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Salvatore Filippone
2017-07-25 14:13:43 +01:00
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@@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds
<BODY >
<!--Navigation Panel-->
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@@ -59,9 +59,9 @@ General Overview
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The M<SMALL>ULTI-</SMALL>L<SMALL>EVEL </SMALL>D<SMALL>OMAIN </SMALL>D<SMALL>ECOMPOSITION </SMALL>P<SMALL>ARALLEL </SMALL>P<SMALL>RECONDITIONERS </SMALL>P<SMALL>ACKAGE BASED ON
</SMALL>PSBLAS (MLD2P4) provides parallel Algebraic MultiGrid (AMG) and Domain
Decomposition preconditioners (see, e.g., [<A
HREF="node27.html#Briggs2000">3</A>,<A
HREF="node27.html#Stuben_01">23</A>,<A
HREF="node27.html#dd2_96">21</A>]),
HREF="node29.html#Briggs2000">3</A>,<A
HREF="node29.html#Stuben_01">23</A>,<A
HREF="node29.html#dd2_96">21</A>]),
to be used in the iterative solution of linear systems,
</FONT></FONT></FONT>
<BR>
@@ -95,8 +95,8 @@ multi-level cycles and smoothers widely used in multigrid methods.
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The multi-level preconditioners implemented in MLD2P4 are obtained by combining
AMG cycles with smoothers and coarsest-level solvers. The V-, W-, and
K-cycles&nbsp;[<A
HREF="node27.html#Briggs2000">3</A>,<A
HREF="node27.html#Notay2008">19</A>] are available, which allow to define
HREF="node29.html#Briggs2000">3</A>,<A
HREF="node29.html#Notay2008">19</A>] are available, which allow to define
almost all the preconditioners in the package, including the multi-level hybrid
Schwarz ones; a specific cycle is implemented to obtain multi-level additive
Schwarz preconditioners. The Jacobi, hybridforward/backward Gauss-Seidel, block-Jacobi, and additive Schwarz methods
@@ -104,8 +104,8 @@ are available as smoothers. An algebraic approach is used to generate a hierarch
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&nbsp;[<A
HREF="node27.html#BREZINA_VANEK">2</A>,<A
HREF="node27.html#VANEK_MANDEL_BREZINA">25</A>]
HREF="node29.html#BREZINA_VANEK">2</A>,<A
HREF="node29.html#VANEK_MANDEL_BREZINA">25</A>]
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,
@@ -126,8 +126,8 @@ interface.
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">MLD2P4 has been designed to implement scalable and easy-to-use
multilevel preconditioners in the context of the PSBLAS (Parallel Sparse BLAS)
computational framework&nbsp;[<A
HREF="node27.html#psblas_00">15</A>,<A
HREF="node27.html#PSBLAS3">14</A>]. PSBLAS provides basic linear algebra
HREF="node29.html#psblas_00">15</A>,<A
HREF="node29.html#PSBLAS3">14</A>]. 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
@@ -150,14 +150,14 @@ 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&nbsp;<A HREF="node24.html#sec:adding">7</A>).
Section&nbsp;<A HREF="node26.html#sec:adding">7</A>).
</FONT></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">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 multi-level hierarchy from
the construction of the smoothers and solvers, and to allow for more flexibility
at each level. The software architecture described in&nbsp;[<A
HREF="node27.html#MLD2P4_TOMS">8</A>] has significantly
HREF="node29.html#MLD2P4_TOMS">8</A>] has significantly
evolved too, in order to fully exploit the Fortran&nbsp;2003 features implemented in PSBLAS 3.
However, compatibility with previous versions has been preserved.
</FONT></FONT></FONT>
@@ -168,37 +168,37 @@ and installation of the package are given in Section&nbsp;<A HREF="node5.html#se
of the preconditioners implemented in MLD2P4 is provided in Section&nbsp;<A HREF="node11.html#sec:background">4</A>,
to help the users in choosing among them. The basics for building and applying the
preconditioners with the Krylov solvers implemented in PSBLAS are reported
in&nbsp;Section&nbsp;<A HREF="node13.html#sec:started">5</A>, where the Fortran codes of a few sample programs
in&nbsp;Section&nbsp;<A HREF="node15.html#sec:started">5</A>, where the Fortran codes of a few sample programs
are also shown. A reference guide for the user interface routines is provided
in Section&nbsp;<A HREF="node15.html#sec:userinterface">6</A>. Information on the extension of the package
through the addition of new smoothers and solvers is reported in Section&nbsp;<A HREF="node24.html#sec:adding">7</A>.
in Section&nbsp;<A HREF="node17.html#sec:userinterface">6</A>. Information on the extension of the package
through the addition of new smoothers and solvers is reported in Section&nbsp;<A HREF="node26.html#sec:adding">7</A>.
The error handling mechanism used by the package
is briefly described in Section&nbsp;<A HREF="node25.html#sec:errors">8</A>. The copyright terms concerning the
distribution and modification of MLD2P4 are reported in Appendix&nbsp;<A HREF="node26.html#sec:license">A</A>.
is briefly described in Section&nbsp;<A HREF="node27.html#sec:errors">8</A>. The copyright terms concerning the
distribution and modification of MLD2P4 are reported in Appendix&nbsp;<A HREF="node28.html#sec:license">A</A>.
</FONT></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT></FONT><HR>
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