From 46355253a5424802f0220aa6c89e505bc7d9aaa5 Mon Sep 17 00:00:00 2001 From: Salvatore Filippone Date: Tue, 16 Jan 2018 12:26:54 +0000 Subject: [PATCH] Changes to docs to highlight new stuff in MLD internals. --- docs/html/index.html | 89 +- docs/html/node1.html | 72 +- docs/html/node10.html | 37 +- docs/html/node11.html | 39 +- docs/html/node12.html | 102 +- docs/html/node13.html | 181 +- docs/html/node14.html | 271 +- docs/html/node15.html | 194 +- docs/html/node16.html | 116 +- docs/html/node17.html | 99 +- docs/html/node18.html | 164 +- docs/html/node19.html | 127 +- docs/html/node2.html | 109 +- docs/html/node20.html | 651 ++--- docs/html/node21.html | 152 +- docs/html/node22.html | 172 +- docs/html/node23.html | 184 +- docs/html/node24.html | 221 +- docs/html/node25.html | 88 +- docs/html/node26.html | 128 +- docs/html/node27.html | 198 +- docs/html/node28.html | 102 +- docs/html/node29.html | 125 +- docs/html/node3.html | 137 +- docs/html/node30.html | 178 +- docs/html/node31.html | 135 +- docs/html/node32.html | 85 + docs/html/node33.html | 183 ++ docs/html/node34.html | 75 + docs/html/node35.html | 98 + docs/html/node36.html | 200 ++ docs/html/node37.html | 67 + docs/html/node4.html | 65 +- docs/html/node5.html | 47 +- docs/html/node6.html | 80 +- docs/html/node7.html | 76 +- docs/html/node8.html | 70 +- docs/html/node9.html | 88 +- docs/html/userhtml.html | 89 +- docs/mld2p4-2.1-guide.pdf | 5300 +++++++++++++++++++---------------- docs/src/gettingstarted.tex | 6 +- docs/src/userinterface.tex | 298 +- 42 files changed, 6040 insertions(+), 4858 deletions(-) create mode 100644 docs/html/node32.html create mode 100644 docs/html/node33.html create mode 100644 docs/html/node34.html create mode 100644 docs/html/node35.html create mode 100644 docs/html/node36.html create mode 100644 docs/html/node37.html diff --git a/docs/html/index.html b/docs/html/index.html index b3fb8403..f026ce9d 100644 --- a/docs/html/index.html +++ b/docs/html/index.html @@ -1,10 +1,6 @@ - + - + userhtml @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -22,7 +18,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + +
next @@ -37,30 +34,30 @@ original version by: Nikos Drakos, CBLU, University of Leeds   Contents
-
+
-MLD2P4 +MLD2P4

-User's and Reference Guide -
A guide for the MultiLevel Domain Decomposition +User's and Reference Guide +
A guide for the MultiLevel Domain Decomposition Parallel Preconditioners Package -based on PSBLAS +based on PSBLAS


-
Pasqua D'Ambra -
IAC-CNR, Naples, Italy +
Pasqua D'Ambra +
IAC-CNR, Naples, Italy


-
Daniela di Serafino -
University of Campania ``Luigi Vanvitelli'', Caserta, Italy +
Daniela di Serafino +
University of Campania “Luigi Vanvitelli”, Caserta, Italy


-
Salvatore Filippone -
Cranfield University, Cranfield, United Kingdom +
Salvatore Filippone +
Cranfield University, Cranfield, United Kingdom


@@ -78,18 +75,18 @@ July 31, 2017
- +

- + - +

- +

-
diff --git a/docs/html/node1.html b/docs/html/node1.html index 69dc84e6..202c3887 100644 --- a/docs/html/node1.html +++ b/docs/html/node1.html @@ -1,10 +1,6 @@ - + - + Abstract @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,35 +21,36 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
- Next: Next: Contents - Up: Up: userhtml - Previous: Previous: userhtml -   Contents
-
+

Abstract -

+ MLD2P4 (MULTILEVEL DOMAIN DECOMPOSITION PARALLEL PRECONDITIONERS PACKAGE BASED ON PSBLAS) is a package of parallel algebraic multilevel preconditioners. @@ -64,55 +61,56 @@ multigrid methods. In the multilevel case, a purely algebraic approach is applie 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. - +

-MLD2P4 has been designed to provide scalable and easy-to-use preconditioners +MLD2P4 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. - +for the “best” preconditioner for the problem at hand. +

-The package employs object-oriented design techniques in +The package employs object-oriented design techniques in 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) 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 +This guide provides a brief description of the functionalities and the user interface of MLD2P4. - +

- + -

+ +
- next - up - previous - contents
- Next: Next: Contents - Up: Up: userhtml - Previous: Previous: userhtml -   Contents +   Contents
diff --git a/docs/html/node10.html b/docs/html/node10.html index 0b6e5a28..a880f838 100644 --- a/docs/html/node10.html +++ b/docs/html/node10.html @@ -1,10 +1,6 @@ - + - + Bug reporting @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,35 +21,36 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
- Next: Next: Example and test programs - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Configuration options -   Contents
-
+

Bug reporting -

+ If you find any bugs in our codes, please report them through our issues page on
https://github.com/sfilippone/mld2p4-2/issues @@ -61,9 +58,9 @@ issues page on
+

- +

diff --git a/docs/html/node11.html b/docs/html/node11.html index fa27b778..7b4e7b1b 100644 --- a/docs/html/node11.html +++ b/docs/html/node11.html @@ -1,10 +1,6 @@ - + - + Example and test programs @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -24,40 +20,41 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
- Next: Next: Multigrid Background - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Bug reporting -   Contents
-
+


Example and test programs -

+ The package contains the examples and tests directories; both of them are further divided into fileread and pdegen subdirectories. Their purpose is as follows: -
+
examples
contains a set of simple example programs with a predefined choice of preconditioners, selectable via integer @@ -70,13 +67,13 @@ both of them are further divided into fileread and subdirectories, to experiment with the full range of preconditioners implemented in the package.
-
+
The fileread directories contain sample programs that read sparse matrices from files, according to the Matrix Market or the Harwell-Boeing storage format; the pdegen programs generate matrices in full parallel mode from the discretization of a sample partial differential equation. - +
diff --git a/docs/html/node12.html b/docs/html/node12.html index eb2ed114..b2da8f7e 100644 --- a/docs/html/node12.html +++ b/docs/html/node12.html @@ -1,10 +1,6 @@ - + - + Multigrid Background @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,49 +21,50 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
- Next: Next: AMG preconditioners - Up: Up: userhtml - Previous: Previous: Example and test programs -   Contents
-
+


Multigrid Background -

+ - +

-Multigrid preconditioners, coupled with Krylov iterative +Multigrid preconditioners, coupled with Krylov iterative solvers, are widely used in the parallel solution of large and sparse linear systems, because of their optimality in the solution of linear systems arising from the discretization of scalar elliptic Partial Differential Equations (PDEs) on regular grids. Optimality, also known as algorithmic scalability, is the property of having a computational cost per iteration that depends linearly 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 +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 methods, such as the Jacobi and Gauss-Seidel ones, or more complex subspace-correction methods, such as the Schwarz ones. @@ -90,75 +87,76 @@ interplay between fine and coarse levels, e.g., when matrices with highly varyin are considered. The second approach performs a fully automatic coarsening and enforces the interplay between fine and coarse level by suitably choosing the coarse space and the coarse-to-fine interpolation (see, e.g., [3,23,21] for details.) - + HREF="node36.html#Briggs2000">3,23,21] for details.) +

-MLD2P4 uses a pure algebraic approach, based on the smoothed +MLD2P4 uses a pure algebraic approach, based on the smoothed aggregation algorithm [2,25], + HREF="node36.html#BREZINA_VANEK">2,25], for building the sequence of coarse matrices and transfer operators, starting from the original one. A decoupled version of this algorithm is implemented, where the smoothed aggregation is applied locally to each submatrix [24]. + HREF="node36.html#TUMINARO_TONG">24]. A brief description of the AMG preconditioners implemented in MLD2P4 is given in Sections 4.1-4.3. For further details the reader is referred to [4,5,7,8]. - + HREF="node36.html#para_04">4,5,7,8]. +

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

- +

Subsections - -
+ +
- next - up - previous - contents
- Next: Next: AMG preconditioners - Up: Up: userhtml - Previous: Previous: Example and test programs -   Contents +   Contents
diff --git a/docs/html/node13.html b/docs/html/node13.html index a6fb5b46..6971e165 100644 --- a/docs/html/node13.html +++ b/docs/html/node13.html @@ -1,10 +1,6 @@ - + - + AMG preconditioners @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,48 +21,50 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
- Next: Next: Smoothed Aggregation - Up: Up: Multigrid Background - Previous: Previous: Multigrid Background -   Contents
-
+


AMG preconditioners -

+

-In order to describe the AMG preconditioners available in MLD2P4, we consider a +In order to describe the AMG preconditioners available in MLD2P4, we consider a linear system - +
-

+
+ - +
\begin{displaymath} Ax=b, \end{displaymath} -(2)
+(2)
-

+

where -$A=(a_{ij}) \in \mathbb{R}^{n \times n}$ is a nonsingular sparse matrix; -for ease of presentation we assume $A=(a_{ij}) \in \mathbb{R}^{n \times n}$ is a nonsingular sparse matrix; +for ease of presentation we assume $A$ has a symmetric sparsity + ALT="$A$"> 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 $A$, i.e., + ALT="$A$">, i.e., -$\Omega = \{1, 2, \ldots, n\}$. + ALT="$\Omega = \{1, 2, \ldots, n\}$">. Any algebraic multilevel preconditioners implemented in MLD2P4 generates a hierarchy of index spaces and a corresponding hierarchy of matrices, - +

-
+
-$\mathbb{R}^{n_{k}}$ is associated with $\mathbb{R}^{n_{k}}$ is associated with $\Omega^k$, -where $\Omega^k$, +where $n_k$ is the size of $n_k$ is the size of $\Omega^k$. -For all $\Omega^k$. +For all $k < nlev$, a restriction operator and a prolongation one are built, -which connect two levels $k < nlev$, a restriction operator and a prolongation one are built, +which connect two levels $k$ and $k$ and $k+1$: - + ALT="$k+1$">: +

-
+
@@ -174,15 +172,15 @@ P^k \in \mathbb{R}^{n_k \times n_{k+1}}, \quad ALT="\begin{displaymath} P^k \in \mathbb{R}^{n_k \times n_{k+1}}, \quad R^k \in \mathbb{R}^{n_{k+1}\times n_k}; \end{displaymath}">

-

-the matrix

+the matrix $A^{k+1}$ is computed by using the previous operators according + ALT="$A^{k+1}$"> is computed by using the previous operators according to the Galerkin approach, i.e., - +

-
+
- next - up - previous - contents
- Next: Next: Smoothed Aggregation - Up: Up: Multigrid Background - Previous: Previous: Multigrid Background -   Contents +   Contents
diff --git a/docs/html/node14.html b/docs/html/node14.html index d989c6eb..a4d6105f 100644 --- a/docs/html/node14.html +++ b/docs/html/node14.html @@ -1,10 +1,6 @@ - + - + Smoothed Aggregation @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,130 +21,132 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
- Next: Next: Smoothers and coarsest-level solvers - Up: Up: Multigrid Background - Previous: Previous: AMG preconditioners -   Contents
-
+


Smoothed Aggregation -

+

-In order to define the prolongator In order to define the prolongator $P^k$, used to compute -the coarse-level matrix $P^k$, used to compute +the coarse-level matrix $A^{k+1}$, MLD2P4 uses the smoothed aggregation + ALT="$A^{k+1}$">, MLD2P4 uses the smoothed aggregation algorithm described in [2,25]. + HREF="node36.html#BREZINA_VANEK">2,25]. The basic idea of this algorithm is to build a coarse set of indices -$\Omega^{k+1}$ by suitably grouping the indices of $\Omega^{k+1}$ by suitably grouping the indices of $\Omega^k$ into disjoint + ALT="$\Omega^k$"> into disjoint subsets (aggregates), and to define the coarse-to-fine space transfer operator -$P^k$ by applying a suitable smoother to a simple piecewise constant + ALT="$P^k$"> by applying a suitable smoother to a simple piecewise constant prolongation operator, with the aim of improving the quality of the coarse-space correction. - +

-Three main steps can be identified in the smoothed aggregation procedure: - +Three main steps can be identified in the smoothed aggregation procedure: +

    -
  1. aggregation of the indices of aggregation of the indices of $\Omega^k$ to obtain $\Omega^k$ to obtain $\Omega^{k+1}$; + ALT="$\Omega^{k+1}$">;
    2. -
  2. construction of the prolongator construction of the prolongator $P^k$; + ALT="$P^k$">;
    3. -
  3. application of application of $P^k$ and $P^k$ and $R^k=(P^k)^T$ to build $R^k=(P^k)^T$ to build $A^{k+1}$. + ALT="$A^{k+1}$">.
    4. -
+

-In order to perform the coarsening step, the smoothed aggregation algorithm +In order to perform the coarsening step, the smoothed aggregation algorithm described in [25] is used. In this algorithm, + HREF="node36.html#VANEK_MANDEL_BREZINA">25] is used. In this algorithm, each index -$j \in \Omega^{k+1}$ corresponds to an aggregate $j \in \Omega^{k+1}$ corresponds to an aggregate $\Omega^k_j$ of $\Omega^k_j$ of $\Omega^k$, + ALT="$\Omega^k$">, consisting of a suitably chosen index -$i \in \Omega^k$ and indices that are (usually) contained in a -strongly-coupled neighborood of $i \in \Omega^k$ and indices that are (usually) contained in a +strongly-coupled neighborood of $i$, i.e., - + ALT="$i$">, i.e., +
-

+
+ - +
\begin{displaymath} \Omega^k_j \subset \mathcal{N}_i^k(\theta) = \left\{ r ... ...vert a_{ii}^ka_{rr}^k\vert} \right \} \cup \left\{ i \right\}, \end{displaymath} -(3)
+(3)
-

+

for a given threshold -$\theta \in [0,1]$ (see [25] for the details). + ALT="$\theta \in [0,1]$"> (see [25] for the details). Since this algorithm has a sequential nature, a decoupled version of it is applied, where each processor independently executes the algorithm on the set of indices assigned to it in the initial data distribution. This version is embarrassingly parallel, since it does not require any data communication. On the other hand, it may produce some nonuniform aggregates and is strongly dependent on the number of processors and on the initial partitioning -of the matrix $A$. Nevertheless, this parallel algorithm has been chosen for + ALT="$A$">. Nevertheless, this parallel algorithm has been chosen for MLD2P4, since it has been shown to produce good results in practice [5,7,24]. - + HREF="node36.html#aaecc_07">5,7,24]. +

-The prolongator The prolongator $P^k$ is built starting from a tentative prolongator + ALT="$P^k$"> is built starting from a tentative prolongator -$\bar{P}^k \in \mathbb{R}^{n_k \times n_{k+1}}$, defined as - + ALT="$\bar{P}^k \in \mathbb{R}^{n_k \times n_{k+1}}$">, defined as +
-

+
+ - +
\begin{displaymath} \bar{P}^k =(\bar{p}_{ij}^k), \quad \bar{p}_{ij}^k = \left\{... ...ega^k_j, 0 & \quad \mbox{otherwise}, \end{array} \right. \end{displaymath} -(4)
+(4)
-

-where

+where $\Omega^k_j$ is the aggregate of $\Omega^k_j$ is the aggregate of $\Omega^k$ + ALT="$\Omega^k$"> corresponding to the index -$j \in \Omega^{k+1}$. -$j \in \Omega^{k+1}$. +$P^k$ is obtained by applying to $P^k$ is obtained by applying to $\bar{P}^k$ a smoother + ALT="$\bar{P}^k$"> a smoother -$S^k \in \mathbb{R}^{n_k \times n_k}$: - + ALT="$S^k \in \mathbb{R}^{n_k \times n_k}$">: +

-
+
-$A^k_F = (\bar{a}_{ij}^k)$ is the filtered matrix defined as - + ALT="$A^k_F = (\bar{a}_{ij}^k)$"> is the filtered matrix defined as +
-
+
+ - +
\begin{displaymath} \bar{a}_{ij}^k = \left \{ \begin{array}{ll} a_{ij}^k & ... ...ii}^k = a_{ii}^k - \sum_{j \ne i} (a_{ij}^k - \bar{a}_{ij}^k), \end{displaymath} -(5)
+(5)
-

-and

+and $\omega^k$ is an approximation of $\omega^k$ is an approximation of $4/(3\rho^k)$, where -$4/(3\rho^k)$, where +$\rho^k$ is the spectral radius of -$(D^k)^{-1}A^k_F$ [2]. + ALT="$(D^k)^{-1}A^k_F$"> [2]. In MLD2P4 this approximation is obtained by using -$\Vert A^k_F \Vert _\infty$ as an estimate -of $\Vert A^k_F \Vert _\infty$ as an estimate +of $\rho^k$. Note that for systems coming from uniformly elliptic -problems, filtering the matrix $\rho^k$. Note that for systems coming from uniformly elliptic +problems, filtering the matrix $A^k$ has little or no effect, and -$A^k$ has little or no effect, and +$A^k$ can be used instead of $A^k$ can be used instead of $A^k_F$. The latter choice is the default in MLD2P4. - + ALT="$A^k_F$">. The latter choice is the default in MLD2P4. +

-

+ +
- next - up - previous - contents
- Next: Next: Smoothers and coarsest-level solvers - Up: Up: Multigrid Background - Previous: Previous: AMG preconditioners -   Contents +   Contents
diff --git a/docs/html/node15.html b/docs/html/node15.html index 5dc80522..bc801420 100644 --- a/docs/html/node15.html +++ b/docs/html/node15.html @@ -1,10 +1,6 @@ - + - + Smoothers and coarsest-level solvers @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -24,119 +20,120 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
- Next: Next: Getting Started - Up: Up: Multigrid Background - Previous: Previous: Smoothed Aggregation -   Contents
-
+


Smoothers and coarsest-level solvers -

+

-The smoothers implemented in MLD2P4 include the Jacobi and block-Jacobi methods, +The smoothers implemented in MLD2P4 include the Jacobi and block-Jacobi methods, a hybrid version of the forward and backward Gauss-Seidel methods, and the additive Schwarz (AS) ones (see, e.g., [20,21]). - + HREF="node36.html#Saad_book">20,21]). +

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

-In the AS methods, the index space In the AS methods, the index space $\Omega^k$ is divided into $\Omega^k$ is divided into $m_k$ -subsets $m_k$ +subsets $\Omega^k_i$ of size $\Omega^k_i$ of size $n_{k,i}$, possibly -overlapping. For each $n_{k,i}$, possibly +overlapping. For each $i$ we consider the restriction + ALT="$i$"> we consider the restriction operator -$R_i^k \in \mathbb{R}^{n_{k,i} \times n_k}$ -that maps a vector $R_i^k \in \mathbb{R}^{n_{k,i} \times n_k}$ +that maps a vector $x^k$ to the vector $x^k$ to the vector $x_i^k$ made of the components of $x_i^k$ made of the components of $x^k$ -with indices in $x^k$ +with indices in $\Omega^k_i$, and the prolongation operator + ALT="$\Omega^k_i$">, and the prolongation operator -$P^k_i = (R_i^k)^T$. These operators are then used to build + ALT="$P^k_i = (R_i^k)^T$">. These operators are then used to build -$A_i^k=R_i^kA^kP_i^k$, which is the restriction of $A_i^k=R_i^kA^kP_i^k$, which is the restriction of $A^k$ to the index -space $A^k$ to the index +space $\Omega^k_i$. -The classical AS preconditioner $\Omega^k_i$. +The classical AS preconditioner $M^k_{AS}$ is defined as - + ALT="$M^k_{AS}$"> is defined as +

-
+
-$z^k=M^k_{AS}w^k$, with -$w^k \in \mathbb{R}^{n_k}$, during the + ALT="$w^k \in \mathbb{R}^{n_k}$">, during the multilevel application phase, requires - +
    -
  • the restriction of the restriction of $w^k$ to the subspaces -$\mathbb{R}^{n_{k,i}}$, + ALT="$\mathbb{R}^{n_{k,i}}$">, i.e. -$w_i^k = R_i^{k} w^k$; + ALT="$w_i^k = R_i^{k} w^k$">;
  • the computation of the vectors -$z_i^k=(A_i^k)^{-1} w_i^k$; + ALT="$z_i^k=(A_i^k)^{-1} w_i^k$">;
  • the prolongation and the sum of the previous vectors, i.e. -$z^k = \sum_{i=1}^{m_k} P_i^k z_i^k$. + ALT="$z^k = \sum_{i=1}^{m_k} P_i^k z_i^k$">.
    • -
+ Variants of the classical AS method, which use modifications of the restriction and prolongation operators, are also implemented in MLD2P4. Among them, the Restricted AS (RAS) preconditioner usually @@ -248,41 +245,42 @@ outperforms the classical AS preconditioner in terms of convergence rate and of computation and communication time on parallel distributed-memory computers, and is therefore the most widely used among the AS preconditioners [6]. - + HREF="node36.html#CAI_SARKIS">6]. +

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

-

+ +
- next - up - previous - contents
- Next: Next: Getting Started - Up: Up: Multigrid Background - Previous: Previous: Smoothed Aggregation -   Contents +   Contents
diff --git a/docs/html/node16.html b/docs/html/node16.html index 15f6ba15..8eef7ca3 100644 --- a/docs/html/node16.html +++ b/docs/html/node16.html @@ -1,10 +1,6 @@ - + - + Getting Started @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,54 +21,55 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
- Next: Next: Examples - Up: Up: userhtml - Previous: Previous: Smoothers and coarsest-level solvers -   Contents
-
+


Getting Started -

+

-We describe the basics for building and applying MLD2P4 one-level and multilevel +We describe the basics for building and applying MLD2P4 one-level and multilevel (i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS [13]. + HREF="node36.html#PSBLASGUIDE">13]. The following steps are required: - +

    -
  1. Declare the preconditioner data structure. It is a derived data type, - mld_xprec_ type, where x may be s, d, c +
  2. Declare the preconditioner data structure. It is a derived data type, + mld_xprec_ type, where x may be s, d, c or z, according to the basic data type of the sparse matrix (s = real single precision; d = real double precision; c = complex single precision; z = complex double precision). This data structure is accessed by the user only through the MLD2P4 routines, following an object-oriented approach.
    3. -
  3. Allocate and initialize the preconditioner data structure, according to - a preconditioner type chosen by the user. This is performed by the routine +
  4. Allocate and initialize the preconditioner data structure, according to + a preconditioner type chosen by the user. This is performed by the routine init, which also sets defaults for each preconditioner type selected by the user. The preconditioner types and the defaults associated with them are given in Table 1, where the strings used by @@ -80,8 +77,8 @@ The following steps are required: Note that these strings are valid also if uppercase letters are substituted by corresponding lowercase ones.
    5. -
  5. Modify the selected preconditioner type, by properly setting - preconditioner parameters. This is performed by the routine set. +
  6. Modify the selected preconditioner type, by properly setting + preconditioner parameters. This is performed by the routine 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 set are given in @@ -89,38 +86,38 @@ The following steps are required: preconditioner parameters and their allowed and default values is provided in Section 6, Tables 2-8.
    7. -
  7. Build the preconditioner for a given matrix. If the selected preconditioner +
  8. Build the preconditioner for a given matrix. If the selected preconditioner is multilevel, then two steps must be performed, as specified next.
    4.1
    -
    Build the aggregation hierarchy for a given matrix. This is +
    Build the aggregation hierarchy for a given matrix. This is performed by the routine hierarchy_build.
    4.2
    -
    Build the preconditioner for a given matrix. This is performed +
    Build the preconditioner for a given matrix. This is performed by the routine smoothers_build.
    If the selected preconditioner is one-level, it is built in a single step, performed by the routine bld.
    9. -
  9. Apply the preconditioner at each iteration of a Krylov solver. - This is performed by the routine aply. When using the PSBLAS Krylov solvers, - this step is completely transparent to the user, since aply is called +
  10. Apply the preconditioner at each iteration of a Krylov solver. + This is performed by the method apply. When using the PSBLAS Krylov solvers, + this step is completely transparent to the user, since apply is called by the PSBLAS routine implementing the Krylov solver (psb_krylov).
    11. -
  11. Free the preconditioner data structure. This is performed by +
  12. Free the preconditioner data structure. This is performed by the routine free. This step is complementary to step 1 and should be performed when the preconditioner is no more used.
    13. -
+

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

- +

@@ -135,8 +132,8 @@ Preconditioner types, corresponding strings and default choices. - - + @@ -177,60 +174,63 @@ Preconditioner types, corresponding strings and default choices. for further details of the preconditioner.
DEFAULT PRECONDITIONER
No preconditioner'NOPREC'Considered only to use the PSBLAS +'NONE'Considered to use the PSBLAS Krylov solvers with no preconditioner.
Diagonal
+

-
+

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

-Remark 1. Coarsest-level solvers based on the LU factorization, +Remark 1. Coarsest-level solvers based on the LU factorization, such as those implemented in UMFPACK, MUMPS, SuperLU, and SuperLU_Dist, 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. +on parallel computers. +

- +

Subsections - -
+ +
- next - up - previous - contents
- Next: Next: Examples - Up: Up: userhtml - Previous: Previous: Smoothers and coarsest-level solvers -   Contents +   Contents
diff --git a/docs/html/node17.html b/docs/html/node17.html index c9f90253..830f4f6c 100644 --- a/docs/html/node17.html +++ b/docs/html/node17.html @@ -1,10 +1,6 @@ - + - + Examples @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -24,38 +20,39 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
- Next: Next: User Interface - Up: Up: Getting Started - Previous: Previous: Getting Started -   Contents
-
+


Examples -

+

-The code reported in Figure 2 shows how to set and apply the default +The code reported in Figure 2 shows how to set and apply the default multilevel preconditioner available in the real double precision version of MLD2P4 (see Table 1). This preconditioner is chosen by simply specifying 'ML' as the second argument of P%init @@ -64,9 +61,9 @@ solver provided by PSBLAS (the matrix of the system to be solved is assumed to be positive definite). As previously observed, the modules psb_base_mod, mld_prec_mod and psb_krylov_mod must be used by the example program. - +

-The part of the code concerning the +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 @@ -77,17 +74,17 @@ Section 3.5). A sample test probl input data is available in examples/fileread/runs. For details on the use of the PSBLAS routines, see the PSBLAS User's Guide [13]. - + HREF="node36.html#PSBLASGUIDE">13]. +

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

- +

Figure 2: @@ -157,9 +154,9 @@ setup and application of the default multilevel preconditioner (example 1).
- +

-Different versions of the multilevel preconditioner can be obtained by changing +Different versions of the multilevel preconditioner can be obtained by changing the default values of the preconditioner parameters. The code reported in Figure 3 shows how to set a V-cycle preconditioner which applies 1 block-Jacobi sweep as pre- and post-smoother, @@ -176,24 +173,25 @@ 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. The code fragments shown in Figures 3 and 4 are +it is used on replicated ones. +The code fragments shown in Figures 3 and 4 are included in the example program file mld_dexample_ml.f90 too. - +

-Finally, Figure 5 shows the setup of a one-level +Finally, Figure 5 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 mld_dexample_1lev.f90. - +

-For all the previous preconditioners, example programs where the sparse matrix and +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 examples/pdegen. - +

- +

Figure 3: @@ -224,9 +222,9 @@ setup of a multilevel preconditioner
- +

- +

Figure 4: @@ -257,9 +255,9 @@ setup of a multilevel preconditioner
- +

- +

Figure 5: @@ -285,31 +283,32 @@ setup of a one-level Schwarz preconditioner.
- +

-

+ +
- next - up - previous - contents
- Next: Next: User Interface - Up: Up: Getting Started - Previous: Previous: Getting Started -   Contents +   Contents
diff --git a/docs/html/node18.html b/docs/html/node18.html index 627daa9b..fc22110c 100644 --- a/docs/html/node18.html +++ b/docs/html/node18.html @@ -1,10 +1,6 @@ - + - + User Interface @@ -13,89 +9,91 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - + - - + next - up - previous - contents
- Next: Subroutine init - Up: Next: Method init + Up: userhtml - Previous: Previous: Examples -   Contents
-
+


User Interface -

+

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

-All the routines are available as methods of the preconditioner object. -For each routine, the same user interface is overloaded with +For each method, the same user interface is overloaded with respect to the real/ complex case and the single/double precision; -arguments with appropriate data types must be passed to the routine, +arguments with appropriate data types must be passed to the method, i.e., - +

  • the sparse matrix data structure, containing the matrix to be - preconditioned, must be of type psb_xspmat_type - with x = s for real single precision, x = d - for real double precision, x = c for complex single precision, - x = z for complex double precision; + preconditioned, must be of type psb_xspmat_type + with x = s for real single precision, x = d + for real double precision, x = c for complex single precision, + x = z for complex double precision;
  • the preconditioner data structure must be of type - mld_xprec_type, with x = + mld_xprec_type, with x = s, d, c, z, according to the sparse matrix data structure;
    • -
  • the arrays containing the vectors the arrays containing the vectors $v$ and $v$ and $w$ involved in - the preconditioner application $w$ involved in + the preconditioner application $w=B^{-1}v$ must be of type - psb_xvect_type with x = + ALT="$w=B^{-1}v$"> must be of type + psb_xvect_type with x = s, d, c, z, in a manner completely analogous to the sparse matrix type;
    • @@ -103,59 +101,73 @@ i.e., according to the precision of the sparse matrix and preconditioner data structures (see Section 6.2). -
-A description of each routine is given in the remainder of this section. - + +A description of each method is given in the remainder of this section. +

- +

- +

Subsections - -
+ +
- next - up - previous - contents
- Next: Subroutine init - Up: Next: Method init + Up: userhtml - Previous: Previous: Examples -   Contents +   Contents
diff --git a/docs/html/node19.html b/docs/html/node19.html index 287fdec4..1ea569b5 100644 --- a/docs/html/node19.html +++ b/docs/html/node19.html @@ -1,19 +1,15 @@ - + - + -Subroutine init - +Method init + - + @@ -25,106 +21,109 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
- Next: Subroutine set - Up: Next: Method set + Up: User Interface - Previous: Previous: User Interface -   Contents
-
+


-Subroutine init -

+Method init +

- -

call p%init(ptype,info) -
+ +
call p%init(ptype,info) +

- -This routine allocates and initializes the preconditioner + +This method allocates and initializes the preconditioner p, according to the preconditioner type chosen by the user. - +

-Arguments +Arguments

- +

- - - +
ptype character(len=*), intent(in).
+ + - - + + - - + + - - + + - - + + -
+ptype character(len=*), intent(in).
- The type of preconditioner. Its values are specified - in Table 1.
+ 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).
+info integer, intent(out).
- Error code. If no error, 0 is returned. See Section 8 for details.
+ Error code. If no error, 0 is returned. See Section 8 for details.
+

-For compatibility with the previous versions of MLD2P4, this routine can be also invoked +For compatibility with the previous versions of MLD2P4, this method can be also invoked as follows: - +

- -

call mld_precinit(p,ptype,info) -
+ +
call mld_precinit(p,ptype,info) +

- +

-

+ +
- next - up - previous - contents
- Next: Subroutine set - Up: Next: Method set + Up: User Interface - Previous: Previous: User Interface -   Contents +   Contents
diff --git a/docs/html/node2.html b/docs/html/node2.html index f996d913..27a15212 100644 --- a/docs/html/node2.html +++ b/docs/html/node2.html @@ -1,10 +1,6 @@ - + - + Contents @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,25 +21,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous
- Next: Next: General Overview - Up: Up: userhtml - Previous: Previous: Abstract
-
+

@@ -52,82 +49,84 @@ Contents - +
+
  • Adding new smoother and solver objects to MLD2P4 +
  • Error Handling +
  • License +
  • Bibliography - +

    - + - +

    - +

    diff --git a/docs/html/node20.html b/docs/html/node20.html index eb63a26e..6d8135bf 100644 --- a/docs/html/node20.html +++ b/docs/html/node20.html @@ -1,19 +1,15 @@ - + - + -Subroutine set - +Method set + - + @@ -25,144 +21,146 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Subroutine build - Up: Next: Method hierarchy_build + Up: User Interface - Previous: Subroutine init -   Previous: Method init +   Contents
    -
    +


    -Subroutine set -

    +Method set +

    - -

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

    - -This routine sets the parameters defining the preconditioner p. More + +This method sets the parameters defining the preconditioner p. More precisely, the parameter identified by what is assigned the value contained in val. - +

    -Arguments +Arguments

    - +

    - - - +
    what character(len=*).
    + + - - + + Tables 2-8. - - + + - - + + it is also treated as case insensitive. - - + + - - + + - - + + - - + + Tables 2-8). - - + + - - + + order starting from the finest one, i.e., level 1 is the finest level. - - + + - - + + -
    +what character(len=*).
    - The parameter to be set. It can be specified through its name; +
    + The parameter to be set. It can be specified through its name; the string is case-insensitive. See - Tables 2-8.
    -val integer or character(len=*) or - real(psb_spk_) or real(psb_dpk_), - intent(in).
    +val integer or character(len=*) or + real(psb_spk_) or real(psb_dpk_), + intent(in).
    - The value of the parameter to be set. The list of allowed +
    + The value of the parameter to be set. The list of allowed values and the corresponding data types is given in Tables 2-8. When the value is of type character(len=*), - it is also treated as case insensitive.
    -info integer, intent(out).
    +info integer, intent(out).
    - Error code. If no error, 0 is returned. See Section 8 - for details.
    + Error code. If no error, 0 is returned. See Section 8 + for details.
    -ilev integer, optional, intent(in).
    +ilev integer, optional, intent(in).
    - For the multilevel preconditioner, the level at which the +
    + For the multilevel preconditioner, the level at which the preconditioner parameter has to be set. The levels are numbered in increasing order starting from the finest one, i.e., level 1 is the finest level. If ilev is not present, the parameter identified by what is set at all the appropriate levels (see - Tables 2-8).
    -ilmax integer, optional, intent(in).
    +ilmax integer, optional, intent(in).
    - For the multilevel preconditioner, when both +
    + For the multilevel preconditioner, when both ilev and ilmax are present, the settings are applied at all levels ilev:ilmax. When ilev is present but ilmax is not, then the default is ilmax=ilev. The levels are numbered in increasing - order starting from the finest one, i.e., level 1 is the finest level.
    -pos charater(len=*), optional, intent(in).
    +pos charater(len=*), optional, intent(in).
    - Whether the other arguments apply only to the pre-smoother ('PRE') +
    + Whether the other arguments apply only to the pre-smoother ('PRE') or to the post-smoother ('POST'). If pos is not present, the other arguments are applied to both smoothers. If the preconditioner is one-level or the parameter identified by what does not concern the smoothers, pos is ignored. -
    +

    -For compatibility with the previous versions of MLD2P4, this routine can be also invoked +For compatibility with the previous versions of MLD2P4, this method can be also invoked as follows: - +

    - -

    call mld_precset(p,what,val,info) -
    + +
    call mld_precset(p,what,val,info) +

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

    -A variety of preconditioners can be obtained +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;
      2. @@ -176,14 +174,14 @@ can be logically divided into four groups, i.e., parameters defining

      -

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

    -Remark 2. A smoother is usually obtained by combining two objects: +Remark 2. A smoother is usually obtained by combining two objects: a smoother (SMOOTHER_TYPE) and a local solver (SUB_SOLVE), as specified in Tables 7-8. For example, the block-Jacobi smoother using @@ -199,30 +197,30 @@ hybrid backward Gauss-Seidel, i.e., the previous smoothers can be defined by setting only SMOOTHER_TYPE to appropriate values (see Tables 7), i.e., without setting SUB_SOLVE too. - +

    -The smoother and solver objects are arranged in a +The smoother and solver objects are arranged in a hierarchical manner. When specifying a smoother object, its parameters, including the local solver, are set to their default values, and when a solver 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 -after the call to set the smoother. - +after the call to set the smoother. +

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

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

    -More precisely, UMFPACK and SuperLU require the coarsest-level +More precisely, UMFPACK and SuperLU require the coarsest-level matrix to be replicated, while SuperLU_Dist requires it to be distributed. In these cases, setting the coarsest-level solver implies that the layout is redefined according to the solver, ovverriding any @@ -234,22 +232,22 @@ 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 single point-Jacobi sweep and a single +correspond to a single point-Jacobi sweep and a single Gauss-Seidel sweep, respectively, which are very poor solvers. - +

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

    - +

    -
    +
    + ALT="$\ge 1$"> @@ -298,11 +296,11 @@ number
    Table 2: Parameters defining the multilevel cycle and the number of cycles to @@ -286,10 +284,10 @@ Note that hybrid Multiplicative Schwarz is equivalent to V-cycle and
    integer Any integer

    -number $\ge 1$

    		 1 Number of multilevel cycles.

    -
    +

    - +

    -
    +
    + ALT="$> 0$"> + ALT="$> 1$"> + ALT="$> 1$"> @@ -377,19 +375,19 @@ Currently, only the decoupled aggregation (DEC) is available; the SYMDEC option applies decoupled aggregation to the sparsity pattern - of $A+A^T$. + ALT="$A+A^T$">. - - + + + HREF="node36.html#VANEK_MANDEL_BREZINA">25]. @@ -398,26 +396,26 @@ Currently, only the - +the coarse size threshold, the - + - +
    Table 3: Parameters defining the aggregation algorithm. @@ -320,20 +318,20 @@ Parameters defining the aggregation algorithm.
    integer Any number

    -$> 0$

    		 -$\lfloor 40 \sqrt[3]{n} \rfloor$, where $\lfloor 40 \sqrt[3]{n} \rfloor$, where $n$ is the dimension + ALT="$n$"> is the dimension of the matrix at the finest level Coarse size threshold. The aggregation stops if the global number of variables of the @@ -345,10 +343,10 @@ Parameters defining the aggregation algorithm. real Any number

    -$> 1$

    		 1.5 Minimum coarsening ratio. The aggregation stops if the ratio between the matrix dimensions @@ -359,10 +357,10 @@ Parameters defining the aggregation algorithm. integer Any integer

    -number $> 1$

    		 20 Maximum number of levels. The aggregation stops if the number of levels reaches this value (see Note).
    'AGGR_TYPE' character(len=*)'VMB''VMB''VMB''VMB' Type of aggregation algorithm: currently, the scalar aggregation algorithm by Vanek, Mandel and Brezina is implemented [25].
    'AGGR_PROL' character(len=*)Prolongator used by the aggregation algorithm: smoothed or unsmoothed (i.e., tentative prolongator).
    Note. The aggregation algorithm stops when +
    Note. The aggregation algorithm stops when at least one of the following criteria is met: -the coarse size threshold, the
    minimum coarsening ratio, or the maximum number -of levels is reached. Therefore, the actual number of levels may be
    minimum coarsening ratio, or the maximum number +of levels is reached. Therefore, the actual number of levels may be
    smaller than the specified maximum number -of levels.
    smaller than the specified maximum number +of levels.

    -
    +

    - +

    -
    +
    - + + + ALT="$\in [0, 1]$"> - @@ -467,24 +466,24 @@ number Matrix used in computing the smoothed prolongator: filtered or unfiltered (see (5) in Section 4.2). - + HREF="node36.html#VANEK_MANDEL_BREZINA">25, Section 5.1], can be easily set by +invoking the rou- - +
    Table 4: Parameters defining the aggregation algorithm (continued). @@ -442,19 +440,20 @@ Parameters defining the aggregation algorithm (continued). descending degrees of the nodes in the matrix graph. -
    'AGGR_THRESH'real(kind_parameter)
    +'AGGR_THRESH'real(kind_parameter) Any real

    -number $\in [0, 1]$

    		 0.01The threshold The threshold $\theta$ in the aggregation algorithm, + ALT="$\theta$"> in the aggregation algorithm, see (3) in Section 4.2. See also the note at the bottom of this table.
    Note. Different thresholds at different levels, such as +
    Note. Different thresholds at different levels, such as those used in [25, Section 5.1], can be easily set by -invoking the rou-
    tine set with -the parameter ilev.
    tine set with +the parameter ilev.

    -
    +

    - +

    -
    +
    - + - + ILU otherwise; - + installed, ILU otherwise.
    Table 5: Parameters defining the coarse-space correction at the coarsest @@ -556,42 +555,42 @@ Note that UMF and SLU require the coarsest
    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($p$), ILU($p,t$), - MILU($p,t$), + MILU($p$), LU from MUMPS, SuperLU or UMFPACK + ALT="$p$">), LU from MUMPS, SuperLU or UMFPACK (plus triangular solve). Note that UMFPACK and SuperLU_Dist are available only in double precision.
    Note. Defaults for COARSE_SOLVE and -COARSE_SUBSOLVE are chosen in the following order:
    Note. Defaults for COARSE_SOLVE and +COARSE_SUBSOLVE are chosen in the following order:
    single precision version - MUMPS if installed, +
    single precision version - MUMPS if installed, then SLU if installed, - ILU otherwise;
    double precision version - UMF if installed, +
    double precision version - UMF if installed, then MUMPS if installed, then SLU if - installed, ILU otherwise.

    -
    +

    - +

    -
    +
    + ALT="$> 0$"> @@ -621,43 +620,43 @@ number integer + ALT="$\ge 0$"> - + ALT="$p$"> of the ILU factorizations. - + + ALT="$\ge 0$"> - + ALT="$p,t$">) factorization.
    Table 6: Parameters defining the coarse-space correction at the coarsest @@ -609,10 +608,10 @@ level (continued).
    integer Any integer

    -number $> 0$

    		 10 Number of sweeps when JACOBI, GS or BJAC is chosen as coarsest-level solver. Any integer

    -number $\ge 0$

    		 0Fill-in level Fill-in level $p$ of the ILU factorizations.
    'COARSE_ILUTHRS'real(kind_parameter)real(kind_parameter) Any real

    -number $\ge 0$

    		 0Drop tolerance Drop tolerance $t$ in the ILU($t$ in the ILU($p,t$) factorization.

    -
    +

    - +

    -
    +
    Table 7: Parameters defining the smoother or the details of the one-level preconditioner. @@ -665,122 +664,126 @@ Parameters defining the smoother or the details of the one-level preconditioner.
    - - - - - - - - - - - + + + + + + + + + + +It is ignored by one-level preconditioners. - - - + + - + - + + Gauss-Seidel. - - - + + - - + + + respectively. - - - + + - - + ALT="$\ge 0$"> + + +
    -what DATA TYPE val DEFAULT -COMMENTS
    'SMOOTHER_TYPE' character(len=*) - 'JACOBI' -

    -'GS' -

    -'BGS' -

    -'BJAC' - -

    -'AS' -

    		'FBGS' - Type of smoother used in the multilevel preconditioner: +
    +what DATA TYPE val DEFAULT +COMMENTS
    +'SMOOTHER_TYPE' character(len=*) + 'JACOBI' +

    +'GS' +

    +'BGS' +

    +'BJAC' + +

    +'AS' +

    		'FBGS' + Type of smoother used in the multilevel preconditioner: point-Jacobi, hybrid (forward) Gauss-Seidel, hybrid backward Gauss-Seidel, block-Jacobi, and - Additive Schwarz. + Additive Schwarz.

    -It is ignored by one-level preconditioners.

    'SUB_SOLVE' character(len=*) - 'JACOBI' +
    +'SUB_SOLVE' character(len=*) + 'JACOBI'

    -'GS' +'GS'

    -'BGS' +'BGS'

    -'ILU' +'ILU'

    -'ILUT' +'ILUT'

    -'MILU' +'MILU'

    -'MUMPS' +'MUMPS'

    -'SLU' +'SLU'

    -'UMF' -

    		GS and BGS for pre- and post-smoothers - of multilevel preconditioners, respectively +'UMF' + GS and BGS for pre- and post-smoothers + of multilevel preconditioners, respectively

    -ILU for block-Jacobi and Additive Schwarz +ILU for block-Jacobi and Additive Schwarz one-level preconditioners -

    		The local solver to be used with the smoother or one-level + The local solver to be used with the smoother or one-level preconditioner (see Remark 2, page 24): point-Jacobi, hybrid (forward) Gauss-Seidel, hybrid backward - Gauss-Seidel, ILU($p$), ILU($p$), ILU($p,t$), MILU($p,t$), MILU($p$), + ALT="$p$">), LU from MUMPS, SuperLU or UMFPACK (plus triangular solve). See Note for details on hybrid - Gauss-Seidel.
    'SMOOTHER_SWEEPS' integer - Any integer +
    +'SMOOTHER_SWEEPS' integer + Any integer

    -number number $\ge 0$ -

    		1 - Number of sweeps of the smoother or one-level preconditioner. + ALT="$\ge 0$"> + 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 together with pos='PRE' or pos='POST, - respectively.
    'SUB_OVR' integer - Any integer +
    +'SUB_OVR' integer + Any integer

    -number number $\ge 0$ -

    		1 - Number of overlap layers, for Additive Schwarz only. 1 + Number of overlap layers, for Additive Schwarz only.

    -
    +

    - +

    -
    +
    Table 8: Parameters defining the smoother or the details of the one-level preconditioner @@ -788,82 +791,87 @@ Parameters defining the smoother or the details of the one-level preconditioner
    - - - - - - - - - - - + + + + + + + + + + - - - - - - + + + + + + +Note that SUM must be chosen for the classical Additive + Schwarz smoother, and NONE for its RAS variant. - - - + + - - + + + ALT="$p$"> of the incomplete LU factorizations. - - - + + - - + + + ALT="$p,t$">) factorization. - + @@ -873,33 +881,34 @@ Parameters defining the smoother or the details of the one-level preconditioner
    -what DATA TYPE val DEFAULT -COMMENTS
    'SUB_RESTR' character(len=*) - 'HALO' -

    -'NONE' -

    		'HALO' - Type of restriction operator, for Additive Schwarz only: +
    +what DATA TYPE val DEFAULT +COMMENTS
    +'SUB_RESTR' character(len=*) + 'HALO' +

    +'NONE' +

    		'HALO' + Type of restriction operator, for Additive Schwarz only: HALO for taking into account the overlap, NONE - for neglecting it. -

    -Note that HALO must be chosen for - the classical Addditive Schwarz smoother and its RAS variant.

    'SUB_PROL' character(len=*) - 'SUM' -

    -'NONE' -

    		'NONE' - Type of prolongation operator, for Additive Schwarz only: + for neglecting it. +

    +Note that HALO must be chosen for + the classical Addditive Schwarz smoother and its RAS variant.

    +'SUB_PROL' character(len=*) + 'SUM' +

    +'NONE' +

    		'NONE' + Type of prolongation operator, for Additive Schwarz only: SUM for adding the contributions from the overlap, NONE - for neglecting them. + for neglecting them.

    -Note that SUM must be chosen for the classical Additive - Schwarz smoother, and NONE for its RAS variant.

    'SUB_FILLIN' integer - Any integer +
    +'SUB_FILLIN' integer + Any integer

    -number number $\ge 0$ -

    		0 - Fill-in level $\ge 0$ + 0 + Fill-in level $p$ of the incomplete LU factorizations.
    'SUB_ILUTHRS' real(kind_parameter) - Any real number  +'SUB_ILUTHRS' real(kind_parameter) + Any real number $\ge 0$ - 0 - Drop tolerance $\ge 0$ + 0 + Drop tolerance $t$ in the ILU($t$ in the ILU($p,t$) factorization.
    +

    -
    +

    - +

    -

    + +
    - next - up - previous - contents
    - Next: Subroutine build - Up: Next: Method hierarchy_build + Up: User Interface - Previous: Subroutine init -   Contents + Previous: Method init +   Contents
    diff --git a/docs/html/node21.html b/docs/html/node21.html index 73892e6c..8a1d324e 100644 --- a/docs/html/node21.html +++ b/docs/html/node21.html @@ -1,19 +1,15 @@ - + - + -Subroutine build - +Method hierarchy_build + - + @@ -25,120 +21,112 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Subroutine hierarchy_build - Up: Next: Method smoothers_build + Up: User Interface - Previous: Subroutine set -   Previous: Method set +   Contents
    -
    +
    -

    +


    -Subroutine build -

    +Method hierarchy_build +

    - -

    call p%build(a,desc_a,info) -
    + +
    call p%hierarchy_build(a,desc_a,info) +

    - -This routine builds the one-level preconditioner p according to the requirements -made by the user through the routines init and set -(see Sections 6.4 and 6.5 for multilevel preconditioners). - + +This method builds the hierarchy of matrices and restriction/prolongation +operators for the multilevel preconditioner p, according to the requirements +made by the user through the methods init and set. +

    -Arguments +Arguments

    - +

    - - - +
    -a type(psb_xspmat_type), intent(in).
    + + - - + + HREF="node36.html#PSBLASGUIDE">13]. - - + + - - + + HREF="node36.html#PSBLASGUIDE">13]. - - + + - - + + -
    +a type(psb_xspmat_type), intent(in).
    - The sparse matrix structure containing the local part of the - matrix to be preconditioned. Note that x must be chosen according - to the real/complex, single/double precision version of MLD2P4 under use. +
    + The sparse matrix structure containing the local part of the + matrix to be preconditioned. Note that x must be chosen according + to the real/complex, +single/double precision version of MLD2P4 under use. See the PSBLAS User's Guide for details [13].
    -desc_a type(psb_desc_type), intent(in).
    +desc_a type(psb_desc_type), intent(in).
    - The communication descriptor of a. See the PSBLAS User's Guide for +
    + The communication descriptor of a. See the PSBLAS User's Guide for details [13].
    info integer, intent(out).
    +info integer, intent(out).
    - Error code. If no error, 0 is returned. See Section 8 for details.
    + Error code. If no error, 0 is returned. See Section 8 for details.
    -

    -For compatibility with the previous versions of MLD2P4, this routine can be also invoked -as follows: - +

    - -

    call mld_precbld(p,what,val,info) -
    +

    - -In this case, the routine can be used to build multilevel preconditioners too. - -

    - -

    -

    + +
    - next - up - previous - contents
    - Next: Subroutine hierarchy_build - Up: Next: Method smoothers_build + Up: User Interface - Previous: Subroutine set -   Contents + Previous: Method set +   Contents
    diff --git a/docs/html/node22.html b/docs/html/node22.html index 57a370bd..0bb9ab16 100644 --- a/docs/html/node22.html +++ b/docs/html/node22.html @@ -1,19 +1,15 @@ - + - + -Subroutine hierarchy_build - +Method smoothers_build + - + @@ -25,109 +21,143 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Subroutine smoothers_build - Up: Next: Method build + Up: User Interface - Previous: Subroutine build -   Previous: Method hierarchy_build +   Contents
    -
    +
    -

    +


    -Subroutine hierarchy_build -

    +Method smoothers_build +

    - -

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

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

    -Arguments +Arguments

    - +

    - - - +
    -a type(psb_xspmat_type), intent(in).
    + + - - + + HREF="node36.html#PSBLASGUIDE">13]. - - + + - - + + HREF="node36.html#PSBLASGUIDE">13]. + + + + + + - - + + - - + + -
    +a type(psb_xspmat_type), intent(in).
    - The sparse matrix structure containing the local part of the - matrix to be preconditioned. Note that x must be chosen according - to the real/complex, -single/double precision version of MLD2P4 under use. +
    + The sparse matrix structure containing the local part of the + matrix to be preconditioned. Note that x must be chosen according + to the real/complex, single/double precision version of MLD2P4 under use. See the PSBLAS User's Guide for details [13].
    -desc_a type(psb_desc_type), intent(in).
    +desc_a type(psb_desc_type), intent(in).
    - The communication descriptor of a. See the PSBLAS User's Guide for +
    + The communication descriptor of a. See the PSBLAS User's Guide for details [13].
    +info integer, intent(out).
    + Error code. If no error, 0 is returned. See Section 8 for details.
    info integer, intent(out).
    +amold class(psb_x_base_sparse_mat), intent(in), optional.
    - Error code. If no error, 0 is returned. See Section 8 for details.
    + The desired dynamic type for internal matrix + components; this allows e.g. running on GPUs; it needs not be the + same on all processes. See the PSBLAS User's Guide for + details [13].
    + + vmold + class(psb_x_base_vect_type), intent(in), optional. + + + + The desired dynamic type for internal vector + components; this 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; this allows e.g. running on GPUs. + +

    - +

    -

    + +
    - next - up - previous - contents
    - Next: Subroutine smoothers_build - Up: Next: Method build + Up: User Interface - Previous: Subroutine build -   Contents + Previous: Method hierarchy_build +   Contents
    diff --git a/docs/html/node23.html b/docs/html/node23.html index f0e392ab..445ce6f3 100644 --- a/docs/html/node23.html +++ b/docs/html/node23.html @@ -1,19 +1,15 @@ - + - + -Subroutine smoothers_build - +Method build + - + @@ -25,108 +21,156 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Subroutine apply - Up: Next: Method apply + Up: User Interface - Previous: Subroutine hierarchy_build -   Previous: Method smoothers_build +   Contents
    -
    +
    -

    +


    -Subroutine smoothers_build -

    +Method build +

    - -

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

    - -This routine builds the smoothers and the coarsest-level solvers for the -multilevel preconditioner p, according to the requirements made by -the user through the routines init and set, and based on the aggregation -hierarchy produced by a previous call to hierarchy_build -(see Section 6.4). - + +This method builds the preconditioner p according to the requirements +made by the user through the methods init and set +(see Sections 6.3 and 6.4 for +multilevel preconditioners). It is mostly provided for backward +compatibility; indeed, it is internally implemented by invoking the +two previous methods hierarchy_build and +smoothers_build, whose nomenclature would however be somewhat +unnatural when dealing with simple one-level preconditioners. +

    -Arguments +Arguments

    - +

    - - - +
    -a type(psb_xspmat_type), intent(in).
    + + - - + + HREF="node36.html#PSBLASGUIDE">13]. - - + + - - + + HREF="node36.html#PSBLASGUIDE">13]. + + + + + + + + + + + + - - + + - - + + -
    +a type(psb_xspmat_type), intent(in).
    - The sparse matrix structure containing the local part of the - matrix to be preconditioned. Note that x must be chosen according +
    + The sparse matrix structure containing the local part of the + matrix to be preconditioned. Note that x must be chosen according to the real/complex, single/double precision version of MLD2P4 under use. See the PSBLAS User's Guide for details [13].
    -desc_a type(psb_desc_type), intent(in).
    +desc_a type(psb_desc_type), intent(in).
    - The communication descriptor of a. See the PSBLAS User's Guide for +
    + The communication descriptor of a. See the PSBLAS User's Guide for details [13].
    +info integer, intent(out).
    + Error code. If no error, 0 is returned. See Section 8 for details.
    +amold class(psb_x_base_sparse_mat), intent(in), optional.
    + The desired dynamic type for internal matrix + components; this allows e.g. running on GPUs; it needs not be the + same on all processes. See the PSBLAS User's Guide for + details [13].
    info integer, intent(out).
    + vmold class(psb_x_base_vect_type), intent(in), optional.
    - Error code. If no error, 0 is returned. See Section 8 for details.
    + The desired dynamic type for internal vector + components; this 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; this allows e.g. running on GPUs. + + +

    +For compatibility with the previous versions of MLD2P4, this method 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. + +

    + +

    - next - up - previous - contents
    - Next: Subroutine apply - Up: Next: Method apply + Up: User Interface - Previous: Subroutine hierarchy_build -   Contents + Previous: Method smoothers_build +   Contents
    diff --git a/docs/html/node24.html b/docs/html/node24.html index 9d240cc5..be5f014a 100644 --- a/docs/html/node24.html +++ b/docs/html/node24.html @@ -1,19 +1,15 @@ - + - + -Subroutine apply - +Method apply + - + @@ -25,191 +21,194 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Subroutine free - Up: Next: Method free + Up: User Interface - Previous: Subroutine smoothers_build -   Previous: Method build +   Contents
    -
    +


    -Subroutine apply -

    +Method apply +

    - -

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

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

    -Arguments +Arguments

    - +

    - - - +
    x type(kind_parameter), dimension(:), intent(in).
    + + - - + + ALT="$x$">. Note that type and + kind_parameter must be chosen according + to the real/complex, single/double precision version of MLD2P4 under use. - - + + - - + + ALT="$y$">. Note that type and + kind_parameter must be chosen according + to the real/complex, single/double precision version of MLD2P4 under use. - - + + - - + + - - + + - - + + - - + + - - + ALT="$B^{-1})$">. - - + + - - + + Note that type and kind_parameter must be chosen according + to the real/complex, single/double precision version of MLD2P4 under use. -
    +x type(kind_parameter), dimension(:), intent(in).
    - The local part of the vector + The local part of the vector $x$. Note that type and - kind_parameter must be chosen according - to the real/complex, single/double precision version of MLD2P4 under use.
    -y type(kind_parameter), dimension(:), intent(out).
    +y type(kind_parameter), dimension(:), intent(out).
    - The local part of the vector + The local part of the vector $y$. Note that type and - kind_parameter must be chosen according - to the real/complex, single/double precision version of MLD2P4 under use.
    -desc_a type(psb_desc_type), intent(in).
    +desc_a type(psb_desc_type), intent(in).
    - The communication descriptor associated to the matrix to be - preconditioned.
    + The communication descriptor associated to the matrix to be + preconditioned.
    -info integer, intent(out).
    +info integer, intent(out).
    - Error code. If no error, 0 is returned. See Section 8 for details.
    + Error code. If no error, 0 is returned. See Section 8 for details.
    -trans character(len=1), optional, intent(in).
    +trans character(len=1), optional, intent(in).
    - If trans = 'N','n' then -$op(B^{-1}) = B^{-1}$; + ALT="$op(B^{-1}) = B^{-1}$">; if trans = 'T','t' then -$op(B^{-1}) = B^{-T}$ - (transpose of $op(B^{-1}) = B^{-T}$ + (transpose of $B^{-1})$; if trans = 'C','c' then -$op(B^{-1}) = B^{-C}$ - (conjugate transpose of $op(B^{-1}) = B^{-C}$ + (conjugate transpose of $B^{-1})$.
    -work type(kind_parameter), dimension(:), optional, target.
    +work type(kind_parameter), dimension(:), optional, target.
    - Workspace. Its size should be at +
    + Workspace. Its size should be at least 4 * psb_cd_get_local_ cols(desc_a) (see the PSBLAS User's Guide). - Note that type and kind_parameter must be chosen according - to the real/complex, single/double precision version of MLD2P4 under use.
    +

    -For compatibility with the previous versions of MLD2P4, this routine can be also invoked +For compatibility with the previous versions of MLD2P4, this method can be also invoked as follows: - +

    - -

    call mld_precaply(p,what,val,info) -
    + +
    call mld_precaply(p,what,val,info) +

    - +

    -

    + +
    - next - up - previous - contents
    - Next: Subroutine free - Up: Next: Method free + Up: User Interface - Previous: Subroutine smoothers_build -   Contents + Previous: Method build +   Contents
    diff --git a/docs/html/node25.html b/docs/html/node25.html index d588ab16..da626cdc 100644 --- a/docs/html/node25.html +++ b/docs/html/node25.html @@ -1,19 +1,15 @@ - + - + -Subroutine free - +Method free + - + @@ -25,70 +21,72 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Subroutine descr - Up: Next: Method descr + Up: User Interface - Previous: Subroutine apply -   Previous: Method apply +   Contents
    -
    +


    -Subroutine free -

    +Method free +

    - -

    call p%free(p,info) -
    + +
    call p%free(p,info) +

    - -This routine deallocates the preconditioner data structure p. - + +This method deallocates the preconditioner data structure p. +

    -Arguments +Arguments

    - +

    - - - +
    info integer, intent(out).
    + + - - + + -
    +info integer, intent(out).
    - Error code. If no error, 0 is returned. See Section 8 for details.
    + Error code. If no error, 0 is returned. See Section 8 for details.
    +

    -For compatibility with the previous versions of MLD2P4, this routine can be also invoked +For compatibility with the previous versions of MLD2P4, this method can be also invoked as follows: - +

    - -

    call mld_precfree(p,info) -
    + +
    call mld_precfree(p,info) +

    - +

    - +

    diff --git a/docs/html/node26.html b/docs/html/node26.html index 93d3abc3..494e7369 100644 --- a/docs/html/node26.html +++ b/docs/html/node26.html @@ -1,128 +1,124 @@ - + - + -Subroutine descr - +Method descr + - + + - - + next - up - previous - contents
    - Next: Adding new smoother and - Up: Next: Auxiliary Methods + Up: User Interface - Previous: Subroutine free -   Previous: Method free +   Contents
    -
    +


    -Subroutine descr -

    +Method descr +

    - -

    call p%descr(info, [iout]) -
    + +
    call p%descr(info, [iout]) +

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

    -Arguments +Arguments

    - +

    - - - +
    info integer, intent(out).
    + + - - + + - - + + - - + + -
    +info integer, intent(out).
    - Error code. If no error, 0 is returned. See Section 8 for details.
    + Error code. If no error, 0 is returned. See Section 8 for details.
    -iout integer, intent(in), optional.
    +iout integer, intent(in), optional.
    - The id of the file where the preconditioner description - will be printed; the default is the standard output.
    + The id of the file where the preconditioner description + will be printed; the default is the standard output.
    +

    -For compatibility with the previous versions of MLD2P4, this routine can be also invoked +For compatibility with the previous versions of MLD2P4, this method can be also invoked as follows: - +

    - -

    call mld_precdescr(p,info [,iout]) -
    + +
    call mld_precdescr(p,info [,iout]) +

    - -

    - -

    -

    + +
    - next - up - previous - contents
    - Next: Adding new smoother and - Up: Next: Auxiliary Methods + Up: User Interface - Previous: Subroutine free -   Contents + Previous: Method free +   Contents
    diff --git a/docs/html/node27.html b/docs/html/node27.html index aec3a8c7..b4165d36 100644 --- a/docs/html/node27.html +++ b/docs/html/node27.html @@ -1,185 +1,79 @@ - + - + -Adding new smoother and solver objects to MLD2P4 - +Auxiliary Methods + - + - - - + + - - + next - + up - previous - contents
    - Next: Error Handling - Up: userhtml - Previous: Subroutine descr -   Next: Method: dump + Up: User Interface + Previous: Method descr +   Contents
    -
    +
    -

    +


    -Adding new smoother and solver objects to MLD2P4 -

    -

    -Developers can add completely new smoother and/or solver classes -derived from the base objects in the library (see Remark 2 in Section 6.2), -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. -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. - +Auxiliary Methods + +Various functionalities are implemented as additional methods of the +preconditioner object. +

    -Once the new smoother/solver class has been developed, to use it in -the context of the multilevel preconditioners it is necessary to: - -

      -
    • declare in the application program a variable of the new type; -
      • -
    • pass that variable as the argument to the set routine as in the -following: -
      -call p%set(smoother,info [,ilev,ilmax,pos]) -
      call p%set(solver,info [,ilev,ilmax,pos]) + +
      + +Subsections -
      -
      • -
    • link the code implementing the various methods into the application executable. -
      • -
    -The new solver object is then dynamically included in the -preconditioner structure, and acts as a mold to which the -preconditioner will conform, even though the MLD2P4 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 (levels containing -smoothers containing in turn solvers), so that it can be eventually caught by -the new solver. - -

    -An example is provided in the source code distribution under the -folder tests/newslv. In this example we are implementing a new -incomplete factorization variant (which is simply the ILU(0) -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). - -

    -The interfaces for the calls shown above are defined using - -

    - - - - - - - - - - - - -
    -smoother class(mld_x_base_smoother_type)
    - 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. -
    -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 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
-
-......
-  !
-  !  prepare the preconditioner: an ML with defaults, but with TLU solver at
-  !  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()
-  call prec%set(tlusv,   info,ilev=1,ilmax=max(1,nlv-1))
-  call prec%smoothers_build(a,desc_a,info)
-
    -
    - - -next - -up - -previous - -contents -
    - Next: Error Handling - Up: userhtml - Previous: Subroutine descr -   Contents - + + +
    diff --git a/docs/html/node28.html b/docs/html/node28.html index 71f156e4..ffbacc9b 100644 --- a/docs/html/node28.html +++ b/docs/html/node28.html @@ -1,77 +1,93 @@ - + - + -Error Handling - +Method: dump + - + - + - - + next - + up - previous - contents
    - Next: License - Up: userhtml - Previous: Adding new smoother and -   Next: Method: clone + Up: Auxiliary Methods + Previous: Auxiliary Methods +   Contents
    -
    +
    -

    -
    -Error Handling -

    +

    +Method: dump +

    +

    + +

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

    + +Dump on file. + +

    +Arguments +

    +

    -The error handling in MLD2P4 is based on the PSBLAS error -handling. Error conditions are signaled via an integer argument -info; whenever an error condition is detected, an error trace -stack is built by the library up to the top-level, user-callable -routine. This routine will then decide, according to the user -preferences, whether the error should be handled by terminating the -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 [13]. - + + + + + + + + + + + + + +
    +info integer, intent(out).
    + Error code. If no error, 0 is returned. See Section 8 for details.
    +amold class(psb_x_base_sparse_mat), intent(in), optional.
    + The desired dynamic type for internal matrix + components; this allows e.g. running on GPUs; it needs not be the + same on all processes. See the PSBLAS User's Guide for + details [13].

    - - +

    diff --git a/docs/html/node29.html b/docs/html/node29.html index 3d3fddd4..888861cf 100644 --- a/docs/html/node29.html +++ b/docs/html/node29.html @@ -1,100 +1,91 @@ - + - + -License - +Method: clone + - + - + - - + next - + up - previous - contents
    - Next: Bibliography - Up: userhtml - Previous: Error Handling -   Next: Method: sizeof + Up: Auxiliary Methods + Previous: Method: dump +   Contents
    -
    +
    -

    -
    -License -

    +

    +Method: clone +

    -The MLD2P4 is freely distributable under the following copyright -terms: 

     
- 
-                           MLD2P4  version 2.1
-  MultiLevel Domain Decomposition Parallel 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
-
-  Redistribution and use in source and binary forms, with or without
-  modification, are permitted provided that the following conditions
-  are met:
-    1. Redistributions of source code must retain the above copyright
-       notice, this list of conditions and the following disclaimer.
-    2. Redistributions in binary form must reproduce the above copyright
-       notice, this list of conditions, and the following disclaimer in the
-       documentation and/or other materials provided with the distribution.
-    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
-  PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
-  BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
-  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
-  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
-  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
-  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.
-
    - - + +
    call p%clone(pout,info) +
    +

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

    +Arguments +

    + +

    + + + + + + + + + + + + + +
    +pout type(mld_xprec_type), intent(out).
    + The copy of the preconditioner data structure. Note + that x must be chosen according + to the real/complex, single/double precision version of MLD2P4 under use.
    +info integer, intent(out).
    + Error code. If no error, 0 is returned. See Section 8 for details.
    +

    +

    diff --git a/docs/html/node3.html b/docs/html/node3.html index 923a4ae2..a5e870ba 100644 --- a/docs/html/node3.html +++ b/docs/html/node3.html @@ -1,10 +1,6 @@ - + - + General Overview @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,53 +21,55 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Next: Code Distribution - Up: Up: userhtml - Previous: Previous: Contents -   Contents
    -
    +


    General Overview -

    +

    -The MULTILEVEL DOMAIN DECOMPOSITION PARALLEL PRECONDITIONERS PACKAGE BASED ON +The MULTILEVEL DOMAIN DECOMPOSITION PARALLEL PRECONDITIONERS PACKAGE BASED ON PSBLAS (MLD2P4) provides parallel Algebraic MultiGrid (AMG) and Domain Decomposition preconditioners (see, e.g., [3,23,21]), + HREF="node36.html#Briggs2000">3,23,21]), to be used in the iterative solution of linear systems, - +
    -

    +
    + - +
    \begin{displaymath} Ax=b, \end{displaymath} -(1)
    +(1)
    -

    -where

    +where $A$ is a square, real or complex, sparse matrix. The name of the package comes from its original implementation, containing + ALT="$A$"> is a square, real or complex, sparse matrix. +The name of the package comes from its original implementation, containing multilevel additive and hybrid Schwarz 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 +The multilevel preconditioners implemented in MLD2P4 are obtained by combining AMG cycles with smoothers and coarsest-level solvers. The V-, W-, and K-cycles [3,19] are available, which allow to define + HREF="node36.html#Briggs2000">3,19] 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, hybridforward/backward Gauss-Seidel, block-Jacobi, and additive Schwarz methods +Schwarz preconditioners. The Jacobi, hybrid +forward/backward Gauss-Seidel, block-Jacobi, and additive Schwarz methods are available as 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 [2,25] + HREF="node36.html#BREZINA_VANEK">2,25] 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 preconditioners. - +

    -MLD2P4 is written in Fortran 2003, following an +MLD2P4 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 parallel implementation is based on a Single Program Multiple Data +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 real and the complex case, which can be used through a single interface. - +

    -MLD2P4 has been designed to implement scalable and easy-to-use +MLD2P4 has been designed to implement scalable and easy-to-use multilevel preconditioners in the context of the PSBLAS (Parallel Sparse BLAS) computational framework [15,14]. PSBLAS provides basic linear algebra + HREF="node36.html#psblas_00">15,14]. 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 mainly motivated by the need of having -a portable and efficient software infrastructure implementing ``de facto'' standard +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 -in the PSBLAS routines;therefore, MLD2P4 can be run on any parallel machine where PSBLAS +in the PSBLAS routines; +therefore, MLD2P4 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 +MLD2P4 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. @@ -150,19 +152,19 @@ 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 and solvers for building new versions of the preconditioners (see -Section 7). - +Section 7). +

    -We note that the user interface of MLD2P4 2.1 has been extended with respect to the +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 + HREF="node36.html#MLD2P4_TOMS">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 +This guide is organized as follows. General information on the distribution of the source code is reported in Section 2, while details on the configuration and installation of the package are given in Section 3. A short description of the preconditioners implemented in MLD2P4 is provided in Section 4, @@ -171,35 +173,36 @@ preconditioners with the Krylov solvers implemented in PSBLAS are reported in Section 5, where the Fortran codes of a few sample programs are also shown. A reference guide for the user interface routines is provided in Section 6. Information on the extension of the package -through the addition of new smoothers and solvers is reported in Section 7. +through the addition of new smoothers and solvers is reported in Section 7. The error handling mechanism used by the package -is briefly described in Section 8. The copyright terms concerning the -distribution and modification of MLD2P4 are reported in Appendix A. - +is briefly described in Section 8. The copyright terms concerning the +distribution and modification of MLD2P4 are reported in Appendix A. +

    -

    + +
    - next - up - previous - contents
    - Next: Next: Code Distribution - Up: Up: userhtml - Previous: Previous: Contents -   Contents +   Contents
    diff --git a/docs/html/node30.html b/docs/html/node30.html index 58113efb..e5cfa8fa 100644 --- a/docs/html/node30.html +++ b/docs/html/node30.html @@ -1,179 +1,67 @@ - + - + -Bibliography - +Method: sizeof + - + - + - - + next - + up - previous - contents
    - Next: About this document ... - Up: userhtml - Previous: License -   Next: Method: allocate_wrk + Up: Auxiliary Methods + Previous: Method: clone +   Contents -

    +
    +
    - -

    -Bibliography -

    +

    +Method: sizeof +

    -

    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 http://mumps.enseeiht.fr.

    2 -
    -M. Brezina, P. Vanek, -A Black-Box Iterative Solver Based on a Two-Level Schwarz Method, -Computing, 63, 1999, 233-263.

    3 -
    -W. L. Briggs, V. E. Henson, S. F. McCormick, -A Multigrid Tutorial, Second Edition, -SIAM, 2000.

    4 -
    -A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone, -Extending PSBLAS to Build Parallel Schwarz Preconditioners, -in J. Dongarra, K. Madsen, J. Wasniewski, editors, -Proceedings of PARA 04 Workshop on State of the Art -in Scientific Computing, Lecture Notes in Computer Science, -Springer, 2005, 593-602.

    5 -
    -A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone, -2LEV-D2P4: a package of high-performance preconditioners -for scientific and engineering applications, -Applicable Algebra in Engineering, Communications and Computing, -18 (3) 2007, 223-239.

    6 -
    -X. C. Cai, M. Sarkis, -A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems, -SIAM Journal on Scientific Computing, 21 (2), 1999, 792-797.

    7 -
    -P. D'Ambra, S. Filippone, D. di Serafino, -On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners, -Applied Numerical Mathematics, Elsevier Science, -57 (11-12), 2007, 1181-1196.

    8 -
    -P. D'Ambra, D. di Serafino, S. Filippone, -MLD2P4: a Package of Parallel Multilevel -Algebraic Domain Decomposition Preconditioners -in Fortran 95, ACM Trans. Math. Softw., 37(3), 2010, art. 30.

    9 -
    -T. A. Davis, -Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal -Method with a Column Pre-ordering Strategy, -ACM Transactions on Mathematical Software, 30, 2004, 196-199. -(See also http://www.cise.ufl.edu/~davis/)

    10 -
    -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 -
    -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 -
    -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 -
    -S. Filippone, A. Buttari, -PSBLAS 3.5.0 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library, 2012, -available from https://github.com/sfilippone/psblas3/tree/master/docs.

    14 -
    -S. Filippone, A. Buttari, -Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003. -ACM Transactions on on Mathematical Software, 38 (4), 2012, art. 23.

    15 -
    -S. Filippone, M. Colajanni, -PSBLAS: A Library for Parallel Linear Algebra -Computation on Sparse Matrices, -ACM Transactions on Mathematical Software, 26 (4), 2000, 527-550.

    16 -
    -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.

    17 -
    -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.

    18 -
    -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.

    19 -
    -Y. Notay, P. S. Vassilevski, -Recursive Krylov-based multigrid cycles, -Numerical Linear Algebra with Applications, 15 (5), 2008, 473-487.

    20 -
    -Y. Saad, -Iterative methods for sparse linear systems, 2nd edition, SIAM, 2003.

    21 -
    -B. Smith, P. Bjorstad, W. Gropp, -Domain Decomposition: Parallel Multilevel Methods for Elliptic -Partial Differential Equations, -Cambridge University Press, 1996.

    22 -
    -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.

    23 -
    -K. Stüben, -An Introduction to Algebraic Multigrid, -in A. Schüller, U. Trottenberg, C. Oosterlee, Multigrid, -Academic Press, 2001.

    24 -
    -R. S. Tuminaro, C. Tong, -Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines, in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000.

    25 -
    -P. Vanek, J. Mandel, M. Brezina, -Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems, -Computing, 56 (3) 1996, 179-196. - + +
    sz = p%sizeof() +

    -

    - + +Return memory footprint in bytes. +

    -

    + +
    diff --git a/docs/html/node31.html b/docs/html/node31.html index 8aef6661..a2044f73 100644 --- a/docs/html/node31.html +++ b/docs/html/node31.html @@ -1,70 +1,127 @@ - + - + -About this document ... - +Method: allocate_wrk + - + + - + + - -next - + +
    + +next + up - previous - contents
    - Up: userhtml - Previous: Bibliography -   Next: Method: free_wrk + Up: Auxiliary Methods + Previous: Method: sizeof +   Contents
    -
    +
    -

    -About this document ... -

    -

    -This document was generated using the -LaTeX2HTML translator Version 2012 (1.2) +

    +Method: allocate_wrk +

    -Copyright © 1993, 1994, 1995, 1996, -Nikos Drakos, -Computer Based Learning Unit, University of Leeds. -
    -Copyright © 1997, 1998, 1999, -Ross Moore, -Mathematics Department, Macquarie University, Sydney. + +

    call p%allocate_wrk(info[, vmold]) +

    -The command line arguments were:
    - latex2html -local_icons -noaddress -dir ../../html userhtml.tex + +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 +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 +the internal workspace outside of the 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 care of based on the dynamic +type of the x argument to the apply method. +

    -The translation was initiated by Salvatore Filippone on 2017-10-23 -

    +Arguments +

    + +

    + + + + + + + + + + + + + +
    +info integer, intent(out).
    + Error code. If no error, 0 is returned. See Section 8 for details.
    + vmold class(psb_x_base_vect_type), intent(in), optional.
    + The desired dynamic type for internal vector + components; this allows e.g. running on GPUs.
    +

    + +

    + + +next + +up + +previous + +contents +
    + Next: Method: free_wrk + Up: Auxiliary Methods + Previous: Method: sizeof +   Contents
    + diff --git a/docs/html/node32.html b/docs/html/node32.html new file mode 100644 index 00000000..66687d38 --- /dev/null +++ b/docs/html/node32.html @@ -0,0 +1,85 @@ + + + + + +Method: free_wrk + + + + + + + + + + + + + + + + + +
    + +next + +up + +previous + +contents +
    + Next: Adding new smoother and + Up: Auxiliary Methods + Previous: Method: allocate_wrk +   Contents +
    +
    + + +

    +Method: free_wrk +

    +

    + +

    call p%free_wrk(info) +
    +

    + +Deallocate internal work vectors. + +

    +Arguments +

    + +

    + + + + + + + +
    +info integer, intent(out).
    + Error code. If no error, 0 is returned. See Section 8 for details.
    +

    + +

    + +

    + +

    + + + diff --git a/docs/html/node33.html b/docs/html/node33.html new file mode 100644 index 00000000..a9e120a5 --- /dev/null +++ b/docs/html/node33.html @@ -0,0 +1,183 @@ + + + + + +Adding new smoother and solver objects to MLD2P4 + + + + + + + + + + + + + + + + + + +
    + +next + +up + +previous + +contents +
    + Next: Error Handling + Up: userhtml + Previous: Method: free_wrk +   Contents +
    +
    + + +

    +
    +Adding new smoother and solver objects to MLD2P4 +

    +

    +Developers can add completely new smoother and/or solver classes +derived from the base objects in the library (see Remark 2 in Section 6.2), +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. +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. + +

    +Once the new smoother/solver class has been developed, to use it in +the context of the multilevel preconditioners it is necessary to: + +

      +
    • declare in the application program a variable of the new type; +
      • +
    • pass that variable as the argument to the set routine as in the +following: +
      +call p%set(smoother,info [,ilev,ilmax,pos]) +
      call p%set(solver,info [,ilev,ilmax,pos]) + +
      +
      • +
    • link the code implementing the various methods into the application executable. +
      • +
    +The new solver object is then dynamically included in the +preconditioner structure, and acts as a mold to which the +preconditioner will conform, even though the MLD2P4 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 (levels containing +smoothers containing in turn solvers), so that it can be eventually caught by +the new solver. + +

    +An example is provided in the source code distribution under the +folder tests/newslv. In this example we are implementing a new +incomplete factorization variant (which is simply the ILU(0) +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). + +

    +The interfaces for the calls shown above are defined using + +

    + + + + + + + + + + + + +
    +smoother class(mld_x_base_smoother_type)
    + 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. +
    +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 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
+
+......
+  !
+  !  prepare the preconditioner: an ML with defaults, but with TLU solver at
+  !  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()
+  call prec%set(tlusv,   info,ilev=1,ilmax=max(1,nlv-1))
+  call prec%smoothers_build(a,desc_a,info)
+
    + +
    + + +next + +up + +previous + +contents +
    + Next: Error Handling + Up: userhtml + Previous: Method: free_wrk +   Contents
    + + + + diff --git a/docs/html/node34.html b/docs/html/node34.html new file mode 100644 index 00000000..150cb8e1 --- /dev/null +++ b/docs/html/node34.html @@ -0,0 +1,75 @@ + + + + + +Error Handling + + + + + + + + + + + + + + + + + + +
    + +next + +up + +previous + +contents +
    + Next: License + Up: userhtml + Previous: Adding new smoother and +   Contents +
    +
    + + +

    +
    +Error Handling +

    +

    +The error handling in MLD2P4 is based on the PSBLAS error +handling. Error conditions are signaled via an integer argument +info; whenever an error condition is detected, an error trace +stack is built by the library up to the top-level, user-callable +routine. This routine will then decide, according to the user +preferences, whether the error should be handled by terminating the +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 [13]. + +

    + + +

    + + + diff --git a/docs/html/node35.html b/docs/html/node35.html new file mode 100644 index 00000000..5a7991e0 --- /dev/null +++ b/docs/html/node35.html @@ -0,0 +1,98 @@ + + + + + +License + + + + + + + + + + + + + + + + + + +
    + +next + +up + +previous + +contents +
    + Next: Bibliography + Up: userhtml + Previous: Error Handling +   Contents +
    +
    + + +

    +
    +License +

    +

    +The MLD2P4 is freely distributable under the following copyright +terms: 

     
+ 
+                           MLD2P4  version 2.1
+  MultiLevel Domain Decomposition Parallel 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
+
+  Redistribution and use in source and binary forms, with or without
+  modification, are permitted provided that the following conditions
+  are met:
+    1. Redistributions of source code must retain the above copyright
+       notice, this list of conditions and the following disclaimer.
+    2. Redistributions in binary form must reproduce the above copyright
+       notice, this list of conditions, and the following disclaimer in the
+       documentation and/or other materials provided with the distribution.
+    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
+  PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
+  BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+  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.
+
    + + +
    + + + diff --git a/docs/html/node36.html b/docs/html/node36.html new file mode 100644 index 00000000..bf1feef1 --- /dev/null +++ b/docs/html/node36.html @@ -0,0 +1,200 @@ + + + + + +Bibliography + + + + + + + + + + + + + + + + + + +
    + +next + +up + +previous + +contents +
    + Next: About this document ... + Up: userhtml + Previous: License +   Contents +

    + + +

    +Bibliography +

    + +

    +

    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 http://mumps.enseeiht.fr. +

    2 +
    +M. Brezina, P. Vanek, +A Black-Box Iterative Solver Based on a Two-Level Schwarz Method, +Computing, 63, 1999, 233-263. +

    3 +
    +W. L. Briggs, V. E. Henson, S. F. McCormick, +A Multigrid Tutorial, Second Edition, +SIAM, 2000. +

    4 +
    +A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone, +Extending PSBLAS to Build Parallel Schwarz Preconditioners, +in J. Dongarra, K. Madsen, J. Wasniewski, editors, +Proceedings of PARA 04 Workshop on State of the Art +in Scientific Computing, Lecture Notes in Computer Science, +Springer, 2005, 593-602. +

    5 +
    +A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone, +2LEV-D2P4: a package of high-performance preconditioners +for scientific and engineering applications, +Applicable Algebra in Engineering, Communications and Computing, +18 (3) 2007, 223-239. +

    6 +
    +X. C. Cai, M. Sarkis, +A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems, +SIAM Journal on Scientific Computing, 21 (2), 1999, 792-797. +

    7 +
    +P. D'Ambra, S. Filippone, D. di Serafino, +On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners, +Applied Numerical Mathematics, Elsevier Science, +57 (11-12), 2007, 1181-1196. +

    8 +
    +P. D'Ambra, D. di Serafino, S. Filippone, +MLD2P4: a Package of Parallel Multilevel +Algebraic Domain Decomposition Preconditioners +in Fortran 95, ACM Trans. Math. Softw., 37(3), 2010, art. 30. +

    9 +
    +T. A. Davis, +Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal +Method with a Column Pre-ordering Strategy, +ACM Transactions on Mathematical Software, 30, 2004, 196-199. +(See also http://www.cise.ufl.edu/~davis/) +

    10 +
    +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 +
    +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 +
    +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 +
    +S. Filippone, A. Buttari, +PSBLAS 3.5.0 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library, 2012, +available from https://github.com/sfilippone/psblas3/tree/master/docs. +

    14 +
    +S. Filippone, A. Buttari, +Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003. +ACM Transactions on on Mathematical Software, 38 (4), 2012, art. 23. +

    15 +
    +S. Filippone, M. Colajanni, +PSBLAS: A Library for Parallel Linear Algebra +Computation on Sparse Matrices, +ACM Transactions on Mathematical Software, 26 (4), 2000, 527-550. +

    16 +
    +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. +

    17 +
    +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. +

    18 +
    +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. +

    19 +
    +Y. Notay, P. S. Vassilevski, +Recursive Krylov-based multigrid cycles, +Numerical Linear Algebra with Applications, 15 (5), 2008, 473-487. +

    20 +
    +Y. Saad, +Iterative methods for sparse linear systems, 2nd edition, SIAM, 2003. +

    21 +
    +B. Smith, P. Bjorstad, W. Gropp, +Domain Decomposition: Parallel Multilevel Methods for Elliptic +Partial Differential Equations, +Cambridge University Press, 1996. +

    22 +
    +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. +

    23 +
    +K. Stüben, +An Introduction to Algebraic Multigrid, +in A. Schüller, U. Trottenberg, C. Oosterlee, Multigrid, +Academic Press, 2001. +

    24 +
    +R. S. Tuminaro, C. Tong, +Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines, in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000. +

    25 +
    +P. Vanek, J. Mandel, M. Brezina, +Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems, +Computing, 56 (3) 1996, 179-196. + +

    +

    + +

    +

    + + + diff --git a/docs/html/node37.html b/docs/html/node37.html new file mode 100644 index 00000000..89b94046 --- /dev/null +++ b/docs/html/node37.html @@ -0,0 +1,67 @@ + + + + + +About this document ... + + + + + + + + + + + + + + + + +
    +next + +up + +previous + +contents +
    + Up: userhtml + Previous: Bibliography +   Contents +
    +
    + + +

    +About this document ... +

    +

    +This document was generated using the +LaTeX2HTML translator Version 2017.2 (Released Jan 23, 2017) +

    +Copyright © 1993, 1994, 1995, 1996, +Nikos Drakos, +Computer Based Learning Unit, University of Leeds. +
    +Copyright © 1997, 1998, 1999, +Ross Moore, +Mathematics Department, Macquarie University, Sydney. +

    +The command line arguments were:
    + latex2html -local_icons -noaddress -dir ../../html userhtml.tex +

    +The translation was initiated on 2018-01-11 +

    + + + diff --git a/docs/html/node4.html b/docs/html/node4.html index 222f9124..7b2ac12c 100644 --- a/docs/html/node4.html +++ b/docs/html/node4.html @@ -1,10 +1,6 @@ - + - + Code Distribution @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,57 +21,58 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Next: Contributors - Up: Up: userhtml - Previous: Previous: General Overview -   Contents
    -
    +


    Code Distribution -

    +

    - + MLD2P4 is available from the web site - -

    https://github.com/sfilippone/mld2p4-2 -
    + +
    https://github.com/sfilippone/mld2p4-2 +
    where contact points for further information can be also found. -     +

    -The software is available under a modified BSD license, as specified -in Appendix A; please note that some of the optional +The software is available under a modified BSD license, as specified +in Appendix A; 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. - +

    -The library defines a version string with the +The library defines a version string with the constant - +

    -
    +
    Subsections - diff --git a/docs/html/node5.html b/docs/html/node5.html index 2e8a25e4..3e5ba8d6 100644 --- a/docs/html/node5.html +++ b/docs/html/node5.html @@ -1,10 +1,6 @@ - + - + Contributors @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -24,49 +20,50 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Next: Configuring and Building MLD2P4 - Up: Up: Code Distribution - Previous: Previous: Code Distribution -   Contents
    -
    +

    Contributors -

    + Contributors to version 2: - +
    • Salvatore Filippone, Cranfield University, UK;
    • Pasqua D'Ambra, IAC-CNR, Naples, IT;
      • -
    • Daniela di Serafino, University of Campania ``L. Vanvitelli'', Caserta, IT; +
    • Daniela di Serafino, University of Campania “L. Vanvitelli”, Caserta, IT;
      • -
    • Ambra Abdullahi Hassan, University of Rome ``Tor Vergata'', IT. +
    • Ambra Abdullahi Hassan, University of Rome “Tor Vergata”, IT.
      • -
    + Contributors to version 1: - +
    • Salvatore Filippone;
      • @@ -76,8 +73,8 @@ Contributors to version 1:
    • Alfredo Buttari, CNRS-IRIT, Toulouse, F.
      • -
    - + +
    diff --git a/docs/html/node6.html b/docs/html/node6.html index 3b2e2f68..8c177d8c 100644 --- a/docs/html/node6.html +++ b/docs/html/node6.html @@ -1,10 +1,6 @@ - + - + Configuring and Building MLD2P4 @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,45 +21,46 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Next: Prerequisites - Up: Up: userhtml - Previous: Previous: Contributors -   Contents
    -
    +


    Configuring and Building MLD2P4 -

    + In order to build MLD2P4 it is necessary to set up a Makefile with appropriate system-dependent variables; this is done by means of the 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. - +

    -MLD2P4 is implemented almost entirely in Fortran 2003, with some +MLD2P4 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 MOLD= feature, which enhances the usability of ALLOCATE. @@ -72,58 +69,59 @@ 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. - +

    -Building MLD2P4 requires some base libraries (see Section 3.1); +Building MLD2P4 requires some base libraries (see Section 3.1); interfaces to optional third-party libraries, which extend the functionalities of MLD2P4 (see Section 3.2), 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 +“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. - +

    - +

    Subsections - -
    + +
    - next - up - previous - contents
    - Next: Next: Prerequisites - Up: Up: userhtml - Previous: Previous: Contributors -   Contents +   Contents
    diff --git a/docs/html/node7.html b/docs/html/node7.html index f1ff2e54..13445741 100644 --- a/docs/html/node7.html +++ b/docs/html/node7.html @@ -1,10 +1,6 @@ - + - + Prerequisites @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,44 +21,45 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Next: Optional third party libraries - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Configuring and Building MLD2P4 -   Contents
    -
    +


    Prerequisites -

    +

    -The following base libraries are needed: -

    +The following base libraries are needed: +
    BLAS
    [11,12,17] Many vendors provide optimized versions + HREF="node36.html#blas3">11,12,17] Many vendors provide optimized versions of BLAS; if no vendor version is available for a given platform, the ATLAS software (
    MPI
    [16,22] A version of MPI is available on most + HREF="node36.html#MPI2">16,22] A version of MPI is available on most high-performance computing systems.
    PSBLAS
    [13,15] Parallel Sparse BLAS (PSBLAS) is + HREF="node36.html#PSBLASGUIDE">13,15] Parallel Sparse BLAS (PSBLAS) is available from github.com/sfilippone/psblas3; version 3.5.0 (or later) is required. Indeed, all the prerequisites listed so far 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 MLD2P4. - +

    -

    + +
    - next - up - previous - contents
    - Next: Next: Optional third party libraries - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Configuring and Building MLD2P4 -   Contents +   Contents
    diff --git a/docs/html/node8.html b/docs/html/node8.html index 6f49fbed..f1b81928 100644 --- a/docs/html/node8.html +++ b/docs/html/node8.html @@ -1,10 +1,6 @@ - + - + Optional third party libraries @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,46 +21,47 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Next: Configuration options - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Prerequisites -   Contents
    -
    +


    Optional third party libraries -

    +

    -We provide interfaces to the following third-party software libraries; +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. - +

    -

    +
    UMFPACK
    [9] + HREF="node36.html#UMFPACK">9] A sparse LU factorization package included in the SuiteSparse library, available from faculty.cse.tamu.edu/davis/suitesparse.html; @@ -75,7 +72,7 @@ for multilevel preconditioners may change to reflect their presence.
    MUMPS
    [1] + HREF="node36.html#MUMPS">1] A sparse LU factorization package available from mumps.enseeiht.fr; it provides sequential and parallel factorizations and triangular system solution @@ -84,7 +81,7 @@ for multilevel preconditioners may change to reflect their presence.
    SuperLU
    [10] + HREF="node36.html#SUPERLU">10] A sparse LU factorization package available from crd.lbl.gov/~xiaoye/SuperLU/; it provides sequential @@ -95,7 +92,7 @@ for multilevel preconditioners may change to reflect their presence.
    SuperLU_Dist
    [18] + HREF="node36.html#SUPERLUDIST">18] A sparse LU factorization package available from the same site as SuperLU; it provides parallel factorization and triangular system solution for double precision real and complex data. @@ -107,31 +104,32 @@ for multilevel preconditioners may change to reflect their presence. glaros.dtc.umn.edu/gkhome/metis/parmetis/overview.
    -
    +

    -

    + +
    - next - up - previous - contents
    - Next: Next: Configuration options - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Prerequisites -   Contents +   Contents
    diff --git a/docs/html/node9.html b/docs/html/node9.html index 71590cc3..ca34a236 100644 --- a/docs/html/node9.html +++ b/docs/html/node9.html @@ -1,10 +1,6 @@ - + - + Configuration options @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -25,51 +21,52 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + next - up - previous - contents
    - Next: Next: Bug reporting - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Optional third party libraries -   Contents
    -
    +

    Configuration options -

    +

    -In order to build MLD2P4, the first step is to use the configure script +In order to build MLD2P4, the first step is to use the configure script in the main directory to generate the necessary makefile. - +

    -As a minimal example consider the following: -

    +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 the standard directories on the system, and specifies only the PSBLAS install directory (note that the latter directory must be specified with an absolute path). The full set of options may be looked at by issuing the command ./configure --help, which produces: -
    +
     `configure' configures MLD2P4 2.1 to adapt to many kinds of systems.
 
 Usage: ./configure [OPTION]... [VAR=VALUE]...
@@ -226,61 +223,62 @@ Use these variables to override the choices made by `configure' or to help
 it to find libraries and programs with nonstandard names/locations.
 
 Report bugs to <https://github.com/sfilippone/mld2p4-2/issues>.
-
    
+

    -For instance, if a user has built and installed PSBLAS 3.5 under the +For instance, if a user has built and installed PSBLAS 3.5 under the /opt directory and is using the SuiteSparse package (which includes UMFPACK), then MLD2P4 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 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 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 -ldmumps -lsmumps -lzmumps -lcmumps -mumps_common -lpord. 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 --with-extra-libs configure option. - +

    -To build the library the user will now enter -

    +To build the library the user will now enter 
+
     make
-
    
+
    followed (optionally) by -
    +
     make install
-
    
+
    +
    - next - up - previous - contents
    - Next: Next: Bug reporting - Up: Up: Configuring and Building MLD2P4 - Previous: Previous: Optional third party libraries -   Contents +   Contents
    diff --git a/docs/html/userhtml.html b/docs/html/userhtml.html index b3fb8403..f026ce9d 100644 --- a/docs/html/userhtml.html +++ b/docs/html/userhtml.html @@ -1,10 +1,6 @@ - + - + userhtml @@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -22,7 +18,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + +
    next @@ -37,30 +34,30 @@ original version by: Nikos Drakos, CBLU, University of Leeds   Contents
    -
    +
    -MLD2P4 +MLD2P4

    -User's and Reference Guide     -
    A guide for the MultiLevel Domain Decomposition +User's and Reference Guide     +
    A guide for the MultiLevel Domain Decomposition Parallel Preconditioners Package -based on PSBLAS     +based on PSBLAS


    -
    Pasqua D'Ambra -
    IAC-CNR, Naples, Italy +
    Pasqua D'Ambra +
    IAC-CNR, Naples, Italy


    -
    Daniela di Serafino -
    University of Campania ``Luigi Vanvitelli'', Caserta, Italy +
    Daniela di Serafino +
    University of Campania “Luigi Vanvitelli”, Caserta, Italy


    -
    Salvatore Filippone -
    Cranfield University, Cranfield, United Kingdom +
    Salvatore Filippone +
    Cranfield University, Cranfield, United Kingdom


    @@ -78,18 +75,18 @@ July 31, 2017
    -     +

    - + - +

    - +

    -
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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 - [(20)]TJ +ET + +endstream +endobj +322 0 obj +<< +/Length 4858 +>> +stream 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 +BT +/F42 10.9091 Tf 93.6 740.002 Td [(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 - [(19)]TJ + [-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 - [(].)]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 +/F45 10.9091 Tf -395.542 -35.866 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 -13.549 Td [("-lsuperlu_dist")]TJ -137.453 -13.549 Td [(--with-superludistdir=DIR)]TJ 137.453 -13.55 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 -13.549 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLUDIST)-525(includes.)]TJ -137.453 -13.549 Td [(--with-superludistlibdir=DIR)]TJ 137.453 -13.55 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 -13.549 Td [(FC)-5250(Fortran)-525(compiler)-525(command)]TJ 0 -13.549 Td [(FCFLAGS)-2625(Fortran)-525(compiler)-525(flags)]TJ 0 -13.55 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 -13.549 Td [(CFLAGS)-3150(C)-525(compiler)-525(flags)]TJ 0 -13.55 Td [(CPPFLAGS)-2100(C/C++/Objective)-525(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 -13.549 Td [(CPP)-4725(C)-525(preprocessor)]TJ -11.455 -27.099 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 -27.098 Td [(Report)-525(bugs)-525(to)-525(.)]TJ/F15 10.9091 Tf 16.937 -18.066 Td [(F)83(or)-301(instance,)-308(if)-302(a)-302(user)-301(has)-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 - [(,)]TJ -1 0 0 rg 1 0 0 RG - [-319(25)]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 +/F45 10.9091 Tf 5.727 -18.066 Td [(./configure)-525(--with-psblas=/opt/psblas-3.5/)-525(\134)]TJ 0 -13.549 Td [(--with-umfpackincdir=/usr/include/suitesparse/)]TJ/F15 10.9091 Tf -5.727 -18.066 Td [(Once)-529(the)-529(c)-1(on)1(\014gure)-530(script)-529(has)-529(completed)-529(execution,)-579(i)1(t)-530(will)-529(ha)28(v)28(e)-530(generated)-529(the)-529(\014le)]TJ/F45 10.9091 Tf 0 -13.549 Td [(Make.inc)]TJ/F15 10.9091 Tf 49.145 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(dir)1(e)-1(ctory)-304(tree)-1(;)-314(this)-305(\014le)-305(will)-305(b)-27(e)]TJ -49.145 -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 -292.456 -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(h)1(as)-429(to)-428(add)-428(the)-429(approp)1(riate)-429(options)]TJ -16.937 -13.549 Td [(to)-342(the)-342(con\014)1(gure)-342(script;)-346(b)28(y)-342(default)-342(w)28(e)-342(are)-342(l)1(o)-28(oking)-342(for)-342(the)-341(libraries)]TJ/F45 10.9091 Tf 315.089 0 Td [(-ldmumps)-525(-lsmumps)]TJ -309.362 -13.55 Td [(-lzmumps)-525(-lcmumps)-525(-mumps_common)-525(-lpord)]TJ/F15 10.9091 Tf 217.634 0 Td [(.)-767(MUMPS)-441(often)-441(u)1(s)-1(es)-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(options)-234(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 0 g 0 G 0 g 0 G ET endstream endobj -347 0 obj +327 0 obj << -/Length 11453 +/Length 3815 >> 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 +/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 - [-378(Mul)67(tigrid)-378(Ba)22(ck)22(gr)23(ound)]TJ/F15 10.9091 Tf 401.542 0 Td [(13)]TJ +/F15 10.9091 Tf -186.329 -35.866 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 -22.515 Td [(make)]TJ/F15 10.9091 Tf 0 -22.516 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 -22.515 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 -20.595 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 -19.218 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 -13.55 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 -29.212 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 - -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 +/F45 10.9091 Tf -169.272 -22.516 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 -13.549 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 -22.516 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 -13.549 Td [(input)-286(\014les)-287(in)-286(the)]TJ/F45 10.9091 Tf 80.438 0 Td [(runs)]TJ/F15 10.9091 Tf 26.033 0 Td [(sub)-28(directories,)-296(to)-286(exp)-28(erimen)28(t)-286(with)-287(the)-286(full)-287(ran)1(ge)-287(of)-286(precon-)]TJ -106.471 -13.549 Td [(ditioners)-333(implemen)28(ted)-334(in)-333(the)-333(pac)27(k)56(age.)]TJ -27.273 -22.516 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 -13.549 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(23)]TJ +0 g 0 G + [(,)]TJ +1 0 0 rg 1 0 0 RG + [-313(21)]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(25)]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 + [(24)]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 + [(20)]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 + [(19)]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(25)]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 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10.9091 Tf 117.454 -25.505 Td [(call)-525(mld_precinit\050p,ptype,info\051)]TJ @@ -3403,9 +3407,9 @@ ET endstream endobj -454 0 obj +484 0 obj << -/Length 7098 +/Length 7103 >> stream 0 g 0 G @@ -3415,10 +3419,10 @@ BT 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(Subroutine)-375(set)]TJ +/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 77.363 -20.594 Td [(call)-525(p%set\050what,val,info)-525([,ilev,)-525(ilmax,)-525(pos]\051)]TJ/F15 10.9091 Tf -77.363 -24.369 Td [(This)-454(routine)-454(sets)-454(the)-453(parameters)-454(de\014ning)-454(the)-454(preconditioner)]TJ/F45 10.9091 Tf 301.822 0 Td [(p)]TJ/F15 10.9091 Tf 5.727 0 Td [(.)-806(More)-454(precisely)84(,)-484(the)]TJ -307.549 -13.549 Td [(parameter)-333(iden)27(ti)1(\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 -15.605 Td [(what)-2114(character\050len=*\051)]TJ/F15 10.9091 Tf 137.606 0 Td [(.)]TJ -91.635 -13.549 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 +/F45 10.9091 Tf 77.363 -20.594 Td [(call)-525(p%set\050what,val,info)-525([,ilev,)-525(ilmax,)-525(pos]\051)]TJ/F15 10.9091 Tf -77.363 -24.369 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 -13.549 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 -15.605 Td [(what)-2114(character\050len=*\051)]TJ/F15 10.9091 Tf 137.606 0 Td [(.)]TJ -91.635 -13.549 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 @@ -3426,7 +3430,7 @@ BT 0 0 1 rg 0 0 1 RG [(8)]TJ 0 g 0 G - [(.)]TJ/F45 10.9091 Tf -45.971 -13.55 Td [(val)-2639(integer)]TJ/F18 10.9091 Tf 105.137 0 Td [(or)]TJ/F45 10.9091 Tf 30.424 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 -13.549 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 + [(.)]TJ/F45 10.9091 Tf -45.971 -13.55 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 -13.549 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 @@ -3434,11 +3438,11 @@ BT 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 24.546 0 Td [(character\050len=*\051)]TJ/F15 10.9091 Tf 91.635 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 -13.55 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 + [(.)-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 -13.55 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/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 -13.549 Td [(parameter)-404(has)-404(to)-404(b)-27(e)-404(set.)-656(T)-1(h)1(e)-404(lev)27(els)-404(are)-403(n)27(um)28(b)-28(ered)-403(in)-404(increasing)-404(order)]TJ 0 -13.55 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 + [-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 -13.549 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 -13.55 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 @@ -3446,7 +3450,7 @@ BT 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 -13.549 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 -13.55 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 -13.549 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 -13.55 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 -51.948 -32.961 Td [(F)83(or)-380(compatibilit)28(y)-381(with)-380(the)-381(pr)1(e)-1(viou)1(s)-381(v)28(ersions)-381(of)-380(MLD2P4,)-392(this)-381(routine)-380(can)-381(b)-27(e)-381(also)]TJ -16.937 -13.549 Td [(in)28(v)28(ok)27(ed)-333(as)-333(follo)28(ws:)]TJ + [(\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 -13.549 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 -13.55 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 -13.549 Td 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If the selected preconditioner is one-level, it is built in a single step, performed by the routine \verb|bld|. \item \emph{Apply the preconditioner at each iteration of a Krylov solver.} - This is performed by the routine \verb|aply|. When using the PSBLAS Krylov solvers, - this step is completely transparent to the user, since \verb|aply| is called + This is performed by the method \verb|apply|. When using the PSBLAS Krylov solvers, + this step is completely transparent to the user, since \verb|apply| is called by the PSBLAS routine implementing the Krylov solver (\verb|psb_krylov|). \item \emph{Free the preconditioner data structure}. This is performed by the routine \verb|free|. This step is complementary to step 1 and should @@ -66,7 +66,7 @@ Examples showing the basic use of MLD2P4 are reported in Section~\ref{sec:exampl \begin{tabular}{|l|p{1.8cm}|p{8.2cm}|} \hline \textsc{type} & \textsc{string} & \textsc{default preconditioner} \\ \hline -No preconditioner &\verb|'NOPREC'|& Considered only to use the PSBLAS +No preconditioner &\verb|'NONE'|& Considered to use the PSBLAS Krylov solvers with no preconditioner. \\ \hline Diagonal & \verb|'DIAG'| or \verb|'JACOBI'| & Diagonal preconditioner. For any zero diagonal entry of the matrix to be preconditioned, diff --git a/docs/src/userinterface.tex b/docs/src/userinterface.tex index a2f366d3..0e3de52d 100644 --- a/docs/src/userinterface.tex +++ b/docs/src/userinterface.tex @@ -2,19 +2,20 @@ \markboth{\textsc{MLD2P4 User's and Reference Guide}} {\textsc{\ref{sec:userinterface} User Interface}} -The basic user interface of MLD2P4 consists of eight routines. The six -routines \verb|init|, \verb|set|, -\verb|hierarchy_build|, \verb|smoothers_build|, -\verb|bld|, and \verb|apply| encapsulate all the -functionalities for the setup and the application of any multilevel and one-level -preconditioner implemented in the package. -The routine \verb|free| deallocates the preconditioner data structure, while +The basic user interface of MLD2P4 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. +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 +stand-alone subroutines. -All the routines are available as methods of the preconditioner object. -For each routine, the same user interface is overloaded with +For each method, the same user interface is overloaded with respect to the real/ complex case and the single/double precision; -arguments with appropriate data types must be passed to the routine, +arguments with appropriate data types must be passed to the method, i.e., \begin{itemize} \item the sparse matrix data structure, containing the matrix to be @@ -35,18 +36,18 @@ i.e., according to the precision of the sparse matrix and preconditioner data structures (see Section~\ref{sec:precset}). \end{itemize} -A description of each routine is given in the remainder of this section. +A description of each method is given in the remainder of this section. \clearpage -\subsection{Subroutine init\label{sec:precinit}} +\subsection{Method init\label{sec:precinit}} \begin{center} \verb|call p%init(ptype,info)| \end{center} \noindent -This routine allocates and initializes the preconditioner +This method allocates and initializes the preconditioner \verb|p|, according to the preconditioner type chosen by the user. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip @@ -71,7 +72,7 @@ This routine allocates and initializes the preconditioner \end{tabular} \vskip1.5\baselineskip -For compatibility with the previous versions of MLD2P4, this routine can be also invoked +For compatibility with the previous versions of MLD2P4, this method can be also invoked as follows: \begin{center} @@ -81,14 +82,14 @@ as follows: \clearpage -\subsection{Subroutine set\label{sec:precset}} +\subsection{Method set\label{sec:precset}} \begin{center} \verb|call p%set(what,val,info [,ilev, ilmax, pos])| \end{center} \noindent -This routine sets the parameters defining the preconditioner \verb|p|. More +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|. @@ -139,7 +140,7 @@ contained in \verb|val|. \end{tabular} \vskip1.5\baselineskip -For compatibility with the previous versions of MLD2P4, this routine can be also invoked +For compatibility with the previous versions of MLD2P4, this method can be also invoked as follows: \begin{center} @@ -623,60 +624,55 @@ level (continued).\label{tab:p_coarse_1}} (continued).\label{tab:p_smoother_1}} \esideways + \clearpage -\subsection{Subroutine build\label{sec:precbld}} +\subsection{Method hierarchy\_build\label{sec:hier_bld}} \begin{center} -\verb|call p%build(a,desc_a,info)|\\ +\verb|call p%hierarchy_build(a,desc_a,info)|\\ \end{center} \noindent -This routine builds the one-level preconditioner \verb|p| according to the requirements -made by the user through the routines \verb|init| and \verb|set| -(see Sections~\ref{sec:hier_bld} and~\ref{sec:smooth_bld} for multilevel preconditioners). +This method builds the hierarchy of matrices and restriction/prolongation +operators for the multilevel preconditioner \verb|p|, according to the requirements +made by the user through the methods \verb|init| and \verb|set|. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip \begin{tabular}{p{1.2cm}p{12cm}} -\verb|a| & \verb|type(psb_|\emph{x}\verb|spmat_type), intent(in)|. \\ +\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, single/double precision version of MLD2P4 under use. + 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)|.\\ +%\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} -\vskip1.5\baselineskip -For compatibility with the previous versions of MLD2P4, this routine can be also invoked -as follows: - -\begin{center} -\verb|call mld_precbld(p,what,val,info)| -\end{center} - -\noindent -In this case, the routine can be used to build multilevel preconditioners too. \clearpage -\subsection{Subroutine hierarchy\_build\label{sec:hier_bld}} - +\subsection{Method smoothers\_build\label{sec:smooth_bld}} + + \begin{center} -\verb|call p%hierarchy_build(a,desc_a,info)|\\ +\verb|call p%smoothers_build(a,desc_a,p,info[,amold,vmold,imold])|\\ \end{center} \noindent -This routine builds the hierarchy of matrices and restriction/prolongation -operators for the multilevel preconditioner \verb|p|, according to the requirements -made by the user through the routines \verb|init| and \verb|set|. +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}). {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip @@ -684,40 +680,51 @@ made by the user through the routines \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, -single/double precision version of MLD2P4 under use. + 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|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|. \\ + & The desired dynamic type for internal matrix + components; this allows e.g. running on GPUs; it needs not be the + same on all processes. See the PSBLAS User's Guide for + details \cite{PSBLASGUIDE}. \\ + \verb|vmold| & \verb|class(psb_|\emph{x}\verb|_base_vect_type), intent(in), optional|. \\ + & The desired dynamic type for internal vector + components; this allows e.g. running on GPUs. \\ + \verb|imold| & \verb|class(psb_i_base_vect_type), intent(in), optional|. \\ + & The desired dynamic type for internal integer vector + components; this allows e.g. running on GPUs. \\ \end{tabular} - \clearpage -\subsection{Subroutine smoothers\_build\label{sec:smooth_bld}} - - +\subsection{Method build\label{sec:precbld}} + \begin{center} -\verb|call p%smoothers_build(a,desc_a,p,info)|\\ +\verb|call p%build(a,desc_a,info[,amold,vmold,imold])|\\ \end{center} \noindent -This routine builds the smoothers and the coarsest-level solvers for the -multilevel preconditioner \verb|p|, according to the requirements made by -the user through the routines \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}). +This method builds the preconditioner \verb|p| according to the requirements +made by the user through the methods \verb|init| and \verb|set| +(see Sections~\ref{sec:hier_bld} and~\ref{sec:smooth_bld} for +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. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip \begin{tabular}{p{1.2cm}p{12cm}} -\verb|a| & \verb|type(psb_|\emph{x}\verb|spmat_type), intent(in)|. \\ +\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, single/double precision version of MLD2P4 under use. @@ -726,26 +733,49 @@ hierarchy produced by a previous call to \verb|hierarchy_build| & 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.\\ +% & 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|. \\ + & The desired dynamic type for internal matrix + components; this allows e.g. running on GPUs; it needs not be the + same on all processes. See the PSBLAS User's Guide for + details \cite{PSBLASGUIDE}. \\ + \verb|vmold| & \verb|class(psb_|\emph{x}\verb|_base_vect_type), intent(in), optional|. \\ + & The desired dynamic type for internal vector + components; this allows e.g. running on GPUs. \\ + \verb|imold| & \verb|class(psb_i_base_vect_type), intent(in), optional|. \\ + & The desired dynamic type for internal integer vector + components; this allows e.g. running on GPUs. \\ \end{tabular} +\vskip1.5\baselineskip +For compatibility with the previous versions of MLD2P4, this method can be also invoked +as follows: + +\begin{center} +\verb|call mld_precbld(p,what,val,info[,amold,vmold,imold])| +\end{center} + +\noindent +The method can be used to build multilevel preconditioners too. + + \clearpage -\subsection{Subroutine apply\label{sec:precapply}} +\subsection{Method apply\label{sec:precapply}} \begin{center} \verb|call p%apply(x,y,desc_a,info [,trans,work])|\\ \end{center} \noindent -This routine computes $y = op(B^{-1})\, x$, where $B$ is a previously built +This method computes $y = op(B^{-1})\, x$, where $B$ is a previously built preconditioner, stored into \verb|p|, and $op$ denotes the preconditioner itself or its transpose, according to the value of \verb|trans|. Note that, when MLD2P4 is used with a Krylov solver from PSBLAS, -\verb|p%apply| is called within the PSBLAS routine \verb|psb_krylov| +\verb|p%apply| is called within the PSBLAS method \verb|psb_krylov| and hence it is completely transparent to the user. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip @@ -781,7 +811,7 @@ and hence it is completely transparent to the user. \end{tabular} \vskip1.5\baselineskip -For compatibility with the previous versions of MLD2P4, this routine can be also invoked +For compatibility with the previous versions of MLD2P4, this method can be also invoked as follows: \begin{center} @@ -790,14 +820,14 @@ as follows: \clearpage -\subsection{Subroutine free\label{sec:precfree}} +\subsection{Method free\label{sec:precfree}} \begin{center} \verb|call p%free(p,info)|\\ \end{center} \noindent -This routine deallocates the preconditioner data structure \verb|p|. +This method deallocates the preconditioner data structure \verb|p|. {\vskip1.5\baselineskip\noindent\large\bfseries Arguments} \smallskip @@ -810,7 +840,7 @@ This routine deallocates the preconditioner data structure \verb|p|. \end{tabular} \vskip1.5\baselineskip -For compatibility with the previous versions of MLD2P4, this routine can be also invoked +For compatibility with the previous versions of MLD2P4, this method can be also invoked as follows: \begin{center} @@ -820,14 +850,14 @@ as follows: \clearpage -\subsection{Subroutine descr\label{sec:precdescr}} +\subsection{Method descr\label{sec:precdescr}} \begin{center} \verb|call p%descr(info, [iout])|\\ \end{center} \noindent -This routine prints a description of the preconditioner \verb|p| to the standard output or +This method prints a description of the preconditioner \verb|p| to the standard output or to a file. It must be called after \verb|hierachy_build| and \verb|smoothers_build|, or \verb|build|, have been called. @@ -845,7 +875,7 @@ or \verb|build|, have been called. \end{tabular} \vskip1.5\baselineskip -For compatibility with the previous versions of MLD2P4, this routine can be also invoked +For compatibility with the previous versions of MLD2P4, this method can be also invoked as follows: \begin{center} @@ -853,6 +883,136 @@ as follows: \end{center} +\subsection{Auxiliary Methods\label{sec:auxil}} +Various functionalities are implemented as additional methods of the +preconditioner object. + +\subsubsection{Method: dump} + +\begin{center} +\verb|call p%dump(info[,istart,iend,prefix,head,ac,rp,smoother,solver,global_num])|\\ +\end{center} + +\noindent +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|. \\ + & The desired dynamic type for internal matrix + components; this allows e.g. running on GPUs; it needs not be the + same on all processes. See the PSBLAS User's Guide for + details \cite{PSBLASGUIDE}. \\ +\end{tabular} + + +\subsubsection{Method: clone} + +\begin{center} +\verb|call p%clone(pout,info)|\\ +\end{center} + +\noindent +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)|.\\ + & The copy of 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} + + + +\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} + +\subsubsection{Method: allocate\_wrk} + +\begin{center} +\verb|call p%allocate_wrk(info[, vmold])|\\ +\end{center} + +\noindent +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 +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 +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. + +{\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|. \\ + & The desired dynamic type for internal vector + components; this allows e.g. running on GPUs. \\ +\end{tabular} + + + +\subsubsection{Method: free\_wrk} + +\begin{center} +\verb|call p%free_wrk(info)|\\ +\end{center} + +\noindent +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} + + + + + %%% Local Variables: %%% mode: latex %%% TeX-master: "userguide"