obj -<< -/Names [(table.2) 423 0 R (table.3) 527 0 R (table.4) 533 0 R (table.5) 503 0 R (table.6) 543 0 R (table.7) 502 0 R] -/Limits [(table.2) (table.7)] ->> -% 729 0 obj -<< -/Names [(table.8) 424 0 R (title.0) 3 0 R] -/Limits [(table.8) (title.0)] ->> -% 730 0 obj -<< -/Kids [705 0 R 706 0 R 707 0 R 708 0 R 709 0 R 710 0 R] -/Limits [(Doc-Start) (cite.blas1)] ->> -% 731 0 obj -<< -/Kids [711 0 R 712 0 R 713 0 R 714 0 R 715 0 R 716 0 R] -/Limits [(cite.blas2) (page.28)] ->> -% 732 0 obj -<< -/Kids [717 0 R 718 0 R 719 0 R 720 0 R 721 0 R 722 0 R] -/Limits [(page.29) (section.2)] ->> -% 733 0 obj -<< -/Kids [723 0 R 724 0 R 725 0 R 726 0 R 727 0 R 728 0 R] -/Limits [(section.3) (table.7)] ->> -% 734 0 obj -<< -/Kids [729 0 R] -/Limits [(table.8) (title.0)] ->> -% 735 0 obj -<< -/Kids [730 0 R 731 0 R 732 0 R 733 0 R 734 0 R] -/Limits [(Doc-Start) (title.0)] ->> -% 736 0 obj -<< -/Dests 735 0 R ->> -% 737 0 obj -<< -/Type /Catalog -/Pages 702 0 R -/Outlines 703 0 R -/Names 736 0 R - /PageMode/UseOutlines/PageLabels<>2<>6<>]>> -/OpenAction 142 0 R ->> - -endstream -endobj -739 0 obj -<< -/Type /XRef -/Index [0 740] -/Size 740 -/W [1 3 1] -/Root 737 0 R -/Info 738 0 R -/ID [<0BD05874B928E22165ED74B47BBCC2DD> <0BD05874B928E22165ED74B47BBCC2DD>] -/Length 3700 ->> -stream -˙;%JÀQÀÎ&ÀÎ9ÀÎNÀ  -ÎOÀ  Î^À Î_À9À9À9 À9*À9,À9EÀ 9UÀ ³À  ³ À -!"³&À #$³2À%& À'( À)* $À+, )À-. /À/0 6À12 7À34 8À56 9€c78 @€b9: A€a;< B€`=> L€_?@ V€^AB Z€]CD ^€\EFGKHI€?€L€F€ONLMROP€E€@US<TWXYZ[\]^_`abcÎÎÎÎÎÎÎÎÎÎ Î -Î Î Î ÎÎÎÎÎÎÎÎVÎ΀>á -ÎÎW“ÎÎÎÎÎ Î!Î"Î#Î$Î%ÎÎ(ÎX^Î'€B€P a€€€ `€€ € Î*Î+Î,Î-Î.Î/Î0Î1Î2Î3Î4Î)w~€Î7Î6Î;Î5ŒÎ8€MÎ:€IÎ=Î>Î?Î@ÎAÎBÎDÎFÎGÎHÎIÎJÎKÎPÎ<™ÉÎMÎCÎEÎL€€ €€€€ -ÎSÎTÎUÎVÎWÎXÎZÎ[ÎRÎ`ÎQ·²Î]ÎYÎ\€ _€€ÎcÎaĊÎb€K999Q9x€Q99* 999 -9:Ì9 9 99 Ih9 99999999999999!9_9€ b c€9#9$9%9&9'9(9-9":9)9+€D€N€J€H€C€G€9690919293949/9;9.Ğù95€A9798999:€R9=9>9?9@9A9F9<Ĝò9B9C9D9I9J9H9L9G”9K€9N9O9P9Q9R9S9_9`9\9M2°9T9V9W9X9Y9Z9[³³J 9a9b9c³³9^³9]Sá³Ü8³³³³ ³ -³ ³ ³ ³³Ğ•³³³³³³³³Íé³€S³³Û.³³³³!³çä³³#³$³'³"³%³*³+³,³-³.³/³0³)³3³( ³1³5³6³7³8³9³:³;³<³B³4$̳=³>³?³@³A ³_³E³N³O³T³U³V³W³X³D³G³CD&³F€T³K³HSŠ³I³M³R³Lb„³P³Q€ ³[³SŒ@³Y³Z³]³`³\¤j³^ ³aÈŻ³b³c)Ħ    Á €U  *Ô       -S        ^+      ! "  % p• # ' * &†m ( - , 0 +¨ .€V 2 3 4 : 1­H 5 = > < C ;½ ? E G Dѐ F J O I M HÔ^ K Q Nñ” P T S W Rù U€W [ X8 Y€ \ŝ ] }€€W€€€qH€€€€€€ €!€"€#€$€%€&€'€(€)€*€+€,v+€-c€.}€/IN€0jĜ€1ó€2ĊB€3îò€4UT€5î€6Ż$€7͟€8ôƒ€9M€:hĞ€;ž€<öż€=€X€Y€Z€[ SyÀÀÀÀÀÀ À!À"À#À$À%À&À'À(À)À*À+À,À-À.À/À0À1À2À3À4À5À6À7À8À9À:À; Pİ s• -endstream -endobj -startxref -619413 -%%EOF diff --git a/docs/src/Makefile b/docs/src/Makefile index 81417e58..e549a598 100644 --- a/docs/src/Makefile +++ b/docs/src/Makefile @@ -140,7 +140,7 @@ PDF = $(join $(BASEFILE),.pdf) PS = $(join $(BASEFILE),.ps) GXS = $(join $(BASEFILE),.gxs) GLX = $(join $(BASEFILE),.glx) -TARGETPDF= ../mld2p4-2.2-guide.pdf +TARGETPDF= ../amg4psblas_1.0-guide.pdf BASEHTML = $(patsubst %.tex,%,$(HTMLFILE)) HTML = $(join $(BASEHTML),.html) HTMLDIR = ../html diff --git a/docs/src/abstract.tex b/docs/src/abstract.tex index ad3e67b4..6146c18d 100644 --- a/docs/src/abstract.tex +++ b/docs/src/abstract.tex @@ -1,25 +1,25 @@ \section*{Abstract} -\addcontentsline{toc}{section}{Abstract} +\addcontentsline{toc}{section}{Abstract} -\textsc{MLD2P4 (MultiLevel Domain Decomposition Parallel Preconditioners Package -based on PSBLAS}) is a package of parallel algebraic multilevel preconditioners. -The first release of MLD2P4 made available multilevel additive and hybrid Schwarz -preconditioners, as well as one-level additive Schwarz preconditioners. The package -has been extended to include further multilevel cycles and smoothers widely used in -multigrid methods. In the multilevel case, a purely algebraic approach is applied to -generate coarse-level corrections, so that no geometric background is needed -concerning the matrix to be preconditioned. The matrix is assumed to be square, -real or complex. +\textsc{AMG4PSBLAS (Algebraic MultiGrid Preconditioners Package +based on PSBLAS}) is a package of parallel algebraic multilevel preconditioners included in the PSCToolkit (Parallel Sparse Computation Toolkit) software framework. +It is a progress of a software development project started in 2007, named MLD2P4, which implemented a multilevel version of some domain decomposition preconditioners of additive-Schwarz type and was based on a parallel decoupled version of the well known smoothed +aggregation method to generate the multilevel hierarchy of coarser matrices. In the last years, within the context of the EU-H2020 EoCoE project (Energy Oriented Center of Excellence), the package was extended including new algorithms and functionalities for setup and application of new AMG preconditioners with the final aims of improving efficiency and scalability when tens of thousands cores are +used and of boosting reliability in dealing with general symmetric positive definite linear systems. Due to the significant number of changes and the increase in scope, we decided to rename the package as AMG4PSBLAS. -MLD2P4 has been designed to provide scalable and easy-to-use preconditioners +AMG4PSBLAS has been designed to provide scalable and easy-to-use preconditioners in the context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms) computational framework and can be used in conjuction with the Krylov solvers -available in this framework. MLD2P4 enables the user to easily specify different -features of an algebraic multilevel preconditioner, thus allowing to search -for the ``best'' preconditioner for the problem at hand. +available in this framework. +Our package is based on a completely algebraic approach and users level interfaces +assume that the system matrix and preconditioners are represented as PSBLAS +distributed sparse matrices. +AMG4PSBLAS enables the user to easily specify different +features of an algebraic multilevel preconditioner, thus allowing to experiment +with different preconditioners for the problem and parallel computers at hand. The package employs object-oriented design techniques in -Fortran~2003, with interfaces to additional third party libraries +Fortran~2003, with interfaces to additional third party libraries such as MUMPS, UMFPACK, SuperLU, and SuperLU\_Dist, which can be exploited in building multilevel preconditioners. The parallel implementation is based on a Single Program Multiple Data (SPMD) @@ -27,4 +27,4 @@ paradigm; the inter-process communication is based on MPI and is managed mainly through PSBLAS. This guide provides a brief description of the functionalities and -the user interface of MLD2P4. +the user interface of AMG4PSBLAS. \ No newline at end of file diff --git a/docs/src/bibliography.tex b/docs/src/bibliography.tex index d6716846..c8b21bbe 100644 --- a/docs/src/bibliography.tex +++ b/docs/src/bibliography.tex @@ -1,6 +1,6 @@ %\section{Bibliography\label{sec:bib}} \begin{thebibliography}{99} -\addcontentsline{toc}{section}{\refname} +\addcontentsline{toc}{section}{\refname} \markboth{\textsc{MLD2P4 User's and Reference Guide}} {\textsc{References}} @@ -18,7 +18,7 @@ M.~Brezina, P.~Van\v{e}k, Computing, 63, 1999, 233--263. % \bibitem{Briggs2000} -W.~L.~Briggs, V.~E.~Henson, S.~F.~McCormick, +W.~L.~Briggs, V.~E.~Henson, S.~F.~McCormick, {\em A Multigrid Tutorial, Second Edition}, SIAM, 2000. % @@ -30,11 +30,11 @@ Proceedings of PARA~04 Workshop on State of the Art in Scientific Computing, Lecture Notes in Computer Science, Springer, 2005, 593--602. % -\bibitem{aaecc_07} +\bibitem{aaecc_07} A.~Buttari, P.~D'Ambra, D.~di~Serafino, S.~Filippone, {\em 2LEV-D2P4: a package of high-performance preconditioners for scientific and engineering applications}, -Applicable Algebra in Engineering, Communications and Computing, +Applicable Algebra in Engineering, Communications and Computing, 18 (3) 2007, 223--239. %Published online: 13 February 2007, {\tt http://dx.doi.org/10.1007/s00200-007-0035-z} % @@ -57,19 +57,29 @@ SIAM Journal on Scientific Computing, 21 (2), 1999, 792--797. \bibitem{apnum_07} P.~D'Ambra, S.~Filippone, D.~di~Serafino, {\em On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners}, -Applied Numerical Mathematics, Elsevier Science, +Applied Numerical Mathematics, Elsevier Science, 57 (11-12), 2007, 1181-1196. %published online 3 February 2007, {\tt % http://dx.doi.org/10.1016/j.apnum.2007.01.006} % -\bibitem{MLD2P4_TOMS} +\bibitem{MLD2P4_TOMS} P.~D'Ambra, D.~di~Serafino, S.~Filippone, \emph{MLD2P4: a Package of Parallel Multilevel Algebraic Domain Decomposition Preconditioners in Fortran 95}, ACM Trans. Math. Softw., 37(3), 2010, art. 30. % +\bibitem{BDDF2007} +A.~Buttari, P.~D'Ambra, D.~di Serafino, S.~Filippone, +\emph{2{LEV}-{D}2{P}4: a Package of High-Performance Preconditioners +for Scientific and Engineering Applications}, Appl. Algebra Engrg. Comm. Comput., +18(3), 2007, 223--239. +% +\bibitem{DDF2020} +P.~D'Ambra, F~Durastante, S.~Filippone, +\emph{AMG preconditioners for Linear Solvers towards Extreme Scale}, 2020, arXiv:2006.16147v2. +% \bibitem{UMFPACK} -T.~A.~Davis, +T.~A.~Davis, {\em Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal Method with a Column Pre-ordering Strategy}, ACM Transactions on Mathematical Software, 30, 2004, 196--199. @@ -96,13 +106,13 @@ ACM Transactions on Mathematical Software, 14 (1) 1988, 1--17. %Lapack Working Note 94, Tech.\ Rep.\ UT-CS-95-281, University of %Tennessee, March 1995 (updated May 1997). % -%\bibitem{EFSTATHIOU} +%\bibitem{EFSTATHIOU} %E.~Efstathiou, J.~G.~Gander, %{\em Why Restricted Additive Schwarz Converges Faster than Additive Schwarz}, %BIT Numerical Mathematics, 43 (5), 2003, 945--959. % \bibitem{PSBLASGUIDE} -S.~Filippone, A.~Buttari, +S.~Filippone, A.~Buttari, {\em PSBLAS 3.5.0 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library}, 2012, available from \texttt{https://github.com/sfilippone/psblas3/tree/master/docs}. % @@ -112,19 +122,19 @@ S.~Filippone, A.~Buttari, ACM Transactions on on Mathematical Software, 38 (4), 2012, art.~23. % \bibitem{psblas_00} -S.~Filippone, M.~Colajanni, +S.~Filippone, M.~Colajanni, {\em PSBLAS: A Library for Parallel Linear Algebra Computation on Sparse Matrices}, ACM Transactions on Mathematical Software, 26 (4), 2000, 527--550. % \bibitem{GrHeJi:16} S. Gratton, P. Henon, P. Jiranek and X. Vasseur, - {\em Reducing complexity of algebraic multigrid by aggregation}, + {\em Reducing complexity of algebraic multigrid by aggregation}, Numerical Lin. Algebra with Applications, 2016, 23:501-518 % \bibitem{MPI2} -W.~Gropp, S.~Huss-Lederman, A.~Lumsdaine, E.~Lusk, B.~Nitzberg, W.~Saphir, M.~Snir, +W.~Gropp, S.~Huss-Lederman, A.~Lumsdaine, E.~Lusk, B.~Nitzberg, W.~Saphir, M.~Snir, {\em MPI: The Complete Reference. Volume 2 - The MPI-2 Extensions}, MIT Press, 1998. % @@ -142,7 +152,7 @@ ACM Transactions on Mathematical Software, 29 (2), 2003, 110--140. \bibitem{Notay2008} Y.~Notay, P.~S.~Vassilevski, {\em Recursive Krylov-based multigrid cycles}, -Numerical Linear Algebra with Applications, 15 (5), 2008, 473--487. +Numerical Linear Algebra with Applications, 15 (5), 2008, 473--487. % \bibitem{Saad_book} Y.~Saad, @@ -173,5 +183,15 @@ R.~S.~Tuminaro, C.~Tong, P.~Van\v{e}k, J.~Mandel, M.~Brezina, {\em Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems}, Computing, 56 (3) 1996, 179--196. - +% +\bibitem{DV2013} +P.~D'Ambra and P.\,S.~Vassilevski, +{\em Adaptive AMG with coarsening based on compatible weighted matching}, +Computing and Visualization in Science, 16, (2013) 59--76. +% +\bibitem{DFV2018} +P.~D'Ambra, S.~Filippone and P.\,S.~Vassilevski, +{\em BootCMatch: a software package for bootstrap AMG based on graph weighted matching}, +ACM Transactions on Mathematical Software, 44, (2018) 39:1--39:25. +% \end{thebibliography} diff --git a/docs/src/building.tex b/docs/src/building.tex index 836e5470..baf47463 100644 --- a/docs/src/building.tex +++ b/docs/src/building.tex @@ -1,33 +1,33 @@ -\section{Configuring and Building MLD2P4\label{sec:building}} -\markboth{\textsc{MLD2P4 User's and Reference Guide}} - {\textsc{\ref{sec:building} Configuring and Building MLD2P4}} -In order to build MLD2P4 it is necessary to set up a Makefile with appropriate +\section{Configuring and Building AMG4PSBLAS\label{sec:building}} +\markboth{\textsc{AMG4PSBLAS User's and Reference Guide}} + {\textsc{\ref{sec:building} Configuring and Building AMG4PSBLAS}} +In order to build AMG4PSBLAS it is necessary to set up a Makefile with appropriate system-dependent variables; this is done by means of the \verb|configure| script. The distribution also includes the autoconf and automake sources employed to generate the script, but usually this is not needed -to build the software. +to build the software. -MLD2P4 is implemented almost entirely in Fortran~2003, with some +AMG4PSBLAS is implemented almost entirely in Fortran~2003, with some interfaces to external libraries in C; the Fortran compiler must support the Fortran~2003 standard plus the extension \verb|MOLD=| -feature, which enhances the usability of \verb|ALLOCATE|. +feature, which enhances the usability of \verb|ALLOCATE|. Many compilers do this; in particular, this is -supported by the GNU Fortran compiler, for which we -recommend to use at least version 4.8. +supported by the GNU Fortran compiler, for which we +recommend to use at least version 4.8. The software defines data types and interfaces for -real and complex data, in both single and double precision. +real and complex data, in both single and double precision. -Building MLD2P4 requires some base libraries (see Section~\ref{sec:prerequisites}); -interfaces to optional third-party libraries, which extend the functionalities of MLD2P4 +Building AMG4PSBLAS requires some base libraries (see Section~\ref{sec:prerequisites}); +interfaces to optional third-party libraries, which extend the functionalities of AMG4PSBLAS (see Section~\ref{sec:third-party}), are also available. Many Linux distributions (e.g., Ubuntu, Fedora, CentOS) provide precompiled packages for the prerequisite and optional software. In many cases these packages are split between a runtime part and a -``developer'' part; in order to build MLD2P4 you need both. A description of the base and -optional software used by MLD2P4 is given in the next sections. +``developer'' part; in order to build AMG4PSBLAS you need both. A description of the base and +optional software used by AMG4PSBLAS is given in the next sections. \subsection{Prerequisites\label{sec:prerequisites}} -The following base libraries are needed: +The following base libraries are needed: \begin{description} \item[BLAS] \cite{blas3,blas2,blas1} Many vendors provide optimized versions of BLAS; if no vendor version is @@ -36,38 +36,38 @@ The following base libraries are needed: may be employed. The reference BLAS from Netlib (\url{www.netlib.org/blas}) are meant to define the standard behaviour of the BLAS interface, so they are not optimized for any - particular plaftorm, and should only be used as a last + particular platform, and should only be used as a last resort. Note that BLAS computations form a relatively small part of - the MLD2P4/PSBLAS computations; they are however critical when using + the AMG4PSBLAS/PSBLAS computations; they are however critical when using preconditioners based on MUMPS, UMFPACK or SuperLU third party libraries. Note that UMFPACK requires a full LAPACK library; our experience is that configuring ATLAS for building full LAPACK does not work in the correct way. Our advice is first to download the LAPACK tarfile from \url{www.netlib.org/lapack} and install it independently of ATLAS. In this case, you need to modify the OPTS and NOOPT definitions for including -fPIC compilation option -in the make.inc file of the LAPACK library. +in the make.inc file of the LAPACK library. \item[MPI] \cite{MPI2,MPI1} A version of MPI is available on most high-performance computing systems. \item[PSBLAS] \cite{PSBLASGUIDE,psblas_00} Parallel Sparse BLAS (PSBLAS) is - available from \url{github.com/sfilippone/psblas3}; version + available from \url{github.com/sfilippone/psblas3} ?? {\bf Mettere tutto sotto psctoolkit}; version 3.5.0 (or later) is required. Indeed, all the prerequisites listed so far are also prerequisites of PSBLAS. \end{description} Please note that the four previous libraries must have Fortran -interfaces compatible with MLD2P4; +interfaces compatible with AMG4PSBLAS; usually this means that they should all be built with the same -compiler as MLD2P4. +compiler as AMG4PSBLAS. \subsection{Optional third party libraries\label{sec:third-party}} We provide interfaces to the following third-party software libraries; note that these are optional, but if you enable them some defaults -for multilevel preconditioners may change to reflect their presence. +for multilevel preconditioners may change to reflect their presence. \begin{description} \item[UMFPACK] \cite{UMFPACK} - A sparse LU factorization package included in the SuiteSparse library, available from - \url{faculty.cse.tamu.edu/davis/suitesparse.html}; + A sparse LU factorization package included in the SuiteSparse library, available from + \url{faculty.cse.tamu.edu/davis/suitesparse.html}; it provides sequential factorization and triangular system solution for double precision real and complex data. We tested version 4.5.4 of SuiteSparse. Note that for configuring SuiteSparse you should provide the right path to the BLAS @@ -97,10 +97,13 @@ for multilevel preconditioners may change to reflect their presence. \subsection{Configuration options} -In order to build MLD2P4, the first step is to use the \verb|configure| script +In order to build AMG4PSBLAS, the first step is to use the \verb|configure| script in the main directory to generate the necessary makefile. %\textbf{Sono necessarie le parentesi intorno a s?} + +\bf{DA RISCRIVERE} + As a minimal example consider the following: \begin{verbatim} ./configure --with-psblas=PSB-INSTALL-DIR @@ -290,7 +293,7 @@ generated the file \verb|Make.inc| which will then be used by all Makefiles in the directory tree; this file will be copied in the install directory under the name \verb|Make.inc.MLD2P4|. -To use the MUMPS solver package, +To use the MUMPS solver package, the user has to add the appropriate options to the configure script; by default we are looking for the libraries \verb|-ldmumps -lsmumps| \verb| -lzmumps -lcmumps -mumps_common -lpord|. @@ -298,30 +301,22 @@ MUMPS often uses additional packages such as ScaLAPACK, ParMETIS, SCOTCH, as well as enabling OpenMP; in such cases it is necessary to add linker options with the \verb|--with-extra-libs| configure option. -To build the library the user will now enter +To build the library the user will now enter \begin{verbatim} make \end{verbatim} -followed (optionally) by +followed (optionally) by \begin{verbatim} make install \end{verbatim} \subsection{Bug reporting} If you find any bugs in our codes, please report them through our issues page on \\[2mm] -\url{https://github.com/sfilippone/mld2p4-2/issues}\\ -% please let us know at -%\begin{rawhtml} -% -%\end{rawhtml} -%\texttt{bugreport@mld2p4.it} -%\begin{rawhtml} -% -%\end{rawhtml} -%; +\url{https://github.com/psctoolkit/amg4psblas/issues}\\ + To enable us to track the bug, please provide a log from the failing application, the test conditions, and ideally a self-contained test -program reproducing the issue. +program reproducing the issue. \subsection{Example and test programs\label{sec:ex_and_test}} The package contains the \verb|examples| and \verb|tests| directories; @@ -331,7 +326,7 @@ both of them are further divided into \verb|fileread| and \item[\tt examples] contains a set of simple example programs with a predefined choice of preconditioners, selectable via integer values. These are intended to get an acquaintance with the - multilevel preconditioners available in MLD2P4. + multilevel preconditioners available in AMG4PSBLAS. \item[\tt tests] contains a set of more sophisticated examples that will allow the user, via the input files in the \verb|runs| subdirectories, to experiment with the full range of preconditioners @@ -341,4 +336,4 @@ The \verb|fileread| directories contain sample programs that read sparse matrices from files, according to the Matrix Market or the Harwell-Boeing storage format; the \verb|pdegen| programs generate matrices in full parallel mode from the discretization of a sample partial -differential equation. +differential equation. diff --git a/docs/src/distribution.tex b/docs/src/distribution.tex index 5682acfe..8aec100c 100644 --- a/docs/src/distribution.tex +++ b/docs/src/distribution.tex @@ -1,11 +1,11 @@ \section{Code Distribution\label{sec:distribution}} -\markboth{\textsc{MLD2P4 User's and Reference Guide}} +\markboth{\textsc{AMG4PSBLAS User's and Reference Guide}} {\textsc{\ref{sec:distribution} Code Distribution}} \noindent -MLD2P4 is available from the web site +AMG4PSBLAS is available from the web site \begin{quotation} -\texttt{https://github.com/sfilippone/mld2p4-2} +\texttt{https://github.com/psctoolkit/amg4psblas} \end{quotation} where contact points for further information can be also found. @@ -13,25 +13,16 @@ The software is available under a modified BSD license, as specified in Appendix~\ref{sec:license}; please note that some of the optional third party libraries may be licensed under a different and more stringent license, most notably the GPL, and this should be taken into -account when treating derived works. +account when treating derived works. The library defines a version string with the -constant -\[ \verb|mld_version_string_|\] -whose current value is \verb|2.1.0|. +constant +\[ \verb|amg_version_string_|\] +whose current value is \verb|1.0|. \subsection*{Contributors} -Contributors to version 2: \begin{itemize} -\item Salvatore Filippone, Cranfield University, UK; -\item Pasqua D'Ambra, IAC-CNR, Naples, IT; -\item Daniela di Serafino, University of Campania ``L. Vanvitelli'', Caserta, IT; -\item Ambra Abdullahi Hassan, University of Rome ``Tor Vergata'', IT. -\end{itemize} -Contributors to version 1: -\begin{itemize} -\item Salvatore Filippone; -\item Pasqua D'Ambra; -\item Daniela di Serafino; -\item Alfredo Buttari, CNRS-IRIT, Toulouse, F. -\end{itemize} +\item Pasqua D'Ambra, IAC-CNR, IT; +\item Fabio Durastante, University of Pisa and IAC-CNR, IT; +\item Salvatore Filippone, University of Rome Tor-Vergata and IAC-CNR, IT; +\end{itemize} \ No newline at end of file diff --git a/docs/src/errors.tex b/docs/src/errors.tex index 67ee191d..5c67ede4 100644 --- a/docs/src/errors.tex +++ b/docs/src/errors.tex @@ -1,8 +1,8 @@ \section{Error Handling\label{sec:errors}} -\markboth{\textsc{MLD2P4 User's and Reference Guide}} +\markboth{\textsc{AMG4PSBLAS User's and Reference Guide}} {\textsc{\ref{sec:errors} Error handling}} -The error handling in MLD2P4 is based on the PSBLAS error +The error handling in AMG4PSBLAS is based on the PSBLAS error handling. Error conditions are signaled via an integer argument \verb|info|; whenever an error condition is detected, an error trace stack is built by the library up to the top-level, user-callable @@ -12,9 +12,9 @@ program or by returning the error condition to the user code, which will then take action, and whether an error message should be printed. These options may be set by using the PSBLAS error handling routines; for further details see the PSBLAS -User's Guide \cite{PSBLASGUIDE}. +User's Guide \cite{PSBLASGUIDE}. -%%% Local Variables: +%%% Local Variables: %%% mode: latex %%% TeX-master: "userguide" -%%% End: +%%% End: diff --git a/docs/src/figures/amg4psblaslibrary.png b/docs/src/figures/amg4psblaslibrary.png new file mode 100644 index 00000000..604d1a53 Binary files /dev/null and b/docs/src/figures/amg4psblaslibrary.png differ diff --git a/docs/src/gettingstarted.tex b/docs/src/gettingstarted.tex index f9565355..f78e9ed2 100644 --- a/docs/src/gettingstarted.tex +++ b/docs/src/gettingstarted.tex @@ -1,17 +1,17 @@ \section{Getting Started\label{sec:started}} -\markboth{\textsc{MLD2P4 User's and Reference Guide}} +\markboth{\textsc{AMG4PSBLAS User's and Reference Guide}} {\textsc{\ref{sec:started} Getting Started}} -We describe the basics for building and applying MLD2P4 one-level and multilevel +We describe the basics for building and applying AMG4PSBLAS one-level and multilevel (i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS \cite{PSBLASGUIDE}. The following steps are required: -\begin{enumerate} +\begin{enumerate} \item \emph{Declare the preconditioner data structure}. It is a derived data type, - \verb|mld_|\-\emph{x}\verb|prec_| \verb|type|, where \emph{x} may be \verb|s|, \verb|d|, \verb|c| + \verb|amg_|\-\emph{x}\verb|prec_| \verb|type|, where \emph{x} may be \verb|s|, \verb|d|, \verb|c| or \verb|z|, according to the basic data type of the sparse matrix (\verb|s| = real single precision; \verb|d| = real double precision; \verb|c| = complex single precision; \verb|z| = complex double precision). - This data structure is accessed by the user only through the MLD2P4 routines, + This data structure is accessed by the user only through the AMG4PSBLAS routines, following an object-oriented approach. \item \emph{Allocate and initialize the preconditioner data structure, according to a preconditioner type chosen by the user}. This is performed by the routine @@ -21,21 +21,14 @@ The following steps are required: \verb|init| to identify the preconditioner types are also given. Note that these strings are valid also if uppercase letters are substituted by corresponding lowercase ones. -%\item \emph{Modify the aggregation parameters (for multilevel preconditioners only).} -% This is performed by the routine \verb|mld_precset|. -% This routine must be called only if the user wants to modify the default values -% of the parameters associated with the aggregation hierarchy construction. -% Examples of use of \verb|mld_precset| are given in -% Section~\ref{sec:examples}; a complete list of all the -% preconditioner parameters and their allowed and default values is provided in -% Section~\ref{sec:userinterface}, Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}. + \item \emph{Modify the selected preconditioner type, by properly setting preconditioner parameters.} This is performed by the routine \verb|set|. This routine must be called only if the user wants to modify the default values of the parameters associated with the selected preconditioner type, to obtain a variant of that preconditioner. Examples of use of \verb|set| are given in Section~\ref{sec:examples}; a complete list of all the - preconditioner parameters and their allowed and default values is provided in + preconditioner parameters and their allowed and default values is provided in Section~\ref{sec:userinterface}, Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}. \item \emph{Build the preconditioner for a given matrix}. If the selected preconditioner is multilevel, then two steps must be performed, as specified next. @@ -58,7 +51,7 @@ performed by the routine \verb|bld|. All the previous routines are available as methods of the preconditioner object. A detailed description of them is given in Section~\ref{sec:userinterface}. -Examples showing the basic use of MLD2P4 are reported in Section~\ref{sec:examples}. +Examples showing the basic use of AMG4PSBLAS are reported in Section~\ref{sec:examples}. \begin{table}[h!] \begin{center} @@ -81,7 +74,7 @@ Block Jacobi & \verb|'BJAC'| & Block-Jacobi with ILU(0) on the local blocks Additive Schwarz & \verb|'AS'| & Additive Schwarz (AS), with overlap~1 and ILU(0) on the local blocks. \\ \hline Multilevel &\verb|'ML'| & V-cycle with one hybrid forward Gauss-Seidel - (GS) sweep as pre-smoother and one hybrid backward + (GS) sweep as pre-smoother and one hybrid backward GS sweep as post-smoother, basic smoothed aggregation as coarsening algorithm, and LU (plus triangular solve) as coarsest-level solver. See the default values in @@ -95,8 +88,8 @@ Multilevel &\verb|'ML'| & V-cycle with one hybrid forward Gauss-Seidel \end{center} \end{table} -Note that the module \verb|mld_prec_mod|, containing the definition of the -preconditioner data type and the interfaces to the routines of MLD2P4, +Note that the module \verb|amg_prec_mod|, containing the definition of the +preconditioner data type and the interfaces to the routines of AMG4PSBLAS, must be used in any program calling such routines. The modules \verb|psb_base_mod|, for the sparse matrix and communication descriptor data types, and \verb|psb_krylov_mod|, for interfacing with the @@ -108,36 +101,30 @@ usually lead to smaller numbers of preconditioned Krylov iterations than inexact solvers, when the linear system comes from a standard discretization of basic scalar elliptic PDE problems. However, this does not necessarily correspond to the smallest execution time -on parallel computers. -% \ \\ -% \textbf{Remark 2.} The include path for MLD2P4 must override -% those for PSBLAS, i.e.\ the former must come first in the sequence -% passed to the compiler, as the MLD2P4 version of the Krylov solver -% interfaces must override that of PSBLAS. This will change in the future -% when the support for the \verb|class| statement becomes widespread in Fortran -% compilers. +on parallel computers. +{\em DA MODIFICARE PER INSERIRE TIPO DI AGGREGAZIONE} \subsection{Examples\label{sec:examples}} The code reported in Figure~\ref{fig:ex1} shows how to set and apply the default multilevel preconditioner available in the real double precision version -of MLD2P4 (see Table~\ref{tab:precinit}). This preconditioner is chosen +of AMG4PSBLAS (see Table~\ref{tab:precinit}). This preconditioner is chosen by simply specifying \verb|'ML'| as the second argument of \verb|P%init| (a call to \verb|P%set| is not needed) and is applied with the CG solver provided by PSBLAS (the matrix of the system to be solved is assumed to be positive definite). As previously observed, the modules -\verb|psb_base_mod|, \verb|mld_prec_mod| and \verb|psb_krylov_mod| +\verb|psb_base_mod|, \verb|amg_prec_mod| and \verb|psb_krylov_mod| must be used by the example program. - + The part of the code concerning the reading and assembling of the sparse matrix and the right-hand side vector, performed through the PSBLAS routines for sparse matrix and vector management, is not reported here for brevity; the statements concerning the deallocation of the PSBLAS data structure are neglected too. -The complete code can be found in the example program file \verb|mld_dexample_ml.f90|, -in the directory \verb|examples/fileread| of the MLD2P4 implementation (see +The complete code can be found in the example program file \verb|amg_dexample_ml.f90|, +in the directory \verb|examples/fileread| of the AMG4PSBLAS implementation (see Section~\ref{sec:ex_and_test}). A sample test problem along with the relevant input data is available in \verb|examples/fileread/runs|. For details on the use of the PSBLAS routines, see the PSBLAS User's @@ -151,11 +138,11 @@ the corresponding codes are available in \verb|examples/fileread/|. \begin{figure}[tbp] \begin{center} -\begin{minipage}{.90\textwidth} +\begin{minipage}{.90\textwidth} {\small \begin{verbatim} use psb_base_mod - use mld_prec_mod + use amg_prec_mod use psb_krylov_mod ... ... ! @@ -164,7 +151,7 @@ the corresponding codes are available in \verb|examples/fileread/|. ! sparse matrix descriptor type(psb_desc_type) :: desc_A ! preconditioner - type(mld_dprec_type) :: P + type(amg_dprec_type) :: P ! right-hand side and solution vectors type(psb_d_vect_type) :: b, x ... ... @@ -174,7 +161,7 @@ the corresponding codes are available in \verb|examples/fileread/|. call psb_info(ictxt,iam,np) ... ... ! -! read and assemble the spd matrix A and the right-hand side b +! read and assemble the spd matrix A and the right-hand side b ! using PSBLAS routines for sparse matrix / vector management ... ... ! @@ -230,41 +217,31 @@ and solves the coarsest-level system with the multifrontal LU factorization implemented in MUMPS. It is specified that the coarsest-level matrix is distributed, since MUMPS can be used on both replicated and distributed matrices, and by default -it is used on replicated ones. +it is used on replicated ones. %Note the use of the parameter \verb|pos| %to specify a property only for the pre-smoother or the post-smoother %(see Section~\ref{sec:precset} for more details). The code fragments shown in Figures~\ref{fig:ex2} and \ref{fig:ex3} are -included in the example program file \verb|mld_dexample_ml.f90| too. +included in the example program file \verb|amg_dexample_ml.f90| too. Finally, Figure~\ref{fig:ex4} shows the setup of a one-level additive Schwarz preconditioner, i.e., RAS with overlap 2. Note also that a Krylov method different from CG must be used to solve the preconditioned system, since the preconditione in nonsymmetric. The corresponding example program is available in the file -\verb|mld_dexample_1lev.f90|. +\verb|amg_dexample_1lev.f90|. For all the previous preconditioners, example programs where the sparse matrix and the right-hand side are generated by discretizing a PDE with Dirichlet boundary conditions are also available in the directory \verb|examples/pdegen|. -% \ \\ -% \textbf{Remark 2.} Any PSBLAS-based program using the basic preconditioners -% implemented in PSBLAS 3.0, i.e.\ the diagonal and block-Jacobi ones, -% can use the diagonal and block-Jacobi preconditioners -% implemented in MLD2P4 without change in the code. -% The PSBLAS-based program must be only recompiled -% and linked to the MLD2P4 library. -% \\ - - \begin{figure}[tbh] \begin{center} -\begin{minipage}{.90\textwidth} +\begin{minipage}{.90\textwidth} {\small \begin{verbatim} ... ... -! build a V-cycle preconditioner with 1 block-Jacobi sweep (with +! build a V-cycle preconditioner with 1 block-Jacobi sweep (with ! ILU(0) on the blocks) as pre- and post-smoother, and 8 block-Jacobi ! sweeps (with ILU(0) on the blocks) as coarsest-level solver call P%init('ML',info) @@ -284,7 +261,7 @@ boundary conditions are also available in the directory \verb|examples/pdegen|. \begin{figure}[h!] \begin{center} -\begin{minipage}{.90\textwidth} +\begin{minipage}{.90\textwidth} {\small \begin{verbatim} ... ... @@ -309,7 +286,7 @@ boundary conditions are also available in the directory \verb|examples/pdegen|. \begin{figure}[h!] \begin{center} -\begin{minipage}{.90\textwidth} +\begin{minipage}{.90\textwidth} {\small \begin{verbatim} ... ... @@ -328,7 +305,7 @@ boundary conditions are also available in the directory \verb|examples/pdegen|. \end{figure} -%%% Local Variables: +%%% Local Variables: %%% mode: latex %%% TeX-master: "userguide" -%%% End: +%%% End: diff --git a/docs/src/license.tex b/docs/src/license.tex index f298af02..c45fa378 100644 --- a/docs/src/license.tex +++ b/docs/src/license.tex @@ -1,20 +1,22 @@ \section{License\label{sec:license}} -\markboth{\textsc{MLD2P4 User's and Reference Guide}} +\markboth{\textsc{AMG4PSBLAS User's and Reference Guide}} {\textsc{\ref{sec:license} License}} -The MLD2P4 is freely distributable under the following copyright +{\bf DA CONTROLLARE E MODIFICARE INCLUDENDO I CREDITS A MLD2P4} + +The AMG4PSBLAS is freely distributable under the following copyright terms: {\small -\begin{verbatim} - - MLD2P4 version 2.1 - MultiLevel Domain Decomposition Parallel Preconditioners Package +\begin{verbatim} + + AMG4PSBLAS version 1.0 + Algebraic MultiGrid Preconditioners Package based on PSBLAS (Parallel Sparse BLAS version 3.5) - + (C) Copyright 2008, 2010, 2012, 2015, 2017 - Salvatore Filippone Cranfield University, Cranfield, UK - Pasqua D'Ambra IAC-CNR, Naples, IT - Daniela di Serafino University of Campania L. Vanvitelli, Caserta, IT + Pasqua D'Ambra IAC-CNR, IT + Fabio Durastante University of Pisa and IAC-CNR, IT + Salvatore Filippone University of Rome Tor-Vergata and IAC-CNR, IT Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions @@ -27,7 +29,7 @@ terms: {\small 3. The name of the MLD2P4 group or the names of its contributors may not be used to endorse or promote products derived from this software without specific written permission. - + THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR @@ -39,6 +41,6 @@ terms: {\small CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. - + \end{verbatim} } diff --git a/docs/src/newobjects.tex b/docs/src/newobjects.tex index c7913c27..abb058c8 100644 --- a/docs/src/newobjects.tex +++ b/docs/src/newobjects.tex @@ -1,21 +1,21 @@ \clearpage -\section{Adding new smoother and solver objects to MLD2P4\label{sec:adding}} +\section{Adding new smoother and solver objects to AMG4PSBLAS\label{sec:adding}} Developers can add completely new smoother and/or solver classes derived from the base objects in the library (see Remark~2 in Section~\ref{sec:precset}), -without recompiling the library itself. +without recompiling the library itself. To do so, it is necessary first to select the base type to be extended. In our experience, it is quite likely that the new application needs only the definition of a ``solver'' object, which is almost -always acting only on the local part of the distributed matrix. +always acting only on the local part of the distributed matrix. The parallel actions required to connect the various solver objects are most often already provided by the block-Jacobi or the additive Schwarz smoothers. To define a new solver, the developer will then have to define its components and methods, perhaps taking one of the -predefined solvers as a starting point, if possible. +predefined solvers as a starting point, if possible. Once the new smoother/solver class has been developed, to use it in the context of the multilevel preconditioners it is necessary to: @@ -30,9 +30,9 @@ following: \item link the code implementing the various methods into the application executable. \end{itemize} The new solver object is then dynamically included in the -preconditioner structure, and acts as a \emph{mold} to which the -preconditioner will conform, even though the MLD2P4 library has not -been modified to account for this new development. +preconditioner structure, and acts as a \emph{mold} to which the +preconditioner will conform, even though the AMG4PSBLAS library has not +been modified to account for this new development. It is possible to define new values for the keyword \verb|WHAT| in the \verb|set| routine; if the library code does not recognize a keyword, @@ -50,35 +50,35 @@ factorization under a new name). Because of the specifics of this case, it is possible to reuse the basic structure of the ILU solver, with its L/D/U components and the methods needed to apply the solver; only a few methods, such as the description and most importantly the build, -need to be ovverridden (rewritten). +need to be ovverridden (rewritten). The interfaces for the calls shown above are defined using \begin{center} \begin{tabular}{p{1.4cm}p{12cm}} -\verb|smoother| & \verb|class(mld_x_base_smoother_type)| \\ +\verb|smoother| & \verb|class(amg_x_base_smoother_type)| \\ & The user-defined new smoother to be employed in the preconditioner.\\ -\verb|solver| & \verb|class(mld_x_base_solver_type)| \\ +\verb|solver| & \verb|class(amg_x_base_solver_type)| \\ & The user-defined new solver to be employed in the preconditioner. \end{tabular} \end{center} The other arguments are defined in the way described in Sec.~\ref{sec:precset}. As an example, in the \verb|tests/newslv| -code we define a new object of type \verb|mld_d_tlu_solver_type|, and +code we define a new object of type \verb|amg_d_tlu_solver_type|, and we pass it as follows: \begin{verbatim} ! sparse matrix and preconditioner type(psb_dspmat_type) :: a - type(mld_dprec_type) :: prec - type(mld_d_tlu_solver_type) :: tlusv + type(amg_dprec_type) :: prec + type(amg_d_tlu_solver_type) :: tlusv ...... ! ! prepare the preconditioner: an ML with defaults, but with TLU solver at - ! intermediate levels. All other parameters are at default values. - ! + ! intermediate levels. All other parameters are at default values. + ! call prec%init('ML', info) call prec%hierarchy_build(a,desc_a,info) nlv = prec%get_nlevs() diff --git a/docs/src/overview.tex b/docs/src/overview.tex index 1c142973..0201787c 100644 --- a/docs/src/overview.tex +++ b/docs/src/overview.tex @@ -1,105 +1,87 @@ \section{General Overview\label{sec:overview}} -\markboth{\textsc{MLD2P4 User's and Reference Guide}} +\markboth{\textsc{AMG4PSBLAS User's and Reference Guide}} {\textsc{\ref{sec:overview} General Overview}} - -The \textsc{MultiLevel Domain Decomposition Parallel Preconditioners Package based on -PSBLAS (MLD2P4}) provides parallel Algebraic MultiGrid (AMG) and Domain -Decomposition preconditioners (see, e.g., \cite{Briggs2000,Stuben_01,dd2_96}), + +The \textsc{Algebraic MultiGrid Preconditioners Package based on +PSBLAS (AMG4PSBLAS)} provides parallel Algebraic MultiGrid (AMG) preconditioners (see, e.g., \cite{Briggs2000,Stuben_01}), to be used in the iterative solution of linear systems, -\begin{equation} -Ax=b, +\begin{equation} +Ax=b, \label{system1} -\end{equation} -where $A$ is a square, real or complex, sparse matrix. +\end{equation} +where $A$ is a square, real or complex, sparse symmetric positive definite (s.p.d) matrix. % -%\textbf{NOTA: Caso non simmetrico, aggregazione con $(A+A^T)$ fatta! +%\textbf{NOTA: Caso non simmetrico, aggregazione con $(A+A^T)$ fatta! %Dovremmo implementare uno smoothed prolongator %adeguato e fare qualcosa di consistente anche con 1-lev Schwarz.} % -The name of the package comes from its original implementation, containing -multilevel additive and hybrid Schwarz preconditioners, as well as one-level additive -Schwarz preconditioners. The current version extends the original plan by including -multilevel cycles and smoothers widely used in multigrid methods. -The multilevel preconditioners implemented in MLD2P4 are obtained by combining -AMG cycles with smoothers and coarsest-level solvers. The V-, W-, and -K-cycles~\cite{Briggs2000,Notay2008} are available, which allow to define -almost all the preconditioners in the package, including the multilevel hybrid -Schwarz ones; a specific cycle is implemented to obtain multilevel additive -Schwarz preconditioners. The Jacobi, hybrid +The preconditioners implemented in AMG4PSBLAS are obtained by combining +3 different types of AMG cycles with smoothers and coarsest-level solvers. The V-, W-, and a version of a Krylov-type cycle (K-cycle)~\cite{Briggs2000,Notay2008} are available, which can be combined with weighted versions of Jacobi, hybrid %\footnote{see Note 2 in Table~\ref{tab:p_coarse}, p.~28.} -forward/backward Gauss-Seidel, block-Jacobi, and additive Schwarz methods -are available as smoothers. An algebraic approach is used to generate a hierarchy of +forward/backward Gauss-Seidel, block-Jacobi, and additive Schwarz smoothers. An algebraic approach is used to generate a hierarchy of coarse-level matrices and operators, without explicitly using any information on the geometry of the original problem, e.g., the discretization of a PDE. To this end, -the smoothed aggregation technique~\cite{BREZINA_VANEK,VANEK_MANDEL_BREZINA} -is applied. Either exact or approximate solvers can be used on the coarsest-level -system. Specifically, different sparse LU factorizations from external -packages, and native incomplete LU factorizations and Jacobi, hybrid Gauss-Seidel, -and block-Jacobi solvers are available. All smoothers can be also exploited as one-level +two different coarsening strategies, based on aggregation, are available: +\begin{itemize} +\item a decoupled version of the well known smoothed aggregation procedure proposed in~\cite{BREZINA_VANEK,VANEK_MANDEL_BREZINA}, and already included in the previous versions of the package~\cite{BDDF2007,MLD2P4_TOMS}; +\item the first parallel implementation of a coupled version of Coarsening based on Compatible Weighted Matching introduced in~\cite{DV2013,DFV2018} and described in details in~\cite{DDF2020}; +\end{itemize} + +Either exact or approximate solvers can be used on the coarsest-level system. Specifically, different sparse LU factorizations from external +packages, native incomplete LU factorizations, weighted Jacobi, hybrid Gauss-Seidel, +and block-Jacobi solvers are available. All the smoothers can be also exploited as one-level preconditioners. -MLD2P4 is written in Fortran~2003, following an +AMG4PSBLAS is written in Fortran~2003, following an object-oriented design through the exploitation of features such as abstract data type creation, type extension, functional overloading, and -dynamic memory management. % \textbf{Va bene cos\'{i} o \`e meglio -% fare riferimento alle classi?} +dynamic memory management. The parallel implementation is based on a Single Program Multiple Data (SPMD) paradigm. Single and -double precision implementations of MLD2P4 are available for both the +double precision implementations of AMG4PSBLAS are available for both the real and the complex case, which can be used through a single -interface. +interface. -MLD2P4 has been designed to implement scalable and easy-to-use +AMG4PSBLAS has been designed to implement scalable and easy-to-use multilevel preconditioners in the context of the PSBLAS (Parallel Sparse BLAS) computational framework~\cite{psblas_00,PSBLAS3}. PSBLAS provides basic linear algebra operators and data management facilities for distributed sparse matrices, -as well as parallel Krylov solvers which can be used with the MLD2P4 preconditioners. +as well as parallel Krylov solvers which can be used with the AMG4PSBLAS preconditioners. The choice of PSBLAS has been mainly motivated by the need of having a portable and efficient software infrastructure implementing ``de facto'' standard parallel sparse linear algebra kernels, to pursue goals such as performance, portability, modularity ed extensibility in the development of the preconditioner -package. On the other hand, the implementation of MLD2P4 has led to some -revisions and extentions of the original PSBLAS kernels. -The inter-process comunication required by MLD2P4 is encapsulated +package. On the other hand, the implementation of AMG4PSBLAS, which was driven by the need to face the exascale challenge, has led to some important revisions and extentions of the PSBLAS infrastructure. +The inter-process comunication required by AMG4PSBLAS is encapsulated in the PSBLAS routines; -% , except few cases where MPI~\cite{MPI1} is explicitly called. -therefore, MLD2P4 can be run on any parallel machine where PSBLAS +therefore, AMG4PSBLAS can be run on any parallel machine where PSBLAS implementations are available. -MLD2P4 has a layered and modular software architecture where three main layers can be +AMG4PSBLAS has a layered and modular software architecture where three main layers can be identified. The lower layer consists of the PSBLAS kernels, the middle one implements the construction and application phases of the preconditioners, and the upper one -provides a uniform interface to all the preconditioners. +provides a uniform interface to all the preconditioners. This architecture allows for different levels of use of the package: few black-box routines at the upper layer allow all users to easily -build and apply any preconditioner available in MLD2P4; -facilities are also available allowing expert users to extend the set of smoothers +build and apply any preconditioner available in AMG4PSBLAS; +facilities are also available allowing expert users to extend the set of smoothers and solvers for building new versions of the preconditioners (see -Section~\ref{sec:adding}). - -We note that the user interface of MLD2P4 2.1 has been extended with respect to the -previous versions in order to separate the construction of the multilevel hierarchy from -the construction of the smoothers and solvers, and to allow for more flexibility -at each level. The software architecture described in~\cite{MLD2P4_TOMS} has significantly -evolved too, in order to fully exploit the Fortran~2003 features implemented in PSBLAS 3. -However, compatibility with previous versions has been preserved. +Section~\ref{sec:adding}). This guide is organized as follows. General information on the distribution of the source code is reported in Section~\ref{sec:distribution}, while details on the configuration -and installation of the package are given in Section~\ref{sec:building}. A short description -of the preconditioners implemented in MLD2P4 is provided in Section~\ref{sec:background}, -to help the users in choosing among them. The basics for building and applying the -preconditioners with the Krylov solvers implemented in PSBLAS are reported +and installation of the package are given in Section~\ref{sec:building}. The basics for building and applying the +preconditioners with the Krylov solvers implemented in PSBLAS are reported in~Section~\ref{sec:started}, where the Fortran codes of a few sample programs are also shown. A reference guide for the user interface routines is provided in Section~\ref{sec:userinterface}. Information on the extension of the package -through the addition of new smoothers and solvers is reported in Section~\ref{sec:adding}. +through the addition of new smoothers and solvers is reported in Section~\ref{sec:adding}. The error handling mechanism used by the package is briefly described in Section~\ref{sec:errors}. The copyright terms concerning the -distribution and modification of MLD2P4 are reported in Appendix~\ref{sec:license}. +distribution and modification of AMG4PSBLAS are reported in Appendix~\ref{sec:license}. -%%% Local Variables: +%%% Local Variables: %%% mode: latex %%% TeX-master: "userguide" -%%% End: +%%% End: diff --git a/docs/src/userguide.tex b/docs/src/userguide.tex index 70e4fab1..84cf8e07 100644 --- a/docs/src/userguide.tex +++ b/docs/src/userguide.tex @@ -5,12 +5,12 @@ \usepackage{ifpdf} % \usepackage{minitoc} % \setcounter{minitocdepth}{2} -\usepackage[bookmarks=true, - bookmarksnumbered=true, - bookmarksopen=false, +\usepackage[bookmarks=true, + bookmarksnumbered=true, + bookmarksopen=false, plainpages=false, pdfpagelabels, - colorlinks, + colorlinks, citecolor=red, linkcolor=blue]{hyperref} \usepackage{html} @@ -26,17 +26,17 @@ \relax \pdfcompresslevel=0 %-- 0 = none, 9 = best \pdfinfo{ %-- Info dictionary of PDF output /Author (PD, DdS, SF) - /Title (MultiLevel Domain Decomposition Parallel Preconditioners Package - based on PSBLAS, V. 2.2) - /Subject (MultiLevel Domain Decomposition Parallel Preconditioners Package) - /Keywords (Parallel Numerical Software, Algebraic Multilevel Preconditioners, Sparse Iterative Solvers, PSBLAS, MPI) + /Title (Algebraic MultiGrid Preconditioners Package + based on PSBLAS, V. 1.0) + /Subject (MultiGrid Parallel Preconditioners Package) + /Keywords (Parallel Numerical Software, Algebraic MultiGrid Preconditioners, Sparse Iterative Solvers, PSBLAS, MPI) /Creator (pdfLaTeX) - /Producer ($Id: userguide.tex 2008-04-08 Pasqua D'Ambra, Daniela di Serafino, + /Producer ($Id: userguide.tex 2021-03-01 Pasqua D'Ambra, Fabio Durastante, Salvatore Filippone$) } \pdfcatalog{ %-- Catalog dictionary of PDF output. % /URI (http://ce.uniroma2.it/psblas) -} +} \setlength\textwidth{1.15\textwidth} \setlength\oddsidemargin{0.3in} @@ -92,7 +92,7 @@ \newcommand{\Ref}[1]{\mbox{(\ref{#1})}} \begin{document} -\pdfbookmark{MLD2P4 User's and Reference Guide}{title} +\pdfbookmark{AMG4PSBLAS User's and Reference Guide}{title} \newlength{\centeroffset} %\setlength{\centeroffset}{-0.5\oddsidemargin} %\addtolength{\centeroffset}{0.5\evensidemargin} @@ -101,23 +101,30 @@ \vspace*{\stretch{1}} \noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth} \flushright -{\Huge\bfseries MLD2P4\\[.8ex] User's and Reference Guide +{\Huge\bfseries AMG4PSBLAS\\[.8ex] User's and Reference Guide } \noindent\rule[-1ex]{\textwidth}{5pt}\\[2.5ex] -\hfill\emph{\Large A guide for the MultiLevel Domain Decomposition \\[.6ex] -Parallel Preconditioners Package -based on PSBLAS} +\hfill\emph{\Large A guide for the Algebraic MultiGrid \\[.6ex] +Preconditioners Package based on PSBLAS} \end{minipage}} +\vspace{\stretch{1}} +\flushleft +\begin{figure*}[htb] +\begin{center} +\includegraphics[width=0.6\textwidth]{amg4psblaslibrary.png} +\end{center} +\end{figure*} + \vspace{\stretch{1}} \noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth} \flushright {\large\bfseries Pasqua D'Ambra}\\ -\large IAC-CNR, Naples, Italy\\[3ex] -{\large\bfseries Daniela di Serafino}\\ -\large University of Campania ``Luigi Vanvitelli'', Caserta, Italy\\[3ex] +\large IAC-CNR, Italy\\[3ex] +{\large\bfseries Fabio Durastante}\\ +\large University of Pisa and IAC-CNR\\[3ex] {\large\bfseries Salvatore Filippone} \\ -\large Cranfield University, Cranfield, United Kingdom +\large University of Rome Tor-Vergata and IAC-CNR %\\[10ex] %\today \end{minipage}} @@ -125,9 +132,9 @@ based on PSBLAS} \vspace{\stretch{1}} \noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth} \flushright -\large Software version: 2.2\\ +\large Software version: 1.0\\ %\today -\large July 31, 2018 +\large March 31, 2021 \end{minipage}} %\addtolength{\textwidth}{\centeroffset} \vspace{\stretch{2}} @@ -151,7 +158,7 @@ based on PSBLAS} \begingroup \renewcommand*{\thepage}{toc} \tableofcontents -\endgroup +\endgroup %\cleardoublepage \clearpage \thispagestyle{empty} @@ -164,8 +171,8 @@ based on PSBLAS} \include{overview} \include{distribution} -\include{building} -\include{background} +\include{building} +%\include{background} \include{gettingstarted} \include{userinterface} \include{newobjects} @@ -177,7 +184,7 @@ based on PSBLAS} \include{bibliography} \end{document} -%%% Local Variables: +%%% Local Variables: %%% mode: latex %%% TeX-master: 'userguide' -%%% End: +%%% End: diff --git a/docs/src/userinterface.tex b/docs/src/userinterface.tex index b1a2424c..f4245802 100644 --- a/docs/src/userinterface.tex +++ b/docs/src/userinterface.tex @@ -1,13 +1,13 @@ \section{User Interface\label{sec:userinterface}} -\markboth{\textsc{MLD2P4 User's and Reference Guide}} +\markboth{\textsc{AMG4PSBLAS User's and Reference Guide}} {\textsc{\ref{sec:userinterface} User Interface}} -The basic user interface of MLD2P4 consists of eight methods. The six -methods \verb|init|, \verb|set|, \verb|build|, +The basic user interface of AMG4PBLAS consists of eight methods. The six +methods \verb|init|, \verb|set|, \verb|build|, \verb|hierarchy_build|, \verb|smoothers_build| and \verb|apply| encapsulate all the functionalities for the setup and the application of any multilevel and one-level preconditioner implemented in the -package. +package. The method \verb|free| deallocates the preconditioner data structure, while \verb|descr| prints a description of the preconditioner setup by the user. For backward compatibility, methods are also accessible as @@ -24,12 +24,12 @@ i.e., for real double precision, \emph{x} = \verb|c| for complex single precision, \emph{x} = \verb|z| for complex double precision; \item the preconditioner data structure must be of type - \verb|mld_|\emph{x}\verb|prec_type|, with \emph{x} = + \verb|amg_|\emph{x}\verb|prec_type|, with \emph{x} = \verb|s|, \verb|d|, \verb|c|, \verb|z|, according to the sparse matrix data structure; \item the arrays containing the vectors $v$ and $w$ involved in - the preconditioner application $w=B^{-1}v$ must be of type - \verb|psb_|\emph{x}\verb|vect_type| with \emph{x} = + the preconditioner application $w=B^{-1}v$ must be of type + \verb|psb_|\emph{x}\verb|vect_type| with \emph{x} = \verb|s|, \verb|d|, \verb|c|, \verb|z|, in a manner completely analogous to the sparse matrix type; \item real parameters defining the preconditioner must be declared @@ -53,10 +53,7 @@ This method allocates and initializes the preconditioner {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip \begin{tabular}{p{1.2cm}p{12cm}} -%\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ -% & The preconditioner data structure. Note that \emph{x} -% must be chosen according to the real/complex, single/double -% precision version of MLD2P4 under use.\\ + \verb|icontxt| & \verb|integer, intent(in)|.\\ & The communication context.\\ \verb|ptype| & \verb|character(len=*), intent(in)|.\\ @@ -65,12 +62,7 @@ This method allocates and initializes the preconditioner & Note that the strings are case insensitive.\\ \verb|info| & \verb|integer, intent(out)|.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\ -%\verb|nlev| & \verb|integer, optional, intent(in)|.\\ - % & The number of levels of the multilevel - % preconditioner. This optional argument is deprecated, - % new codes should set the number of levels with \verb|mld_precset|.\\ - % If \verb|nlev| is not present and \verb|ptype|=\verb|'ML'|, \verb|'ml'|, - % then \verb|nlev|=2 is assumed. Otherwise, \verb|nlev| is ignored.\\ + \end{tabular} \vskip1.5\baselineskip @@ -78,7 +70,7 @@ For compatibility with the previous versions of MLD2P4, this method can be also as follows: \begin{center} -\verb|call mld_precinit(p,ptype,info)| +\verb|call amg_precinit(p,ptype,info)| \end{center} @@ -93,19 +85,15 @@ as follows: \noindent This method sets the parameters defining the preconditioner \verb|p|. More precisely, the parameter identified by \verb|what| is assigned the value -contained in \verb|val|. +contained in \verb|val|. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip \begin{tabular}{p{1.2cm}p{12cm}} -%\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ -% & The preconditioner data structure. Note that \emph{x} must -% be chosen according to the real/complex, single/double precision -% version of MLD2P4 under use.\\ \verb|what| & \verb|character(len=*)|. \\ & The parameter to be set. It can be specified through its name; the string is case-insensitive. See - Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}.\\ + Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}.\\ \verb|val | & \verb|integer| \emph{or} \verb|character(len=*)| \emph{or} \verb|real(psb_spk_)| \emph{or} \verb|real(psb_dpk_)|, \verb|intent(in)|.\\ @@ -149,7 +137,7 @@ For compatibility with the previous versions of MLD2P4, this method can be also as follows: \begin{center} -\verb|call mld_precset(p,what,val,info)| +\verb|call amg_precset(p,what,val,info)| \end{center} \noindent @@ -198,7 +186,7 @@ object is specified, its defaults are also set, overriding in both cases any previous settings even if explicitly specified. Therefore if the user sets a smoother, and wishes to use a solver different from the default one, the call to set the solver must come -\emph{after} the call to set the smoother. +\emph{after} the call to set the smoother. Similar considerations apply to the point-Jacobi, Gauss-Seidel and block-Jacobi coarsest-level solvers, and shortcuts are available @@ -221,7 +209,7 @@ It is worth noting that, when the matrix is replicated, the point-Jacobi, hybrid Gauss-Seidel and block-Jacobi solvers reduce to the corresponding local solver objects (see Remark~2). For the point-Jacobi and Gauss-Seidel solvers, these objects -correspond to a \emph{single} point-Jacobi sweep and a \emph{single} +correspond to a \emph{single} point-Jacobi sweep and a \emph{single} Gauss-Seidel sweep, respectively, which are very poor solvers. On the other hand, the distributed layout can be used with any solver @@ -236,10 +224,10 @@ solver is changed to the default sequential solver. control for those solvers; for instance, by specifying the keyword \verb|MUMPS_IPAR_ENTRY| and an appropriate value for \verb|idx|, it is possible to set any entry in the MUMPS integer control array. -See also Sec.~\ref{sec:adding}. +See also Sec.~\ref{sec:adding}. %The \verb|what,val| pairs described here are those of the predefined %moother/solver objects; newly developed solvers may define new pairs -%according to their needs. +%according to their needs. \bsideways @@ -249,8 +237,6 @@ See also Sec.~\ref{sec:adding}. \hline \verb|what| & \textsc{data type} & \verb|val| & \textsc{default} & \textsc{comments} \\ \hline -%\multicolumn{5}{|c|}{\emph{type of the multilevel preconditioner}}\\ \hline -%\verb|mld_ml_cycle_| \par \verb|'ML_CYCLE'| & \verb|character(len=*)| & \texttt{'VCYCLE'} \par \texttt{'WCYCLE'} \par \texttt{'KCYCLE'} \par \texttt{'MULT'} \par \texttt{'ADD'} @@ -259,28 +245,17 @@ See also Sec.~\ref{sec:adding}. and Additive Schwarz. \par Note that hybrid Multiplicative Schwarz is equivalent to V-cycle and is included for compatibility with previous versions of MLD2P4. \\ \hline -%\verb|mld_outer_sweeps_| \par \verb|'OUTER_SWEEPS'| & \texttt{integer} & Any integer \par number $\ge 1$ & 1 & Number of multilevel cycles. \\ \hline -%\verb|mld_smoother_type_| \par \verb|SMOOTHER_TYPE| & \verb|character(len=*)| -% & \texttt{'JACOBI'} \ \ \ \texttt{'BJAC'} \ \ \ \texttt{'AS'} -% & \texttt{'AS'} -% & Basic predefined one-level preconditioner -% (i.e., smoother): Jacobi, block Jacobi, AS. \\ \hline -%\verb|mld_smoother_pos_| \par \verb|SMOOTHER_POS| & \verb|character(len=*)| -% & \texttt{'PRE'} \ \ \ \texttt{'POST'} \ \ \ \texttt{'TWOSIDE'} -% & \texttt{'TWOSIDE'} -% & ``Position'' of the smoother: pre-smoother, post-smoother, -% pre- and post-smoother. \\ -%\hline + \end{tabular} \end{center} \caption{Parameters defining the multilevel cycle and the number of cycles to be applied. -\label{tab:p_cycle}} +\label{tab:p_cycle}} \esideways - + \bsideways \begin{center} %\begin{tabular}{|p{5cm}|l|p{2.4cm}|p{2.5cm}|p{5cm}|} @@ -288,8 +263,6 @@ be applied. \hline \verb|what| & \textsc{data type} & \verb|val| & \textsc{default} & \textsc{comments} \\ \hline -%\multicolumn{5}{|c|}{\emph{aggregation algorithm}} \\ \hline -%\verb|mld_min_coarse_size_| \par \verb|'MIN_COARSE_SIZE'| & \verb|integer| & Any number \par $> 0$ & $\lfloor 40 \sqrt[3]{n} \rfloor$, where $n$ is the dimension @@ -299,27 +272,23 @@ be applied. computed coarsest matrix is lower than or equal to this threshold (see Note). -% or \par -% the coarsening ratio is lower than or equal to -% its value (see \verb|mld_min_aggr_ratio_|), or \par -% the maximum number of levels is reached -% (see \verb|mld_n_prec_levs_|). - \\ \hline -%\verb|mld_min_cr_ratio_| \par + + \\ \hline + \verb|'MIN_CR_RATIO'| & \verb|real| & Any number \par $> 1$ & 1.5 & Minimum coarsening ratio. The aggregation stops if the ratio between the matrix dimensions at two consecutive levels is lower than or equal to this - threshold (see Note).\\ \hline -%\verb|mld_max_levs_| \par + threshold (see Note).\\ \hline + \verb|'MAX_LEVS'| & \verb|integer| & Any integer \par number $> 1$ & 20 & Maximum number of levels. The aggregation stops - if the number of levels reaches this value (see Note). \\ \hline -%\verb|mld_par_aggr_alg_| \par + if the number of levels reaches this value (see Note). \\ \hline + \verb|'PAR_AGGR_ALG'| & \verb|character(len=*)| \hspace*{-3mm} & \texttt{'DEC'}, \texttt{'SYMDEC'} & \texttt{'DEC'} @@ -328,24 +297,24 @@ be applied. \verb|SYMDEC| option applies decoupled aggregation to the sparsity pattern of $A+A^T$.\\ \hline -%\verb|mld_aggr_type_| \par + \verb|'AGGR_TYPE'| & \verb|character(len=*)| \hspace*{-3mm} & \textbf{\texttt{'SOC1'}} & \textbf{\texttt{'SOC1'}}, - \textbf{\texttt{'SOC2'}} + \textbf{\texttt{'SOC2'}} & Type of aggregation algorithm: currently, - we implement two measures of strength of + we implement to measures of strength of connection, the one by Van\v{e}k, Mandel and Brezina~\cite{VANEK_MANDEL_BREZINA}, and the one by Gratton et al~\cite{GrHeJi:16}. \\ \hline -%\verb|mld_aggr_prol_| \par + \verb|'AGGR_PROL'| & \verb|character(len=*)| \hspace*{-3mm} & \texttt{'SMOOTHED'}, \texttt{'UNSMOOTHED'} & \texttt{'SMOOTHED'} & Prolongator used by the aggregation algorithm: smoothed or unsmoothed (i.e., tentative prolongator). \\ \hline \multicolumn{5}{|l|}{{\bfseries Note.} The aggregation algorithm stops when -at least one of the following criteria is met: +at least one of the following criteria is met: the coarse size threshold, the} \\ \multicolumn{5}{|l|}{minimum coarsening ratio, or the maximum number of levels is reached. Therefore, the actual number of levels may be} \\ @@ -355,7 +324,7 @@ of levels. } \\ \end{tabular} \end{center} \caption{Parameters defining the aggregation algorithm. -\label{tab:p_aggregation}} +\label{tab:p_aggregation}} \esideways \bsideways @@ -365,67 +334,31 @@ of levels. } \\ \hline \verb|what| & \textsc{data type} & \verb|val| & \textsc{default} & \textsc{comments} \\ \hline -%\verb|mld_aggr_ord_| \par + \verb|'AGGR_ORD'| & \verb|character(len=*)| & \texttt{'NATURAL'} \par \texttt{'DEGREE'} & \texttt{'NATURAL'} & Initial ordering of indices for the aggregation algorithm: either natural ordering or sorted by descending degrees of the nodes in the - matrix graph. \\ \hline + matrix graph. \\ \hline %Since aggregation is %heuristic, results will be different. -%\verb|mld_aggr_thresh_| \par + \verb|'AGGR_THRESH'| & \verb|real(|\emph{kind\_parameter}\verb|)| & Any~real \par number~$\in [0, 1]$ & 0.01 & The threshold $\theta$ in the aggregation algorithm, see (\ref{eq:strongly_coup}) in Section~\ref{sec:aggregation}. See also the note at the bottom of this table. \\ \hline -%%\verb|mld_aggr_scale_| \par -% \verb|AGGR_SCALE| & \verb|real(|\emph{kind\_parameter}\verb|)| -% & Any~real \par number~$\in [0, 1]$ -% & 1.0 -% & Scale factor applied to the threshold in going -% from level $ilev$ to level $ilev+1$. \\ \hline -%\verb|mld_aggr_omega_alg_| \par -%\verb|'AGGR_OMEGA_ALG'|& \verb|character(len=*)| -% & \texttt{'EIG\_EST'} \par \texttt{'USER\_CHOICE'} -% & \texttt{'EIG\_EST'} -% & How the damping parameter $\omega$ in the -% smoothed aggregation is obtained: -% either via an estimate of the spectral radius of -% $D^{-1}A$, where $A$ is the matrix at the current -% level and $D$ is the diagonal matrix with -% the same diagonal entires as $A$, or explicily -% specified by the user. \\ \hline -%\verb|mld_aggr_eig_| \par -%\verb|'AGGR_EIG'| & \verb|character(len=*)| -% & \texttt{'A\_NORMI'} -% & \texttt{'A\_NORMI'} -% & How to estimate the spectral radius of $D^{-1}A$. -% Currently only the infinity norm estimate -% is available. \\ \hline -%\verb|mld_aggr_omega_val_| \par -%\verb|'AGGR_OMEGA_VAL'| & \verb|real(|\emph{kind\_parameter}\verb|)| -% & Any real \par number $>0$ -% & $4/(3\rho(D^{-1}A))$ -% & Damping parameter $\omega$ in the smoothed aggregation algorithm. -% It must be set by the user if -% \verb|USER_CHOICE| was specified for -% \verb|mld_aggr_omega_alg_|, -% otherwise it is computed by the library, using the -% selected estimate of the spectral radius $\rho(D^{-1}A)$ of -% $D^{-1}A$.\\ \hline -%\verb|mld_aggr_filter_| \par -\verb|'AGGR_FILTER'| +\verb|'AGGR_FILTER'| & \verb|character(len=*)| & \texttt{'FILTER'} \par \texttt{'NOFILTER'} & \texttt{'NOFILTER'} & Matrix used in computing the smoothed prolongator: filtered or unfiltered (see~(\ref{eq:filtered}) in Section~\ref{sec:aggregation}). \\ \hline \multicolumn{5}{|l|}{{\bfseries Note.} Different thresholds at different levels, such as -those used in \cite[Section~5.1]{VANEK_MANDEL_BREZINA}, can be easily set by +those used in \cite[Section~5.1]{VANEK_MANDEL_BREZINA}, can be easily set by invoking the rou-} \\ \multicolumn{5}{|l|}{tine \texttt{set} with the parameter \texttt{ilev}.} \\ @@ -433,31 +366,28 @@ the parameter \texttt{ilev}.} \\ \end{tabular} \end{center} \caption{Parameters defining the aggregation algorithm (continued). -\label{tab:p_aggregation_1}} +\label{tab:p_aggregation_1}} \esideways - + \bsideways \begin{center} \begin{tabular}{|p{3.9cm}|l|p{1.7cm}|p{1.7cm}|p{8.6cm}|} \hline \verb|what| & \textsc{data type} & \verb|val| & \textsc{default} & \textsc{comments} \\ \hline -%\multicolumn{5}{|c|}{\emph{coarse-space correction at the coarsest level}}\\ \hline -%\verb|mld_coarse_mat_| \par \verb|'COARSE_MAT'| & \verb|character(len=*)| & \texttt{'DIST'} \par \texttt{'REPL'} & \texttt{'REPL'} & Coarsest matrix layout: distributed among the processes or replicated on each of them. \\ \hline -%\verb|mld_coarse_solve_| \par \verb|'COARSE_SOLVE'| & \verb|character(len=*)| - & \texttt{'MUMPS'} \par \texttt{'UMF'} \par - \texttt{'SLU'} \par \texttt{'SLUDIST'} \par - \texttt{'JACOBI'} \par \texttt{'GS'} \par \texttt{'BJAC'} + & \texttt{'MUMPS'} \par \texttt{'UMF'} \par + \texttt{'SLU'} \par \texttt{'SLUDIST'} \par + \texttt{'JACOBI'} \par \texttt{'GS'} \par \texttt{'BJAC'} & See~Note. & Solver used at the coarsest level: sequential LU from MUMPS, UMFPACK, or SuperLU - (plus tri\-an\-gular solve); + (plus tri\-an\-gular solve); distributed LU from MUMPS or SuperLU\_Dist (plus triangular solve); point-Jacobi, hybrid Gauss-Seidel or block-Jacobi. \par @@ -467,35 +397,34 @@ the parameter \texttt{ilev}.} \\ distributed, and \texttt{MUMPS} can be used with either a replicated or a distributed matrix. When any of the previous solvers is specified, the matrix layout is set to a default - value which allows the use of the solver (see Remark 3, p.~24). + value which allows the use of the solver (see Remark 3, p.~24). Note also that UMFPACK and SuperLU\_Dist are available only in double precision. \\ \hline -%\verb|mld_coarse_subsolve_| \par \verb|'COARSE_SUBSOLVE'| & \verb|character(len=*)| & \texttt{'ILU'} \par \texttt{'ILUT'} \par \texttt{'MILU'} \par - \texttt{'MUMPS'} \par \texttt{'SLU'} \par \texttt{'UMF'} + \texttt{'MUMPS'} \par \texttt{'SLU'} \par \texttt{'UMF'} & See~Note. & Solver for the diagonal blocks of the coarse matrix, in case the block Jacobi solver is chosen as coarsest-level solver: ILU($p$), ILU($p,t$), - MILU($p$), LU from MUMPS, SuperLU or UMFPACK + MILU($p$), LU from MUMPS, SuperLU or UMFPACK (plus triangular solve). Note that UMFPACK and SuperLU\_Dist are available only in double precision. \\ \hline -\multicolumn{5}{|l|}{{\bfseries Note.} Defaults for \texttt{COARSE\_SOLVE} and +\multicolumn{5}{|l|}{{\bfseries Note.} Defaults for \texttt{COARSE\_SOLVE} and \texttt{COARSE\_SUBSOLVE} are chosen in the following order:} \\ -\multicolumn{5}{|l|}{single precision version -- \texttt{MUMPS} if installed, - then \texttt{SLU} if installed, +\multicolumn{5}{|l|}{single precision version -- \texttt{MUMPS} if installed, + then \texttt{SLU} if installed, \texttt{ILU} otherwise;}\\ -\multicolumn{5}{|l|}{double precision version -- \texttt{UMF} if installed, - then \texttt{MUMPS} if installed, then \texttt{SLU} if +\multicolumn{5}{|l|}{double precision version -- \texttt{UMF} if installed, + then \texttt{MUMPS} if installed, then \texttt{SLU} if installed, \texttt{ILU} otherwise.}\\ \hline \end{tabular} \end{center} \caption{Parameters defining the coarse-space correction at the coarsest -level.\label{tab:p_coarse}} +level.\label{tab:p_coarse}} \esideways \bsideways @@ -504,19 +433,15 @@ level.\label{tab:p_coarse}} \hline \verb|what| & \textsc{data type} & \verb|val| & \textsc{default} & \textsc{comments} \\ \hline -%\multicolumn{5}{|c|}{\emph{coarse-space correction at the coarsest level}}\\ \hline -%\verb|mld_coarse_sweeps_| \par -\verb|'COARSE_SWEEPS'| & \verb|integer| +\verb|'COARSE_SWEEPS'| & \verb|integer| & Any integer \par number $> 0$ & 10 & Number of sweeps when \verb|JACOBI|, \verb|GS| or \verb|BJAC| is chosen as coarsest-level solver. \\ \hline -%\verb|mld_coarse_fillin_| \par \verb|'COARSE_FILLIN'| & \verb|integer| & Any integer \par number $\ge 0$ & 0 & Fill-in level $p$ of the ILU factorizations. \\ \hline -%\verb|mld_coarse_iluthrs_| \par \verb|'COARSE_ILUTHRS'| & \verb|real(|\emph{kind\_parameter}\verb|)| & Any real \par number $\ge 0$ @@ -526,7 +451,7 @@ level.\label{tab:p_coarse}} \end{tabular} \end{center} \caption{Parameters defining the coarse-space correction at the coarsest -level (continued).\label{tab:p_coarse_1}} +level (continued).\label{tab:p_coarse_1}} \esideways \bsideways @@ -536,8 +461,7 @@ level (continued).\label{tab:p_coarse_1}} \hline \verb|what| & \textsc{data type} & \verb|val| & \textsc{default} & \textsc{comments} \\ \hline -%\multicolumn{5}{|c|}{\emph{basic one-level preconditioner (smoother)}} \\ \hline -%\verb|mld_smoother_type_| \par + \verb|'SMOOTHER_TYPE'| & \verb|character(len=*)| & \verb|'JACOBI'| \par \verb|'GS'| \par \verb|'BGS'| \par \verb|'BJAC'| \par \verb|'AS'| @@ -547,11 +471,10 @@ level (continued).\label{tab:p_coarse_1}} hybrid backward Gauss-Seidel, block-Jacobi, and Additive Schwarz. \par It is ignored by one-level preconditioners. \\ \hline -%\verb|mld_sub_solve_| \par \verb|'SUB_SOLVE'| & \verb|character(len=*)| & \texttt{'JACOBI'} \par - \texttt{'GS'} \par \texttt{'BGS'} \par \texttt{'ILU'} \par - \texttt{'ILUT'} \par \texttt{'MILU'} \par + \texttt{'GS'} \par \texttt{'BGS'} \par \texttt{'ILU'} \par + \texttt{'ILUT'} \par \texttt{'MILU'} \par \par \texttt{'MUMPS'} \par \texttt{'SLU'} \par \texttt{'UMF'} & \texttt{GS} and \texttt{BGS} for pre- and post-smoothers of multilevel preconditioners, respectively \par @@ -564,16 +487,14 @@ level (continued).\label{tab:p_coarse_1}} LU from MUMPS, SuperLU or UMFPACK (plus triangular solve). See Note for details on hybrid Gauss-Seidel. \\ \hline -%\verb|mld_moother_sweeps_| \par \verb|'SMOOTHER_SWEEPS'| & \verb|integer| & Any integer \par number~$\ge 0$ & 1 & Number of sweeps of the smoother or one-level preconditioner. In the multilevel case, no pre-smother or - post-smoother is used if this parameter is set to 0 + post-smoother is used if this parameter is set to 0 together with \verb|pos='PRE'| or \verb|pos='POST|, respectively. \\ \hline -%\verb|mld_sub_ovr_| \par \verb|'SUB_OVR'| & \verb|integer| & Any integer \par number~$\ge 0$ & 1 @@ -582,7 +503,7 @@ level (continued).\label{tab:p_coarse_1}} \end{tabular} \end{center} \caption{Parameters defining the smoother or the details of the one-level preconditioner. -\label{tab:p_smoother}} +\label{tab:p_smoother}} \esideways \bsideways @@ -592,16 +513,14 @@ level (continued).\label{tab:p_coarse_1}} \hline \verb|what| & \textsc{data type} & \verb|val| & \textsc{default} & \textsc{comments} \\ \hline -%\verb|mld_sub_restr_| \par \verb|'SUB_RESTR'| & \verb|character(len=*)| & \texttt{'HALO'} \par \texttt{'NONE'} & \texttt{'HALO'} & Type of restriction operator, for Additive Schwarz only: - \texttt{HALO} for taking into account the overlap, \texttt{NONE} + \texttt{HALO} for taking into account the overlap, \texttt{NONE} for neglecting it. \par Note that \texttt{HALO} must be chosen for the classical Addditive Schwarz smoother and its RAS variant.\\ \hline -%\verb|mld_sub_prol_| \par \verb|'SUB_PROL'| & \verb|character(len=*)| & \texttt{'SUM'} \par \texttt{'NONE'} & \texttt{'NONE'} @@ -610,12 +529,10 @@ level (continued).\label{tab:p_coarse_1}} for neglecting them. \par Note that \texttt{SUM} must be chosen for the classical Additive Schwarz smoother, and \texttt{NONE} for its RAS variant. \\ \hline -%\verb|mld_sub_fillin_| \par \verb|'SUB_FILLIN'| & \verb|integer| & Any integer \par number~$\ge 0$ & 0 & Fill-in level $p$ of the incomplete LU factorizations. \\ \hline -%\verb|mld_sub_iluthrs_| \par \verb|'SUB_ILUTHRS'| & \verb|real(|\emph{kind\_parameter}\verb|)| & Any real number~$\ge 0$ & 0 @@ -637,30 +554,18 @@ level (continued).\label{tab:p_coarse_1}} & 0 & Set an entry in the MUMPS real control array, as chosen via the \verb|idx| optional argument. \\ %\hline -%\verb|mld_sub_ren_| \par \verb|SUB_REN| & \verb|character(len=*)| -% & \texttt{'RENUM\_NONE'} \texttt{'RENUM\_GLOBAL'} %, \texttt{'RENUM_GPS'} -% & \texttt{'RENUM\_NONE'} -% & Row and column reordering of the local submatrices: no reordering, -% or reordering according to the global numbering of the rows and -% columns of the whole matrix. \\ -% \verb|mld_solver_eps_| \par \verb|SOLVER_EPS| & \verb|real| -% & Any~real number -% & 0 -% & Stopping tolerance for iterative local solver -% (currently only Gauss-Seidel); if $\le0$, then -% perform prespecified number of iterations. \\ \hline \hline \end{tabular} \end{center} \caption{Parameters defining the smoother or the details of the one-level preconditioner -(continued).\label{tab:p_smoother_1}} +(continued).\label{tab:p_smoother_1}} \esideways \clearpage \subsection{Method hierarchy\_build\label{sec:hier_bld}} - + \begin{center} \verb|call p%hierarchy_build(a,desc_a,info)|\\ \end{center} @@ -676,15 +581,13 @@ made by the user through the methods \verb|init| and \verb|set|. \verb|a| & \verb|type(psb_|\emph{x}\verb|spmat_type), intent(in)|. \\ & The sparse matrix structure containing the local part of the matrix to be preconditioned. Note that \emph{x} must be chosen according - to the real/complex, + to the real/complex, single/double precision version of MLD2P4 under use. See the PSBLAS User's Guide for details \cite{PSBLASGUIDE}.\\ \verb|desc_a| & \verb|type(psb_desc_type), intent(in)|. \\ & The communication descriptor of \verb|a|. See the PSBLAS User's Guide for details \cite{PSBLASGUIDE}.\\ -%\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ -% & The preconditioner data structure. Note that \emph{x} must be chosen according -% to the real/complex, single/double precision version of MLD2P4 under use.\\ + \verb|info| & \verb|integer, intent(out)|.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\ \end{tabular} @@ -693,7 +596,7 @@ single/double precision version of MLD2P4 under use. \clearpage \subsection{Method smoothers\_build\label{sec:smooth_bld}} - + \begin{center} \verb|call p%smoothers_build(a,desc_a,p,info[,amold,vmold,imold])|\\ @@ -704,7 +607,7 @@ This method builds the smoothers and the coarsest-level solvers for the multilevel preconditioner \verb|p|, according to the requirements made by the user through the methods \verb|init| and \verb|set|, and based on the aggregation hierarchy produced by a previous call to \verb|hierarchy_build| -(see Section~\ref{sec:hier_bld}). +(see Section~\ref{sec:hier_bld}). {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip @@ -717,9 +620,6 @@ hierarchy produced by a previous call to \verb|hierarchy_build| \verb|desc_a| & \verb|type(psb_desc_type), intent(in)|. \\ & The communication descriptor of \verb|a|. See the PSBLAS User's Guide for details \cite{PSBLASGUIDE}.\\ -%\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ -% & The preconditioner data structure. Note that \emph{x} must be chosen according -% to the real/complex, single/double precision version of MLD2P4 under use.\\ \verb|info| & \verb|integer, intent(out)|.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\ \verb|amold| & \verb|class(psb_|\emph{x}\verb|_base_sparse_mat), intent(in), optional|. \\ @@ -738,7 +638,7 @@ hierarchy produced by a previous call to \verb|hierarchy_build| \clearpage \subsection{Method build\label{sec:precbld}} - + \begin{center} \verb|call p%build(a,desc_a,info[,amold,vmold,imold])|\\ \end{center} @@ -750,8 +650,8 @@ made by the user through the methods \verb|init| and \verb|set| multilevel preconditioners). It is mostly provided for backward compatibility; indeed, it is internally implemented by invoking the two previous methods \verb|hierarchy_build| and -\verb|smoothers_build|, whose nomenclature would however be somewhat -unnatural when dealing with simple one-level preconditioners. +\verb|smoothers_build|, whose nomenclature would however be somewhat +unnatural when dealing with simple one-level preconditioners. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip @@ -764,9 +664,6 @@ unnatural when dealing with simple one-level preconditioners. \verb|desc_a| & \verb|type(psb_desc_type), intent(in)|. \\ & The communication descriptor of \verb|a|. See the PSBLAS User's Guide for details \cite{PSBLASGUIDE}.\\ -%\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ -% & The preconditioner data structure. Note that \emph{x} must be chosen according -% to the real/complex, single/double precision version of MLD2P4 under use.\\ \verb|info| & \verb|integer, intent(out)|.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\ \verb|amold| & \verb|class(psb_|\emph{x}\verb|_base_sparse_mat), intent(in), optional|. \\ @@ -787,7 +684,7 @@ For compatibility with the previous versions of MLD2P4, this method can be also as follows: \begin{center} -\verb|call mld_precbld(p,what,val,info[,amold,vmold,imold])| +\verb|call amg_precbld(p,what,val,info[,amold,vmold,imold])| \end{center} \noindent @@ -813,12 +710,8 @@ and hence it is completely transparent to the user. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip \begin{tabular}{p{1.2cm}p{12cm}} -%\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ -% & The preconditioner data structure, containing the local part of $M$. -% Note that \emph{x} must be chosen according -% to the real/complex, single/double precision version of MLD2P4 under use.\\ \verb|x| & \emph{type}\verb|(|\emph{kind\_parameter}\verb|), dimension(:), intent(in)|.\\ - & The local part of the vector $x$. Note that \emph{type} and + & The local part of the vector $x$. Note that \emph{type} and \emph{kind\_parameter} must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.\\ \verb|y| & \emph{type}\verb|(|\emph{kind\_parameter}\verb|), dimension(:), intent(out)|.\\ @@ -847,7 +740,7 @@ For compatibility with the previous versions of MLD2P4, this method can be also as follows: \begin{center} -\verb|call mld_precaply(p,what,val,info)| +\verb|call amg_precaply(p,what,val,info)| \end{center} \clearpage @@ -864,9 +757,6 @@ This method deallocates the preconditioner data structure \verb|p|. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip \begin{tabular}{p{1.2cm}p{10.5cm}} -%\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ -% & The preconditioner data structure. Note that \emph{x} must be chosen according - % to the real/complex, single/double precision version of MLD2P4 under use.\\ \verb|info| & \verb|integer, intent(out)|.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\ \end{tabular} @@ -876,7 +766,7 @@ For compatibility with the previous versions of MLD2P4, this method can be also as follows: \begin{center} -\verb|call mld_precfree(p,info)| +\verb|call amg_precfree(p,info)| \end{center} @@ -896,9 +786,6 @@ or \verb|build|, have been called. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip \begin{tabular}{p{1.2cm}p{12cm}} -%\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(in)|.\\ -% & The preconditioner data structure. Note that \emph{x} must be chosen according -% to the real/complex, single/double precision version of MLD2P4 under use.\\ \verb|info| & \verb|integer, intent(out)|.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\ \verb|iout| & \verb|integer, intent(in), optional|.\\ @@ -911,16 +798,16 @@ For compatibility with the previous versions of MLD2P4, this method can be also as follows: \begin{center} -\verb|call mld_precdescr(p,info [,iout])| +\verb|call amg_precdescr(p,info [,iout])| \end{center} \subsection{Auxiliary Methods\label{sec:auxil}} Various functionalities are implemented as additional methods of the -preconditioner object. +preconditioner object. \subsubsection{Method: dump} - + \begin{center} \verb|call p%dump(info[,istart,iend,prefix,head,ac,rp,smoother,solver,global_num])|\\ \end{center} @@ -931,9 +818,6 @@ Dump on file. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip \begin{tabular}{p{1.2cm}p{12cm}} -%\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ -% & The preconditioner data structure. Note that \emph{x} must be chosen according -% to the real/complex, single/double precision version of MLD2P4 under use.\\ \verb|info| & \verb|integer, intent(out)|.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\ \verb|amold| & \verb|class(psb_|\emph{x}\verb|_base_sparse_mat), intent(in), optional|. \\ @@ -945,20 +829,20 @@ Dump on file. \subsubsection{Method: clone} - + \begin{center} \verb|call p%clone(pout,info)|\\ \end{center} \noindent -Create a (deep) copy of the preconditioner object. +Create a (deep) copy of the preconditioner object. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip \begin{tabular}{p{1.2cm}p{12cm}} -\verb|pout| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(out)|.\\ +\verb|pout| & \verb|type(amg_|\emph{x}\verb|prec_type), intent(out)|.\\ & The copy of the preconditioner data structure. Note - that \emph{x} must be chosen according + that \emph{x} must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.\\ \verb|info| & \verb|integer, intent(out)|.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\ @@ -967,26 +851,16 @@ Create a (deep) copy of the preconditioner object. \subsubsection{Method: sizeof} - + \begin{center} \verb|sz = p%sizeof()|\\ \end{center} \noindent -Return memory footprint in bytes. - -% {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip - -% \begin{tabular}{p{1.2cm}p{12cm}} -% %\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ -% % & The preconditioner data structure. Note that \emph{x} must be chosen according -% % to the real/complex, single/double precision version of MLD2P4 under use.\\ -% \verb|info| & \verb|integer, intent(out)|.\\ -% & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\ -% \end{tabular} +Return memory footprint in bytes. \subsubsection{Method: allocate\_wrk} - + \begin{center} \verb|call p%allocate_wrk(info[, vmold])|\\ \end{center} @@ -996,23 +870,20 @@ Allocate internal work vectors. Each application of the preconditioner uses a number of work vectors which are allocated internally as necessary; therefore allocation and deallocation of memory occurs multiple times during the execution of a Krylov method. In most cases -this strategy is perfectly acceptable, but +this strategy is perfectly acceptable, but on some platforms, most notably GPUs, memory allocation is a slow operation, and the default behaviour would lead to a -slowdown. This method allows to trade space for time by preallocating +slowdown. This method allows to trade space for time by preallocating the internal workspace outside of the invocation of a Krylov method. When using GPUs or other specialized devices, the \verb|vmold| argument is also necessary to ensure the internal work vectors are of the appropriate dynamic type to exploit the accelerator hardware; when allocation occurs internally this is taken care of based on the dynamic -type of the \verb|x| argument to the \verb|apply| method. +type of the \verb|x| argument to the \verb|apply| method. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip \begin{tabular}{p{1.2cm}p{12cm}} -%\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ -% & The preconditioner data structure. Note that \emph{x} must be chosen according -% to the real/complex, single/double precision version of MLD2P4 under use.\\ \verb|info| & \verb|integer, intent(out)|.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\ \verb|vmold| & \verb|class(psb_|\emph{x}\verb|_base_vect_type), intent(in), optional|. \\ @@ -1023,20 +894,17 @@ type of the \verb|x| argument to the \verb|apply| method. \subsubsection{Method: free\_wrk} - + \begin{center} \verb|call p%free_wrk(info)|\\ \end{center} \noindent -Deallocate internal work vectors. +Deallocate internal work vectors. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip \begin{tabular}{p{1.2cm}p{12cm}} -%\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\ -% & The preconditioner data structure. Note that \emph{x} must be chosen according -% to the real/complex, single/double precision version of MLD2P4 under use.\\ \verb|info| & \verb|integer, intent(out)|.\\ & Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\ \end{tabular} @@ -1045,7 +913,7 @@ Deallocate internal work vectors. -%%% Local Variables: +%%% Local Variables: %%% mode: latex %%% TeX-master: "userguide" -%%% End: +%%% End: