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<BR></DIV>
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<!--End of Navigation Panel-->
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<BIG CLASS="XXLARGE"><B>MLD2P4
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<FONT SIZE="+2"><B>MLD2P4
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<BR>
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<BR>
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User's and Reference Guide</B></BIG>
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<BR><SPAN CLASS="textit"><BIG CLASS="LARGE">A guide for the Multi-Level Domain Decomposition
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User's and Reference Guide</B></FONT>
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<BR><I><FONT SIZE="+1">A guide for the Multi-Level Domain Decomposition
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Parallel Preconditioners Package
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based on PSBLAS</BIG></SPAN>
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based on PSBLAS</FONT></I>
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@@ -62,9 +61,9 @@ University of Rome ``Tor Vergata'', Italy
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<BR>
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<BR>
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<BR>
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Software version: 2.0
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Software version: 2.1
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<BR>
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Oct. 12, 2015
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Mar. 31, 2016
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HREF="node4.html">Code Distribution</A>
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HREF="node5.html">Configuring and Building MLD2P4</A>
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HREF="node12.html">Multi-level Schwarz Preconditioners</A>
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HREF="node12.html">Multi-level Schwarz Preconditioners</A>
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<LI><A NAME="tex2html31"
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HREF="node17.html">Subroutine mld_precinit</A>
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HREF="node18.html">Subroutine mld_precset</A>
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HREF="node17.html">Subroutine mld_precinit</A>
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HREF="node19.html">Subroutine mld_precbld</A>
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HREF="node20.html">Subroutine mld_precaply</A>
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HREF="node19.html">Subroutine mld_precbld</A>
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HREF="node21.html">Subroutine mld_precfree</A>
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HREF="node21.html">Subroutine mld_precfree</A>
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</H1>
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<P>
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<SPAN CLASS="textit">Domain Decomposition</SPAN> (DD) preconditioners, coupled with Krylov iterative
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<I>Domain Decomposition</I> (DD) preconditioners, coupled with Krylov iterative
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solvers, are widely used in the parallel solution of large and sparse linear systems.
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These preconditioners are based on the divide and conquer technique: the matrix
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to be preconditioned is divided into submatrices, a ``local'' linear system
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HREF="node25.html#dd2_96">22</A>].
|
||||
HREF="node25.html#dd2_96">23</A>].
|
||||
|
||||
<P>
|
||||
<SPAN CLASS="textit">Additive Schwarz</SPAN> preconditioners are DD preconditioners using overlapping
|
||||
<I>Additive Schwarz</I> preconditioners are DD preconditioners using overlapping
|
||||
submatrices, i.e. with some common rows, to couple the local information
|
||||
related to the submatrices (see, e.g., [<A
|
||||
HREF="node25.html#dd2_96">22</A>]).
|
||||
HREF="node25.html#dd2_96">23</A>]).
|
||||
The main motivation for choosing Additive Schwarz preconditioners is their
|
||||
intrinsic parallelism. A drawback of these
|
||||
preconditioners is that the number of iterations of the preconditioned solvers
|
||||
@@ -90,15 +89,15 @@ in a coarse space, which globally couples the information related to the single
|
||||
submatrices.
|
||||
|
||||
<P>
|
||||
<SPAN CLASS="textit">Two-level Schwarz</SPAN> preconditioners are obtained
|
||||
<I>Two-level Schwarz</I> preconditioners are obtained
|
||||
by combining basic (one-level) Schwarz preconditioners with a coarse-level
|
||||
correction. In this context, the one-level preconditioner is often
|
||||
called `smoother'. Different two-level preconditioners are obtained by varying the
|
||||
choice of the smoother and of the coarse-level correction, and the
|
||||
way they are combined [<A
|
||||
HREF="node25.html#dd2_96">22</A>]. The same reasoning can be applied starting
|
||||
HREF="node25.html#dd2_96">23</A>]. The same reasoning can be applied starting
|
||||
from the coarse-level system, i.e. a coarse-space correction can be built
|
||||
from this system, thus obtaining <SPAN CLASS="textit">multi-level</SPAN> preconditioners.
|
||||
from this system, thus obtaining <I>multi-level</I> preconditioners.
|
||||
|
||||
<P>
|
||||
It is worth noting that optimal preconditioners do not necessarily correspond
|
||||
@@ -120,17 +119,17 @@ are considered. The algebraic approach builds coarse-space corrections using onl
|
||||
information. It performs a fully automatic coarsening and enforces the interplay between
|
||||
the fine and coarse levels by suitably choosing the coarse space and the coarse-to-fine
|
||||
interpolation [<A
|
||||
HREF="node25.html#StubenGMD69_99">24</A>].
|
||||
HREF="node25.html#StubenGMD69_99">25</A>].
|
||||
|
||||
<P>
|
||||
MLD2P4 uses a pure algebraic approach for building the sequence of coarse matrices
|
||||
starting from the original matrix. The algebraic approach is based on the <SPAN CLASS="textit">smoothed
|
||||
aggregation</SPAN> algorithm [<A
|
||||
starting from the original matrix. The algebraic approach is based on the <I>smoothed
|
||||
aggregation</I> algorithm [<A
|
||||
HREF="node25.html#BREZINA_VANEK">1</A>,<A
|
||||
HREF="node25.html#VANEK_MANDEL_BREZINA">26</A>]. A decoupled version
|
||||
HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>]. A decoupled version
|
||||
of this algorithm is implemented, where the smoothed aggregation is applied locally
|
||||
to each submatrix [<A
|
||||
HREF="node25.html#TUMINARO_TONG">25</A>]. In the next two subsections we provide
|
||||
HREF="node25.html#TUMINARO_TONG">26</A>]. In the next two subsections we provide
|
||||
a brief description of the multi-level Schwarz preconditioners and of the smoothed
|
||||
aggregation technique as implemented in MLD2P4. For further details the reader
|
||||
is referred to [<A
|
||||
@@ -138,44 +137,43 @@ is referred to [<A
|
||||
HREF="node25.html#aaecc_07">3</A>,<A
|
||||
HREF="node25.html#apnum_07">4</A>,<A
|
||||
HREF="node25.html#MLD2P4_TOMS">8</A>,<A
|
||||
HREF="node25.html#dd2_96">22</A>].
|
||||
HREF="node25.html#dd2_96">23</A>].
|
||||
|
||||
<P>
|
||||
<BR><HR>
|
||||
<!--Table of Child-Links-->
|
||||
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||||
|
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<UL CLASS="ChildLinks">
|
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<LI><A NAME="tex2html197"
|
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HREF="node12.html">Multi-level Schwarz Preconditioners</A>
|
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<UL>
|
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<LI><A NAME="tex2html198"
|
||||
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
|
||||
<LI><A NAME="tex2html199"
|
||||
HREF="node13.html">Smoothed Aggregation</A>
|
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HREF="node2.html">Contents</A></B>
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<BR>
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<BR>
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@@ -295,7 +295,7 @@ ILU(<IMG
|
||||
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img36.png"
|
||||
ALT="$p,t$">) [<A
|
||||
HREF="node25.html#Saad_book">21</A>, Chapter 10].
|
||||
HREF="node25.html#Saad_book">22</A>, Chapter 10].
|
||||
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||||
<P>
|
||||
A variant of the classical AS preconditioner that outperforms it
|
||||
@@ -303,7 +303,7 @@ in terms of convergence rate and of computation and communication
|
||||
time on parallel distributed-memory computers is the so-called <I>Restricted AS
|
||||
(RAS)</I> preconditioner [<A
|
||||
HREF="node25.html#CAI_SARKIS">5</A>,<A
|
||||
HREF="node25.html#EFSTATHIOU">14</A>]. It
|
||||
HREF="node25.html#EFSTATHIOU">15</A>]. It
|
||||
is obtained by zeroing the components of <IMG
|
||||
WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img33.png"
|
||||
@@ -387,7 +387,7 @@ of <IMG
|
||||
SRC="img11.png"
|
||||
ALT="$W$"> increases [<A
|
||||
HREF="node25.html#dd1_94">7</A>,<A
|
||||
HREF="node25.html#dd2_96">22</A>]. To reduce the dependency
|
||||
HREF="node25.html#dd2_96">23</A>]. To reduce the dependency
|
||||
of the number of iterations on the degree of parallelism we may
|
||||
introduce a global coupling among the overlapping partitions by defining
|
||||
a coarse-space approximation <IMG
|
||||
@@ -642,12 +642,12 @@ in which the coarse-level correction is re-applied starting from the current
|
||||
coarse-level system. The corresponding preconditioners, called <I>multi-level</I>
|
||||
preconditioners, can significantly reduce the computational cost of preconditioning
|
||||
with respect to the two-level case (see [<A
|
||||
HREF="node25.html#dd2_96">22</A>, Chapter 3]).
|
||||
HREF="node25.html#dd2_96">23</A>, Chapter 3]).
|
||||
Additive and hybrid multilevel preconditioners
|
||||
are obtained as direct extensions of the two-level counterparts.
|
||||
For a detailed descrition of them, the reader is
|
||||
referred to [<A
|
||||
HREF="node25.html#dd2_96">22</A>, Chapter 3].
|
||||
HREF="node25.html#dd2_96">23</A>, Chapter 3].
|
||||
The algorithm for the application of a multi-level hybrid
|
||||
post-smoothed preconditioner <IMG
|
||||
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
@@ -685,7 +685,7 @@ denoted by <IMG
|
||||
SRC="img67.png"
|
||||
ALT="$R_l$">.
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:mlhpost_alg"></A><A NAME="509"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:mlhpost_alg"></A><A NAME="514"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1:</STRONG>
|
||||
Application of the multi-level hybrid post-smoothed preconditioner.</CAPTION>
|
||||
@@ -726,7 +726,7 @@ $w = y_1$;
|
||||
\begin{tabbing}
|
||||
\quad \=\quad...
|
||||
...= y_l+r_l$\\
|
||||
\textbf{endfor} [1mm]
|
||||
\textbf{endfor} \\ [1mm]
|
||||
$w = y_1$;
|
||||
\end{tabbing}}
|
||||
\end{minipage}}">
|
||||
@@ -738,26 +738,26 @@ $w = y_1$;
|
||||
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@@ -66,7 +66,7 @@ the coarse-level matrix <IMG
|
||||
ALT="$A_C$">, MLD2P4 uses the <I>smoothed aggregation</I>
|
||||
algorithm described in [<A
|
||||
HREF="node25.html#BREZINA_VANEK">1</A>,<A
|
||||
HREF="node25.html#VANEK_MANDEL_BREZINA">26</A>].
|
||||
HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>].
|
||||
The basic idea of this algorithm is to build a coarse set of vertices
|
||||
<IMG
|
||||
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
@@ -115,7 +115,7 @@ Three main steps can be identified in the smoothed aggregation procedure:
|
||||
To perform the coarsening step, we have implemented the aggregation algorithm sketched
|
||||
in [<A
|
||||
HREF="node25.html#apnum_07">4</A>]. According to [<A
|
||||
HREF="node25.html#VANEK_MANDEL_BREZINA">26</A>], a modification of
|
||||
HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>], a modification of
|
||||
this algorithm has been actually considered,
|
||||
in which each aggregate <IMG
|
||||
WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
@@ -173,7 +173,7 @@ since it has been shown to produce good results in practice
|
||||
[<A
|
||||
HREF="node25.html#aaecc_07">3</A>,<A
|
||||
HREF="node25.html#apnum_07">4</A>,<A
|
||||
HREF="node25.html#TUMINARO_TONG">25</A>].
|
||||
HREF="node25.html#TUMINARO_TONG">26</A>].
|
||||
|
||||
<P>
|
||||
The prolongator <IMG
|
||||
@@ -252,7 +252,7 @@ in order to remove oscillatory components from the range of the prolongator
|
||||
and hence to improve the convergence properties of the multi-level
|
||||
Schwarz method [<A
|
||||
HREF="node25.html#BREZINA_VANEK">1</A>,<A
|
||||
HREF="node25.html#StubenGMD69_99">24</A>].
|
||||
HREF="node25.html#StubenGMD69_99">25</A>].
|
||||
A simple choice for <IMG
|
||||
WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img84.png"
|
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@@ -288,26 +288,26 @@ using some estimate of the spectral radius of <IMG
|
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@@ -59,7 +59,7 @@ Getting Started
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<P>
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We describe the basics for building and applying MLD2P4 one-level and multi-level
|
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Schwarz preconditioners with the Krylov solvers included in PSBLAS [<A
|
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HREF="node25.html#PSBLASGUIDE">15</A>].
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HREF="node25.html#PSBLASGUIDE">16</A>].
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The following steps are required:
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<OL>
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@@ -131,7 +131,7 @@ for the coarsest-level solvers available in MLD2P4).
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="924"></A>
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<DIV ALIGN="CENTER"><A NAME="943"></A>
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<TABLE>
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<CAPTION><STRONG>Table 1:</STRONG>
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Preconditioner types, corresponding strings and default choices.
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@@ -197,32 +197,32 @@ Preconditioner types, corresponding strings and default choices.
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<H2><A NAME="SECTION00071000000000000000"></A><A NAME="sec:examples"></A>
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@@ -76,7 +75,7 @@ in the directory <code>examples/fileread</code> of the MLD2P4 tree (see
|
||||
Section <A HREF="node10.html#sec:ex_and_test">3.5</A>).
|
||||
For details on the use of the PSBLAS routines, see the PSBLAS User's
|
||||
Guide [<A
|
||||
HREF="node25.html#PSBLASGUIDE">15</A>].
|
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HREF="node25.html#PSBLASGUIDE">16</A>].
|
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||||
<P>
|
||||
The setup and application of the default multi-level
|
||||
@@ -87,7 +86,7 @@ the corresponding Fortran 95 codes are available in <code>examples/fileread/</co
|
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|
||||
<P>
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_default"></A><A NAME="930"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_default"></A><A NAME="946"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2:</STRONG>
|
||||
Setup and application of the default multi-level Schwarz preconditioner.
|
||||
@@ -164,6 +163,10 @@ preconditioner, which uses block Jacobi with ILU(0) on the
|
||||
local blocks as post-smoother, has a coarsest matrix replicated on the processors,
|
||||
and solves the coarsest-level system with the LU factorization from UMFPACK [<A
|
||||
HREF="node25.html#UMFPACK">9</A>].
|
||||
Figure <A HREF="#fig:ex_3lhm">4</A> shows how to set a three-level preconditioner similar to the one of <A HREF="#fig:ex_3lh">3</A>, but the coarsest-level systems is solved with the multifrontal factorization from MUMPS [<A
|
||||
HREF="node25.html#UMFPACK">9</A>].
|
||||
Note that MUMPS can be used on both replicated and distributed coarsest level matrices,
|
||||
as a global and local solver respectively.
|
||||
The number of levels is specified by using <code>mld_precinit</code>; the other
|
||||
preconditioner parameters are set by calling <code>mld_precset</code>. Note that
|
||||
the type of multilevel framework (i.e. multiplicative among the levels
|
||||
@@ -171,7 +174,7 @@ with post-smoothing only) is not specified since it is the default
|
||||
set by <code>mld_precinit</code>.
|
||||
|
||||
<P>
|
||||
Figure <A HREF="#fig:ex_3la">4</A> shows how to
|
||||
Figure <A HREF="#fig:ex_3la">5</A> shows how to
|
||||
set a three-level additive Schwarz preconditioner,
|
||||
which uses RAS, with overlap 1 and ILU(0) on the blocks,
|
||||
as pre- and post-smoother, and applies five block-Jacobi sweeps, with
|
||||
@@ -180,11 +183,11 @@ solver. Again, <code>mld_precset</code> is used only to set
|
||||
non-default values of the parameters (see Tables <A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">5</A>).
|
||||
In both cases, the construction and the application of the preconditioner
|
||||
are carried out as for the default multi-level preconditioner.
|
||||
The code fragments shown in in Figures <A HREF="#fig:ex_3lh">3</A>-<A HREF="#fig:ex_3la">4</A> are
|
||||
The code fragments shown in in Figures <A HREF="#fig:ex_3lh">3</A> <A HREF="#fig:ex_3lhm">4</A>-<A HREF="#fig:ex_3la">5</A> are
|
||||
included in the example program file <code>mld_dexample_ml.f90</code> too.
|
||||
|
||||
<P>
|
||||
Finally, Figure <A HREF="#fig:ex_1l">5</A> shows the setup of a one-level
|
||||
Finally, Figure <A HREF="#fig:ex_1l">6</A> shows the setup of a one-level
|
||||
additive Schwarz preconditioner, i.e. RAS with overlap 2. The corresponding
|
||||
example program is available in <code>mld_dexample_</code> <code>1lev.f90</code>.
|
||||
|
||||
@@ -195,7 +198,7 @@ boundary conditions are also available in the directory <code>examples/pdegen</c
|
||||
|
||||
<P>
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_3lh"></A><A NAME="932"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_3lh"></A><A NAME="948"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 3:</STRONG>
|
||||
Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
|
||||
@@ -228,9 +231,43 @@ Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
|
||||
|
||||
<P>
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_3la"></A><A NAME="934"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_3lhm"></A><A NAME="950"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
|
||||
Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
|
||||
<TR><TD>
|
||||
<DIV ALIGN="CENTER">
|
||||
</DIV><TABLE WIDTH="90%">
|
||||
<TR><TD>
|
||||
<PRE>
|
||||
... ...
|
||||
! set a three-level hybrid Schwarz preconditioner, which uses
|
||||
! block Jacobi (with ILU(0) on the blocks) as post-smoother,
|
||||
! a coarsest matrix replicated on the processors, and the
|
||||
! multifrontal solver in MUMPS as coarse-level solver
|
||||
|
||||
call mld_precinit(P,'ML',info,nlev=3)
|
||||
call mld_precset(P,mld_smoother_type_,'BJAC',info)
|
||||
call mld_precset(P,mld_coarse_mat_,'REPL',info)
|
||||
call mld_precset(P,mld_coarse_solve_,'MUMPS',info)
|
||||
|
||||
... ...
|
||||
</PRE>
|
||||
</TD></TR>
|
||||
</TABLE>
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<DIV ALIGN="CENTER">
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</DIV>
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<DIV ALIGN="CENTER">
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||||
</DIV></TD></TR>
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</TABLE>
|
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</DIV>
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||||
<P>
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_3la"></A><A NAME="952"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
|
||||
Setup of an additive three-level Schwarz preconditioner.</CAPTION>
|
||||
<TR><TD>
|
||||
<DIV ALIGN="CENTER">
|
||||
@@ -260,9 +297,9 @@ Setup of an additive three-level Schwarz preconditioner.</CAPTION>
|
||||
|
||||
<P>
|
||||
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_1l"></A><A NAME="936"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:ex_1l"></A><A NAME="954"></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 6:</STRONG>
|
||||
Setup of a one-level Schwarz preconditioner.</CAPTION>
|
||||
<TR><TD>
|
||||
<DIV ALIGN="CENTER">
|
||||
@@ -284,30 +321,29 @@ Setup of a one-level Schwarz preconditioner.</CAPTION>
|
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</DIV>
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<H1><A NAME="SECTION00080000000000000000"></A><A NAME="sec:userinterface"></A>
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@@ -73,28 +72,28 @@ i.e.
|
||||
|
||||
<UL>
|
||||
<LI>the sparse matrix data structure, containing the matrix to be
|
||||
preconditioned, must be of type <code>psb_</code><SPAN CLASS="textit">x</SPAN><code>spmat_type</code>
|
||||
with <SPAN CLASS="textit">x</SPAN> = <code>s</code> for real single precision, <SPAN CLASS="textit">x</SPAN> = <code>d</code>
|
||||
for real double precision, <SPAN CLASS="textit">x</SPAN> = <code>c</code> for complex single precision,
|
||||
<SPAN CLASS="textit">x</SPAN> = <code>z</code> for complex double precision;
|
||||
preconditioned, must be of type <code>psb_</code><I>x</I><code>spmat_type</code>
|
||||
with <I>x</I> = <code>s</code> for real single precision, <I>x</I> = <code>d</code>
|
||||
for real double precision, <I>x</I> = <code>c</code> for complex single precision,
|
||||
<I>x</I> = <code>z</code> for complex double precision;
|
||||
</LI>
|
||||
<LI>the preconditioner data structure must be of type
|
||||
<code>mld_</code><SPAN CLASS="textit">x</SPAN><code>prec_type</code>, with <SPAN CLASS="textit">x</SPAN> =
|
||||
<code>mld_</code><I>x</I><code>prec_type</code>, with <I>x</I> =
|
||||
<code>s</code>, <code>d</code>, <code>c</code>, <code>z</code>, according to the sparse
|
||||
matrix data structure;
|
||||
</LI>
|
||||
<LI>the arrays containing the vectors <SPAN CLASS="MATH"><IMG
|
||||
<LI>the arrays containing the vectors <IMG
|
||||
WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img22.png"
|
||||
ALT="$v$"></SPAN> and <SPAN CLASS="MATH"><IMG
|
||||
ALT="$v$"> and <IMG
|
||||
WIDTH="17" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img89.png"
|
||||
ALT="$w$"></SPAN> involved in
|
||||
the preconditioner application <SPAN CLASS="MATH"><IMG
|
||||
ALT="$w$"> involved in
|
||||
the preconditioner application <IMG
|
||||
WIDTH="86" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img61.png"
|
||||
ALT="$w=M^{-1}v$"></SPAN> must be of type
|
||||
<code>psb_</code><SPAN CLASS="textit">x</SPAN><code>vect_type</code> with <SPAN CLASS="textit">x</SPAN> =
|
||||
ALT="$w=M^{-1}v$"> must be of type
|
||||
<code>psb_</code><I>x</I><code>vect_type</code> with <I>x</I> =
|
||||
<code>s</code>, <code>d</code>, <code>c</code>, <code>z</code>, in a manner completely
|
||||
analogous to the sparse matrix type;
|
||||
</LI>
|
||||
@@ -112,45 +111,44 @@ A description of each routine is given in the remainder of this section.
|
||||
<!--Table of Child-Links-->
|
||||
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||||
|
||||
<UL CLASS="ChildLinks">
|
||||
<LI><A NAME="tex2html256"
|
||||
HREF="node17.html">Subroutine mld_precinit</A>
|
||||
<UL>
|
||||
<LI><A NAME="tex2html257"
|
||||
HREF="node18.html">Subroutine mld_precset</A>
|
||||
HREF="node17.html">Subroutine mld_precinit</A>
|
||||
<LI><A NAME="tex2html258"
|
||||
HREF="node19.html">Subroutine mld_precbld</A>
|
||||
HREF="node18.html">Subroutine mld_precset</A>
|
||||
<LI><A NAME="tex2html259"
|
||||
HREF="node20.html">Subroutine mld_precaply</A>
|
||||
HREF="node19.html">Subroutine mld_precbld</A>
|
||||
<LI><A NAME="tex2html260"
|
||||
HREF="node21.html">Subroutine mld_precfree</A>
|
||||
HREF="node20.html">Subroutine mld_precaply</A>
|
||||
<LI><A NAME="tex2html261"
|
||||
HREF="node21.html">Subroutine mld_precfree</A>
|
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<LI><A NAME="tex2html262"
|
||||
HREF="node22.html">Subroutine mld_precdescr</A>
|
||||
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|
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<H2><A NAME="SECTION00081000000000000000"></A><A NAME="sec:precinit"></A>
|
||||
@@ -69,15 +68,15 @@ This routine allocates and initializes the preconditioner data structure,
|
||||
according to the preconditioner type chosen by the user.
|
||||
|
||||
<P>
|
||||
<BIG CLASS="LARGE"><B>Arguments</B></BIG>
|
||||
<FONT SIZE="+1"><B>Arguments</B></FONT>
|
||||
|
||||
<P>
|
||||
<TABLE CELLPADDING=3>
|
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><SPAN CLASS="textit">x</SPAN><code>prec_type), intent(inout)</code>.</TD>
|
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <SPAN CLASS="textit">x</SPAN>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I>
|
||||
must be chosen according to the real/complex, single/double
|
||||
precision version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
@@ -110,30 +109,29 @@ according to the preconditioner type chosen by the user.
|
||||
<P>
|
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@@ -1,4 +1,4 @@
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<!--Converted with LaTeX2HTML 2012 (1.2)
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original version by: Nikos Drakos, CBLU, University of Leeds
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@@ -25,31 +25,30 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<B> Next:</B> <A NAME="tex2html285"
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<B> Next:</B> <A NAME="tex2html286"
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HREF="node19.html">Subroutine mld_precbld</A>
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<B> Up:</B> <A NAME="tex2html281"
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<B> Up:</B> <A NAME="tex2html282"
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HREF="node16.html">User Interface</A>
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<B> Previous:</B> <A NAME="tex2html276"
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HREF="node17.html">Subroutine mld_precinit</A>
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<B> <A NAME="tex2html284"
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HREF="node2.html">Contents</A></B>
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<!--End of Navigation Panel-->
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|
||||
<H2><A NAME="SECTION00082000000000000000"></A><A NAME="sec:precset"></A>
|
||||
@@ -89,25 +88,25 @@ the new smoother/solver variable to the setup routine as follows:
|
||||
<BR><code>call p%set(solver,info [,ilev])</code>
|
||||
|
||||
</DIV>
|
||||
In this way, the variable will act as a <SPAN CLASS="textit">mold</SPAN> to which the
|
||||
In this way, the variable will act as a <I>mold</I> to which the
|
||||
preconditioner will conform, even though the MLD2P4 library is not
|
||||
modified, and thus has no direct knowledge about the new type.
|
||||
|
||||
<P>
|
||||
<BIG CLASS="LARGE"><B>Arguments</B></BIG>
|
||||
<FONT SIZE="+1"><B>Arguments</B></FONT>
|
||||
|
||||
<P>
|
||||
<TABLE CELLPADDING=3>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><SPAN CLASS="textit">x</SPAN><code>prec_type), intent(inout)</code>.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <SPAN CLASS="textit">x</SPAN> must
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must
|
||||
be chosen according to the real/complex, single/double precision
|
||||
version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>what</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(in)</code> <SPAN CLASS="textit">or</SPAN> <code>character(len=*)</code>.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(in)</code> <I>or</I> <code>character(len=*)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The parameter to be set. It can be specified by
|
||||
@@ -116,8 +115,8 @@ modified, and thus has no direct knowledge about the new type.
|
||||
Tables <A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">5</A>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>val </code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer</code> <SPAN CLASS="textit">or</SPAN> <code>character(len=*)</code> <SPAN CLASS="textit">or</SPAN>
|
||||
<code>real(psb_spk_)</code> <SPAN CLASS="textit">or</SPAN> <code>real(psb_dpk_)</code>,
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer</code> <I>or</I> <code>character(len=*)</code> <I>or</I>
|
||||
<code>real(psb_spk_)</code> <I>or</I> <code>real(psb_dpk_)</code>,
|
||||
<code>intent(in)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
@@ -180,7 +179,7 @@ object is specified its defaults are also set, overriding in both
|
||||
cases any previous settings even if explicitly specified. Therefore if
|
||||
the user sets a new smoother, and wishes to use a solver
|
||||
different from the default one, the call to set the solver must come
|
||||
<SPAN CLASS="textit">after</SPAN> the call to set the smoother.
|
||||
<I>after</I> the call to set the smoother.
|
||||
<P>
|
||||
The combination of a Jacobi smoother with a Diagonal Scaling local
|
||||
solver is equivalent to the strategy called Point Jacobi in the
|
||||
@@ -203,7 +202,7 @@ according to their needs.
|
||||
|
||||
<P>
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER"><A NAME="1271"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="1302"></A>
|
||||
<TABLE>
|
||||
<CAPTION><STRONG>Table 2:</STRONG>
|
||||
Parameters defining the type of multi-level preconditioner.
|
||||
@@ -247,7 +246,7 @@ Parameters defining the type of multi-level preconditioner.
|
||||
|
||||
<P>
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER"><A NAME="1273"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="1304"></A>
|
||||
<TABLE>
|
||||
<CAPTION><STRONG>Table 3:</STRONG>
|
||||
Parameters defining the one-level preconditioner used as smoother.
|
||||
@@ -263,10 +262,10 @@ Parameters defining the one-level preconditioner used as smoother.
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_ovr_</code> <BR><code>SUB_OVR</code></TD>
|
||||
<TD ALIGN="LEFT"><code>integer</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>any int. num. <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>any int. num. <IMG
|
||||
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img90.png"
|
||||
ALT="$\ge 0$"></SPAN></TD>
|
||||
ALT="$\ge 0$"></TD>
|
||||
<TD ALIGN="LEFT">1</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Number of overlap layers.</TD>
|
||||
</TR>
|
||||
@@ -311,30 +310,30 @@ Parameters defining the one-level preconditioner used as smoother.
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_fillin_</code> <BR><code>SUB_FILLIN</code></TD>
|
||||
<TD ALIGN="LEFT"><code>integer</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any int. num. <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any int. num. <IMG
|
||||
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img90.png"
|
||||
ALT="$\ge 0$"></SPAN></TD>
|
||||
ALT="$\ge 0$"></TD>
|
||||
<TD ALIGN="LEFT">0</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Fill-in level <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Fill-in level <IMG
|
||||
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img35.png"
|
||||
ALT="$p$"></SPAN> of the incomplete LU factorizations.</TD>
|
||||
ALT="$p$"> of the incomplete LU factorizations.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_iluthrs_</code> <BR><code>SUB_ILUTHRS</code></TD>
|
||||
<TD ALIGN="LEFT"><code>real(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>)</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any real num. <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any real num. <IMG
|
||||
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img90.png"
|
||||
ALT="$\ge 0$"></SPAN></TD>
|
||||
ALT="$\ge 0$"></TD>
|
||||
<TD ALIGN="LEFT">0</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Drop tolerance <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Drop tolerance <IMG
|
||||
WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img91.png"
|
||||
ALT="$t$"></SPAN> in the ILU(<SPAN CLASS="MATH"><IMG
|
||||
ALT="$t$"> in the ILU(<IMG
|
||||
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img36.png"
|
||||
ALT="$p,t$"></SPAN>) factorization.</TD>
|
||||
ALT="$p,t$">) factorization.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_ren_</code> <BR><code>SUB_REN</code></TD>
|
||||
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
|
||||
@@ -347,7 +346,7 @@ Parameters defining the one-level preconditioner used as smoother.
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_solver_sweeps_</code> <BR><code>SOLVER_SWEEPS</code></TD>
|
||||
<TD ALIGN="LEFT"><code>integer</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any int. num. <IMG
|
||||
WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img92.png"
|
||||
ALT="$\ge 1$"></TD>
|
||||
<TD ALIGN="LEFT">1</TD>
|
||||
@@ -363,7 +362,7 @@ Parameters defining the one-level preconditioner used as smoother.
|
||||
|
||||
<P>
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER"><A NAME="1275"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="1306"></A>
|
||||
<TABLE>
|
||||
<CAPTION><STRONG>Table 4:</STRONG>
|
||||
Parameters defining the aggregation algorithm.
|
||||
@@ -396,6 +395,16 @@ Parameters defining the aggregation algorithm.
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Aggregation algorithm. Currently, only the
|
||||
decoupled aggregation is available.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_ord_</code> <BR><code>AGGR_ORD</code></TD>
|
||||
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'NAT'</TT></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'DEGREE'</TT></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Initial ordering of indices for aggregation
|
||||
algorithm: natural ordering or sorted by
|
||||
descending degree of the node in the
|
||||
matrix graph. Since aggregation is
|
||||
heuristics, results will be different.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_kind_</code> <BR><code>AGGR_KIND</code></TD>
|
||||
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'SMOOTHED'</TT> <TT>'NONSMOOTHED'</TT></TD>
|
||||
@@ -404,16 +413,16 @@ Parameters defining the aggregation algorithm.
|
||||
(i.e. using the tentative prolongator).</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_thresh_</code> <BR><code>AGGR_THRESH</code></TD>
|
||||
<TD ALIGN="LEFT"><code>real(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>)</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>Any real num. <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>Any real num. <IMG
|
||||
WIDTH="56" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img93.png"
|
||||
ALT="$\in [0, 1]$"></SPAN></TD>
|
||||
ALT="$\in [0, 1]$"></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>0.05</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Threshold <IMG
|
||||
WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img94.png"
|
||||
ALT="$\theta$"></SPAN> in the aggregation algorithm.</TD>
|
||||
ALT="$\theta$"> in the aggregation algorithm.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_scale_</code> <BR><code>AGGR_SCALE</code></TD>
|
||||
<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
|
||||
@@ -435,55 +444,55 @@ Parameters defining the aggregation algorithm.
|
||||
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'EIG_EST'</TT> <TT>'USER_CHOICE'</TT></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'EIG_EST'</TT></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>How the damping parameter <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>How the damping parameter <IMG
|
||||
WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img86.png"
|
||||
ALT="$\omega$"></SPAN> in the
|
||||
ALT="$\omega$"> in the
|
||||
smoothed aggregation should be computed:
|
||||
either via an estimate of the spectral radius of
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
<IMG
|
||||
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img87.png"
|
||||
ALT="$D^{-1}A$"></SPAN>, or explicily
|
||||
ALT="$D^{-1}A$">, or explicily
|
||||
specified by the user.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_eig_</code> <BR><code>AGGR_EIG</code></TD>
|
||||
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'A_NORMI'</TT></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'A_NORMI'</TT></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>How to estimate the spectral radius of <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>How to estimate the spectral radius of <IMG
|
||||
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img87.png"
|
||||
ALT="$D^{-1}A$"></SPAN>.
|
||||
ALT="$D^{-1}A$">.
|
||||
Currently only the infinity norm estimate
|
||||
is available.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_omega_val_</code> <BR><code>AGGR_OMEGA_VAL</code></TD>
|
||||
<TD ALIGN="LEFT"><code>real(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>)</code></TD>
|
||||
<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>Any nonnegative real num.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><!-- MATH
|
||||
$4/(3\rho(D^{-1}A))$
|
||||
-->
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
<IMG
|
||||
WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img97.png"
|
||||
ALT="$4/(3\rho(D^{-1}A))$"></SPAN></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Damping parameter <SPAN CLASS="MATH"><IMG
|
||||
ALT="$4/(3\rho(D^{-1}A))$"></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Damping parameter <IMG
|
||||
WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img86.png"
|
||||
ALT="$\omega$"></SPAN> in the smoothed aggregation algorithm.
|
||||
ALT="$\omega$"> in the smoothed aggregation algorithm.
|
||||
It must be set by the user if
|
||||
<code>USER_CHOICE</code> was specified for
|
||||
<code>mld_aggr_omega_alg_</code>,
|
||||
otherwise it is computed by the library, using the
|
||||
selected estimate of the spectral radius <SPAN CLASS="MATH"><IMG
|
||||
selected estimate of the spectral radius <IMG
|
||||
WIDTH="73" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img98.png"
|
||||
ALT="$\rho(D^{-1}A)$"></SPAN> of
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
ALT="$\rho(D^{-1}A)$"> of
|
||||
<IMG
|
||||
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img87.png"
|
||||
ALT="$D^{-1}A$"></SPAN>.</TD>
|
||||
ALT="$D^{-1}A$">.</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
@@ -494,7 +503,7 @@ Parameters defining the aggregation algorithm.
|
||||
|
||||
<P>
|
||||
<BR><P></P>
|
||||
<DIV ALIGN="CENTER"><A NAME="1278"></A>
|
||||
<DIV ALIGN="CENTER"><A NAME="1309"></A>
|
||||
<TABLE>
|
||||
<CAPTION><STRONG>Table 5:</STRONG>
|
||||
Parameters defining the coarse-space correction at the coarsest
|
||||
@@ -535,63 +544,63 @@ level.</CAPTION>
|
||||
<TD ALIGN="LEFT">See note</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Solver for the diagonal blocks of the coarse matrix,
|
||||
in case the block Jacobi solver
|
||||
is chosen as coarsest-level solver: ILU(<SPAN CLASS="MATH"><IMG
|
||||
is chosen as coarsest-level solver: ILU(<IMG
|
||||
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img35.png"
|
||||
ALT="$p$"></SPAN>), MILU(<SPAN CLASS="MATH"><IMG
|
||||
ALT="$p$">), MILU(<IMG
|
||||
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img35.png"
|
||||
ALT="$p$"></SPAN>),
|
||||
ILU(<SPAN CLASS="MATH"><IMG
|
||||
ALT="$p$">),
|
||||
ILU(<IMG
|
||||
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img36.png"
|
||||
ALT="$p,t$"></SPAN>), LU from UMFPACK,
|
||||
ALT="$p,t$">), LU from UMFPACK,
|
||||
LU from SuperLU, plus triangular solve.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_sweeps_</code> <BR><code>COARSE_SWEEPS</code></TD>
|
||||
<TD ALIGN="LEFT"><code>integer</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any int. num. <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any int. num. <IMG
|
||||
WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img99.png"
|
||||
ALT="$> 0$"></SPAN></TD>
|
||||
ALT="$> 0$"></TD>
|
||||
<TD ALIGN="LEFT">4</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Number of Block-Jacobi sweeps when 'BJAC' is used as
|
||||
coarsest-level solver.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_fillin_</code> <BR><code>COARSE_FILLIN</code></TD>
|
||||
<TD ALIGN="LEFT"><code>integer</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any int. num. <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any int. num. <IMG
|
||||
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img90.png"
|
||||
ALT="$\ge 0$"></SPAN></TD>
|
||||
ALT="$\ge 0$"></TD>
|
||||
<TD ALIGN="LEFT">0</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Fill-in level <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Fill-in level <IMG
|
||||
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img35.png"
|
||||
ALT="$p$"></SPAN> of the incomplete LU factorizations.</TD>
|
||||
ALT="$p$"> of the incomplete LU factorizations.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_iluthrs_</code> <BR><code>COARSE_ILUTHRS</code></TD>
|
||||
<TD ALIGN="LEFT"><code>real(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>)</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any real. num. <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any real. num. <IMG
|
||||
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img90.png"
|
||||
ALT="$\ge 0$"></SPAN></TD>
|
||||
ALT="$\ge 0$"></TD>
|
||||
<TD ALIGN="LEFT">0</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Drop tolerance <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Drop tolerance <IMG
|
||||
WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img91.png"
|
||||
ALT="$t$"></SPAN> in the ILU(<SPAN CLASS="MATH"><IMG
|
||||
ALT="$t$"> in the ILU(<IMG
|
||||
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img36.png"
|
||||
ALT="$p,t$"></SPAN>) factorization.</TD>
|
||||
ALT="$p,t$">) factorization.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" COLSPAN=5><SPAN><B>Note:</B> defaults for
|
||||
<TT>m</TT>ld_coarse_subsolve_ are chosen as </SPAN></TD>
|
||||
<TR><TD ALIGN="LEFT" COLSPAN=5><B>Note:</B> defaults for
|
||||
<TT>m</TT>ld_coarse_subsolve_ are chosen as</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" COLSPAN=5><SPAN>single precision version: 'SLU' if installed, 'ILU' otherwise</SPAN></TD>
|
||||
<TR><TD ALIGN="LEFT" COLSPAN=5>single precision version: 'SLU' if installed, 'ILU' otherwise</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" COLSPAN=5><SPAN>double precision version: 'UMF' if installed,
|
||||
else 'SLU' if installed, 'ILU' otherwise</SPAN></TD>
|
||||
<TR><TD ALIGN="LEFT" COLSPAN=5>double precision version: 'UMF' if installed,
|
||||
else 'SLU' if installed, 'ILU' otherwise</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
@@ -603,30 +612,29 @@ level.</CAPTION>
|
||||
<P>
|
||||
|
||||
<P>
|
||||
|
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<BR>
|
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<BR></DIV>
|
||||
<BR>
|
||||
<!--End of Navigation Panel-->
|
||||
|
||||
<H2><A NAME="SECTION00083000000000000000"></A><A NAME="sec:precbld"></A>
|
||||
@@ -68,20 +67,20 @@ This routine builds the preconditioner according to the requirements made by
|
||||
the user through the routines <code>mld_precinit</code> and <code>mld_precset</code>.
|
||||
|
||||
<P>
|
||||
<BIG CLASS="LARGE"><B>Arguments</B></BIG>
|
||||
<FONT SIZE="+1"><B>Arguments</B></FONT>
|
||||
|
||||
<P>
|
||||
<TABLE CELLPADDING=3>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>a</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_</code><SPAN CLASS="textit">x</SPAN><code>spmat_type), intent(in)</code>.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_</code><I>x</I><code>spmat_type), intent(in)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The sparse matrix structure containing the local part of the
|
||||
matrix to be preconditioned. Note that <SPAN CLASS="textit">x</SPAN> must be chosen according
|
||||
matrix to be preconditioned. Note that <I>x</I> must be chosen according
|
||||
to the real/complex,
|
||||
single/double precision version of MLD2P4 under use.
|
||||
See the PSBLAS User's Guide for details [<A
|
||||
HREF="node25.html#PSBLASGUIDE">15</A>].</TD>
|
||||
HREF="node25.html#PSBLASGUIDE">16</A>].</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
|
||||
@@ -89,13 +88,13 @@ single/double precision version of MLD2P4 under use.
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
|
||||
details [<A
|
||||
HREF="node25.html#PSBLASGUIDE">15</A>].</TD>
|
||||
HREF="node25.html#PSBLASGUIDE">16</A>].</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><SPAN CLASS="textit">x</SPAN><code>prec_type), intent(inout)</code>.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <SPAN CLASS="textit">x</SPAN> must be chosen according
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
|
||||
@@ -108,29 +107,29 @@ single/double precision version of MLD2P4 under use.
|
||||
|
||||
<P>
|
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|
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<B> Next:</B> <A NAME="tex2html297"
|
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<B> Next:</B> <A NAME="tex2html298"
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HREF="node20.html">Subroutine mld_precaply</A>
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|
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HREF="node2.html">Contents</A></B> </DIV>
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HREF="node2.html">Contents</A></B>
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@@ -1,4 +1,4 @@
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@@ -25,26 +25,25 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<!--End of Navigation Panel-->
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<BR>
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|
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@@ -53,64 +52,64 @@ Contents</A>
|
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</H2>
|
||||
<!--Table of Contents-->
|
||||
|
||||
<UL CLASS="TofC">
|
||||
<LI><A NAME="tex2html63"
|
||||
HREF="node3.html">General Overview</A>
|
||||
<UL>
|
||||
<LI><A NAME="tex2html64"
|
||||
HREF="node4.html">Code Distribution</A>
|
||||
HREF="node3.html">General Overview</A>
|
||||
<LI><A NAME="tex2html65"
|
||||
HREF="node4.html">Code Distribution</A>
|
||||
<LI><A NAME="tex2html66"
|
||||
HREF="node5.html">Configuring and Building MLD2P4</A>
|
||||
<UL>
|
||||
<LI><A NAME="tex2html66"
|
||||
HREF="node6.html">Prerequisites</A>
|
||||
<LI><A NAME="tex2html67"
|
||||
HREF="node7.html">Optional third party libraries</A>
|
||||
HREF="node6.html">Prerequisites</A>
|
||||
<LI><A NAME="tex2html68"
|
||||
HREF="node8.html">Configuration options</A>
|
||||
HREF="node7.html">Optional third party libraries</A>
|
||||
<LI><A NAME="tex2html69"
|
||||
HREF="node9.html">Bug reporting</A>
|
||||
HREF="node8.html">Configuration options</A>
|
||||
<LI><A NAME="tex2html70"
|
||||
HREF="node9.html">Bug reporting</A>
|
||||
<LI><A NAME="tex2html71"
|
||||
HREF="node10.html">Example and test programs</A>
|
||||
</UL>
|
||||
<BR>
|
||||
<LI><A NAME="tex2html71"
|
||||
<LI><A NAME="tex2html72"
|
||||
HREF="node11.html">Multi-level Domain Decomposition Background</A>
|
||||
<UL>
|
||||
<LI><A NAME="tex2html72"
|
||||
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
|
||||
<LI><A NAME="tex2html73"
|
||||
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
|
||||
<LI><A NAME="tex2html74"
|
||||
HREF="node13.html">Smoothed Aggregation</A>
|
||||
</UL>
|
||||
<BR>
|
||||
<LI><A NAME="tex2html74"
|
||||
<LI><A NAME="tex2html75"
|
||||
HREF="node14.html">Getting Started</A>
|
||||
<UL>
|
||||
<LI><A NAME="tex2html75"
|
||||
<LI><A NAME="tex2html76"
|
||||
HREF="node15.html">Examples</A>
|
||||
</UL>
|
||||
<BR>
|
||||
<LI><A NAME="tex2html76"
|
||||
<LI><A NAME="tex2html77"
|
||||
HREF="node16.html">User Interface</A>
|
||||
<UL>
|
||||
<LI><A NAME="tex2html77"
|
||||
HREF="node17.html">Subroutine mld_precinit</A>
|
||||
<LI><A NAME="tex2html78"
|
||||
HREF="node18.html">Subroutine mld_precset</A>
|
||||
HREF="node17.html">Subroutine mld_precinit</A>
|
||||
<LI><A NAME="tex2html79"
|
||||
HREF="node19.html">Subroutine mld_precbld</A>
|
||||
HREF="node18.html">Subroutine mld_precset</A>
|
||||
<LI><A NAME="tex2html80"
|
||||
HREF="node20.html">Subroutine mld_precaply</A>
|
||||
HREF="node19.html">Subroutine mld_precbld</A>
|
||||
<LI><A NAME="tex2html81"
|
||||
HREF="node21.html">Subroutine mld_precfree</A>
|
||||
HREF="node20.html">Subroutine mld_precaply</A>
|
||||
<LI><A NAME="tex2html82"
|
||||
HREF="node21.html">Subroutine mld_precfree</A>
|
||||
<LI><A NAME="tex2html83"
|
||||
HREF="node22.html">Subroutine mld_precdescr</A>
|
||||
</UL>
|
||||
<BR>
|
||||
<LI><A NAME="tex2html83"
|
||||
HREF="node23.html">Error Handling</A>
|
||||
<LI><A NAME="tex2html84"
|
||||
HREF="node24.html">License</A>
|
||||
HREF="node23.html">Error Handling</A>
|
||||
<LI><A NAME="tex2html85"
|
||||
HREF="node24.html">License</A>
|
||||
<LI><A NAME="tex2html86"
|
||||
HREF="node25.html">Bibliography</A>
|
||||
</UL>
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<!--End of Table of Contents-->
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||||
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@@ -1,4 +1,4 @@
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<!--Converted with LaTeX2HTML 2012 (1.2)
|
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original version by: Nikos Drakos, CBLU, University of Leeds
|
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@@ -25,31 +25,30 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<B> Next:</B> <A NAME="tex2html309"
|
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<B> Next:</B> <A NAME="tex2html310"
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HREF="node21.html">Subroutine mld_precfree</A>
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<B> Up:</B> <A NAME="tex2html305"
|
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<B> Previous:</B> <A NAME="tex2html299"
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<B> Previous:</B> <A NAME="tex2html300"
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HREF="node19.html">Subroutine mld_precbld</A>
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<B> <A NAME="tex2html307"
|
||||
<B> <A NAME="tex2html308"
|
||||
HREF="node2.html">Contents</A></B>
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<BR>
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<BR></DIV>
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<!--End of Navigation Panel-->
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|
||||
<H2><A NAME="SECTION00084000000000000000"></A><A NAME="sec:precaply"></A>
|
||||
@@ -68,17 +67,17 @@ Subroutine mld_precaply
|
||||
This routine computes <!-- MATH
|
||||
$y = op(M^{-1})\, x$
|
||||
-->
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
WIDTH="117" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
<IMG
|
||||
WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img100.png"
|
||||
ALT="$y = op(M^{-1}) x$"></SPAN>, where <SPAN CLASS="MATH"><IMG
|
||||
ALT="$y = op(M^{-1})\, x$">, where <IMG
|
||||
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img60.png"
|
||||
ALT="$M$"></SPAN> is a previously built
|
||||
preconditioner, stored into <code>p</code>, and <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
ALT="$M$"> is a previously built
|
||||
preconditioner, stored into <code>p</code>, and <IMG
|
||||
WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img101.png"
|
||||
ALT="$op$"></SPAN>
|
||||
ALT="$op$">
|
||||
denotes the preconditioner itself or its transpose, according to
|
||||
the value of <code>trans</code>.
|
||||
Note that, when MLD2P4 is used with a Krylov solver from PSBLAS,
|
||||
@@ -86,41 +85,41 @@ Note that, when MLD2P4 is used with a Krylov solver from PSBLAS,
|
||||
and hence it is completely transparent to the user.
|
||||
|
||||
<P>
|
||||
<BIG CLASS="LARGE"><B>Arguments</B></BIG>
|
||||
<FONT SIZE="+1"><B>Arguments</B></FONT>
|
||||
|
||||
<P>
|
||||
<TABLE CELLPADDING=3>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><SPAN CLASS="textit">x</SPAN><code>prec_type), intent(inout)</code>.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure, containing the local part of <SPAN CLASS="MATH"><IMG
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure, containing the local part of <IMG
|
||||
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img60.png"
|
||||
ALT="$M$"></SPAN>.
|
||||
Note that <SPAN CLASS="textit">x</SPAN> must be chosen according
|
||||
ALT="$M$">.
|
||||
Note that <I>x</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>x</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><SPAN CLASS="textit">type</SPAN><code>(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>), dimension(:), intent(in)</code>.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(in)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
|
||||
WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img102.png"
|
||||
ALT="$x$"></SPAN>. Note that <SPAN CLASS="textit">type</SPAN> and
|
||||
<SPAN CLASS="textit">kind_parameter</SPAN> must be chosen according
|
||||
ALT="$x$">. Note that <I>type</I> and
|
||||
<I>kind_parameter</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>y</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><SPAN CLASS="textit">type</SPAN><code>(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>), dimension(:), intent(out)</code>.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(out)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <SPAN CLASS="MATH"><IMG
|
||||
WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
|
||||
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img103.png"
|
||||
ALT="$y$"></SPAN>. Note that <SPAN CLASS="textit">type</SPAN> and
|
||||
<SPAN CLASS="textit">kind_parameter</SPAN> must be chosen according
|
||||
ALT="$y$">. Note that <I>type</I> and
|
||||
<I>kind_parameter</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
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@@ -143,39 +142,39 @@ and hence it is completely transparent to the user.
|
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>If <code>trans</code> = <code>'N','n'</code> then <!-- MATH
|
||||
$op(M^{-1}) = M^{-1}$
|
||||
-->
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
<IMG
|
||||
WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img104.png"
|
||||
ALT="$op(M^{-1}) = M^{-1}$"></SPAN>;
|
||||
ALT="$op(M^{-1}) = M^{-1}$">;
|
||||
if <code>trans</code> = <code>'T','t'</code> then <!-- MATH
|
||||
$op(M^{-1}) = M^{-T}$
|
||||
-->
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
<IMG
|
||||
WIDTH="135" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img105.png"
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||||
ALT="$op(M^{-1}) = M^{-T}$"></SPAN>
|
||||
(transpose of <SPAN CLASS="MATH"><IMG
|
||||
ALT="$op(M^{-1}) = M^{-T}$">
|
||||
(transpose of <IMG
|
||||
WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img106.png"
|
||||
ALT="$M^{-1})$"></SPAN>; if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
|
||||
ALT="$M^{-1})$">; if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
|
||||
$op(M^{-1}) = M^{-C}$
|
||||
-->
|
||||
<SPAN CLASS="MATH"><IMG
|
||||
<IMG
|
||||
WIDTH="136" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img107.png"
|
||||
ALT="$op(M^{-1}) = M^{-C}$"></SPAN>
|
||||
(conjugate transpose of <SPAN CLASS="MATH"><IMG
|
||||
ALT="$op(M^{-1}) = M^{-C}$">
|
||||
(conjugate transpose of <IMG
|
||||
WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img106.png"
|
||||
ALT="$M^{-1})$"></SPAN>.</TD>
|
||||
ALT="$M^{-1})$">.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>work</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><SPAN CLASS="textit">type</SPAN><code>(</code><SPAN CLASS="textit">kind_parameter</SPAN><code>), dimension(:), optional, target</code>.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), optional, target</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Workspace. Its size should be at
|
||||
least <code>4 * psb_cd_get_local_</code> <code>cols(desc_a)</code> (see the PSBLAS User's Guide).
|
||||
Note that <SPAN CLASS="textit">type</SPAN> and <SPAN CLASS="textit">kind_parameter</SPAN> must be chosen according
|
||||
Note that <I>type</I> and <I>kind_parameter</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
@@ -183,30 +182,29 @@ and hence it is completely transparent to the user.
|
||||
<P>
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HREF="node20.html">Subroutine mld_precaply</A>
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<B> <A NAME="tex2html320"
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||||
<H2><A NAME="SECTION00085000000000000000"></A><A NAME="sec:precfree"></A>
|
||||
@@ -67,15 +66,15 @@ Subroutine mld_precfree
|
||||
This routine deallocates the preconditioner data structure.
|
||||
|
||||
<P>
|
||||
<BIG CLASS="LARGE"><B>Arguments</B></BIG>
|
||||
<FONT SIZE="+1"><B>Arguments</B></FONT>
|
||||
|
||||
<P>
|
||||
<TABLE CELLPADDING=3>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><code>type(mld_</code><SPAN CLASS="textit">x</SPAN><code>prec_type), intent(inout)</code>.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>The preconditioner data structure. Note that <SPAN CLASS="textit">x</SPAN> must be chosen according
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>The preconditioner data structure. Note that <I>x</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
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@@ -1,4 +1,4 @@
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original version by: Nikos Drakos, CBLU, University of Leeds
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HREF="node21.html">Subroutine mld_precfree</A>
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<B> <A NAME="tex2html329"
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<B> <A NAME="tex2html330"
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HREF="node2.html">Contents</A></B>
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<H2><A NAME="SECTION00086000000000000000"></A><A NAME="sec:precdescr"></A>
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@@ -68,15 +67,15 @@ This routine prints a description of the preconditioner to the standard output o
|
||||
to a file. It must be called after <code>mld_precbld</code> has been called.
|
||||
|
||||
<P>
|
||||
<BIG CLASS="LARGE"><B>Arguments</B></BIG>
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<FONT SIZE="+1"><B>Arguments</B></FONT>
|
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||||
<P>
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<TABLE CELLPADDING=3>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><SPAN CLASS="textit">x</SPAN><code>prec_type), intent(in)</code>.</TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(in)</code>.</TD>
|
||||
</TR>
|
||||
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <SPAN CLASS="textit">x</SPAN> must be chosen according
|
||||
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must be chosen according
|
||||
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
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||||
</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
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@@ -1,4 +1,4 @@
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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original version by: Nikos Drakos, CBLU, University of Leeds
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<B> Previous:</B> <A NAME="tex2html334"
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HREF="node22.html">Subroutine mld_precdescr</A>
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<B> <A NAME="tex2html342"
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<H1><A NAME="SECTION00090000000000000000"></A><A NAME="sec:errors"></A>
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@@ -69,7 +68,7 @@ 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
|
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User's Guide [<A
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HREF="node25.html#PSBLASGUIDE">16</A>].
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<H1><A NAME="SECTION000100000000000000000"></A><A NAME="sec:license"></A>
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HREF="node26.html">About this document ...</A>
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HREF="node2.html">Contents</A></B>
|
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<BR><BR>
|
||||
<!--End of Navigation Panel-->
|
||||
@@ -102,35 +102,44 @@ T.A. Davis,
|
||||
<EM>Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal
|
||||
Method with a Column Pre-ordering Strategy</EM>,
|
||||
ACM Transactions on Mathematical Software, 30, 2004, 196-199.
|
||||
(See also <TT>http://www.cise.ufl.edu/ davis/</TT>)<P></P><DT><A NAME="SUPERLU">10</A>
|
||||
(See also <TT>http://www.cise.ufl.edu/ davis/</TT>)
|
||||
<P>
|
||||
<P></P><DT><A NAME="MUMPS">10</A>
|
||||
<DD>
|
||||
P.R. Amestoy, C. Ashcraft, O. Boiteau, A. Buttari, J. L'Excellent, C. Weisbecker
|
||||
<EM>Improving multifrontal methods by means of block low-rank representations</EM>,
|
||||
SIAM SISC, volume 37, number 3, pages A1452-A1474.
|
||||
(See also <TT>http://mumps.enseeiht.fr</TT>)
|
||||
<P>
|
||||
<P></P><DT><A NAME="SUPERLU">11</A>
|
||||
<DD>
|
||||
J.W. Demmel, S.C. Eisenstat, J.R. Gilbert, X.S. Li and J.W.H. Liu,
|
||||
A supernodal approach to sparse partial pivoting,
|
||||
SIAM Journal on Matrix Analysis and Applications, 20, 3, 1999, 720-755.<P></P><DT><A NAME="blas3">11</A>
|
||||
SIAM Journal on Matrix Analysis and Applications, 20, 3, 1999, 720-755.<P></P><DT><A NAME="blas3">12</A>
|
||||
<DD>
|
||||
J. J. Dongarra, J. Du Croz, I. S. Duff, S. Hammarling,
|
||||
<I>A set of Level 3 Basic Linear Algebra Subprograms</I>,
|
||||
ACM Transactions on Mathematical Software, 16, 1990, 1-17.<P></P><DT><A NAME="blas2">12</A>
|
||||
ACM Transactions on Mathematical Software, 16, 1990, 1-17.<P></P><DT><A NAME="blas2">13</A>
|
||||
<DD>
|
||||
J. J. Dongarra, J. Du Croz, S. Hammarling, R. J. Hanson,
|
||||
<I>An extended set of FORTRAN Basic Linear Algebra Subprograms</I>,
|
||||
ACM Transactions on Mathematical Software, 14, 1988, 1-17.<P></P><DT><A NAME="BLACS">13</A>
|
||||
ACM Transactions on Mathematical Software, 14, 1988, 1-17.<P></P><DT><A NAME="BLACS">14</A>
|
||||
<DD>
|
||||
J. J. Dongarra and R. C. Whaley,
|
||||
<EM>A User's Guide to the BLACS v. 1.1</EM>,
|
||||
Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of
|
||||
Tennessee, March 1995 (updated May 1997).<P></P><DT><A NAME="EFSTATHIOU">14</A>
|
||||
Tennessee, March 1995 (updated May 1997).<P></P><DT><A NAME="EFSTATHIOU">15</A>
|
||||
<DD>
|
||||
E. Efstathiou, J. G. Gander,
|
||||
<EM>Why Restricted Additive Schwarz Converges Faster than Additive Schwarz</EM>,
|
||||
BIT Numerical Mathematics, 43, 2003, 945-959.<P></P><DT><A NAME="PSBLASGUIDE">15</A>
|
||||
BIT Numerical Mathematics, 43, 2003, 945-959.<P></P><DT><A NAME="PSBLASGUIDE">16</A>
|
||||
<DD>
|
||||
S. Filippone, A. Buttari,
|
||||
<EM>PSBLAS-3.0 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library</EM>, 2012,
|
||||
available from <TT>http://www.ce.uniroma2.it/psblas/</TT>.
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="PSBLAS3">16</A>
|
||||
<P></P><DT><A NAME="PSBLAS3">17</A>
|
||||
<DD>
|
||||
Salvatore Filippone and Alfredo Buttari.
|
||||
<EM>Object-Oriented Techniques for Sparse Matrix Computations in Fortran
|
||||
@@ -138,49 +147,49 @@ Salvatore Filippone and Alfredo Buttari.
|
||||
ACM Trans. on Math Software, 38(4), 2012.
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="psblas_00">17</A>
|
||||
<P></P><DT><A NAME="psblas_00">18</A>
|
||||
<DD>
|
||||
S. Filippone, M. Colajanni,
|
||||
<EM>PSBLAS: A Library for Parallel Linear Algebra
|
||||
Computation on Sparse Matrices</EM>,
|
||||
ACM Transactions on Mathematical Software, 26, 4, 2000, 527-550.<P></P><DT><A NAME="MPI2">18</A>
|
||||
ACM Transactions on Mathematical Software, 26, 4, 2000, 527-550.<P></P><DT><A NAME="MPI2">19</A>
|
||||
<DD>
|
||||
W. Gropp, S. Huss-Lederman, A. Lumsdaine, E. Lusk, B. Nitzberg, W. Saphir, M. Snir,
|
||||
<EM>MPI: The Complete Reference. Volume 2 - The MPI-2 Extensions</EM>,
|
||||
MIT Press, 1998.<P></P><DT><A NAME="blas1">19</A>
|
||||
MIT Press, 1998.<P></P><DT><A NAME="blas1">20</A>
|
||||
<DD>
|
||||
C. L. Lawson, R. J. Hanson, D. Kincaid, F. T. Krogh,
|
||||
<I>Basic Linear Algebra Subprograms for FORTRAN usage</I>,
|
||||
ACM Transactions on Mathematical Software, 5, 1979, 308-323.<P></P><DT><A NAME="SUPERLUDIST">20</A>
|
||||
ACM Transactions on Mathematical Software, 5, 1979, 308-323.<P></P><DT><A NAME="SUPERLUDIST">21</A>
|
||||
<DD>
|
||||
X. S. Li, J. W. Demmel, <EM>SuperLU_DIST: A Scalable Distributed-memory
|
||||
Sparse Direct Solver for Unsymmetric Linear Systems</EM>,
|
||||
ACM Transactions on Mathematical Software, 29, 2, 2003, 110-140.<P></P><DT><A NAME="Saad_book">21</A>
|
||||
ACM Transactions on Mathematical Software, 29, 2, 2003, 110-140.<P></P><DT><A NAME="Saad_book">22</A>
|
||||
<DD>
|
||||
Y. Saad,
|
||||
<I>Iterative methods for sparse linear systems</I>, 2nd edition,
|
||||
SIAM, 2003
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="dd2_96">22</A>
|
||||
<P></P><DT><A NAME="dd2_96">23</A>
|
||||
<DD>
|
||||
B. Smith, P. Bjorstad, W. Gropp,
|
||||
<EM>Domain Decomposition: Parallel Multilevel Methods for Elliptic
|
||||
Partial Differential Equations</EM>,
|
||||
Cambridge University Press, 1996.<P></P><DT><A NAME="MPI1">23</A>
|
||||
Cambridge University Press, 1996.<P></P><DT><A NAME="MPI1">24</A>
|
||||
<DD>
|
||||
M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra,
|
||||
<EM>MPI: The Complete Reference. Volume 1 - The MPI Core</EM>, second edition,
|
||||
MIT Press, 1998.<P></P><DT><A NAME="StubenGMD69_99">24</A>
|
||||
MIT Press, 1998.<P></P><DT><A NAME="StubenGMD69_99">25</A>
|
||||
<DD>
|
||||
K. Stüben,
|
||||
<EM>Algebraic Multigrid (AMG): an Introduction with Applications</EM>,
|
||||
in A. Schüller, U. Trottenberg, C. Oosterlee, editors, Multigrid,
|
||||
Academic Press, 2000.<P></P><DT><A NAME="TUMINARO_TONG">25</A>
|
||||
Academic Press, 2000.<P></P><DT><A NAME="TUMINARO_TONG">26</A>
|
||||
<DD>
|
||||
R. S. Tuminaro, C. Tong,
|
||||
<EM>Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines</EM>,
|
||||
in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000.<P></P><DT><A NAME="VANEK_MANDEL_BREZINA">26</A>
|
||||
in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000.<P></P><DT><A NAME="VANEK_MANDEL_BREZINA">27</A>
|
||||
<DD>
|
||||
P. Vanek, J. Mandel and M. Brezina,
|
||||
<EM>Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems</EM>,
|
||||
|
||||
@@ -25,21 +25,21 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<BR>
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<BR>
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||||
@@ -63,7 +63,7 @@ Mathematics Department, Macquarie University, Sydney.
|
||||
The command line arguments were: <BR>
|
||||
<STRONG>latex2html</STRONG> <TT>-local_icons -noaddress -dir ../../html userhtml.tex</TT>
|
||||
<P>
|
||||
The translation was initiated by Salvatore Filippone on 2016-02-29
|
||||
The translation was initiated by Salvatore Filippone on 2016-05-09
|
||||
<BR><HR>
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</BODY>
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@@ -1,4 +1,4 @@
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<!--Converted with LaTeX2HTML 2012 (1.2)
|
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original version by: Nikos Drakos, CBLU, University of Leeds
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@@ -25,31 +25,30 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<!--End of Navigation Panel-->
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<H1><A NAME="SECTION00030000000000000000"></A><A NAME="sec:overview"></A>
|
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@@ -59,18 +58,17 @@ General Overview
|
||||
|
||||
<P>
|
||||
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 <SPAN CLASS="textit">multi-level Schwarz preconditioners</SPAN> [<A
|
||||
HREF="node25.html#dd2_96">22</A>],
|
||||
</SMALL>PSBLAS (MLD2P4) provides <I>multi-level Schwarz preconditioners</I> [<A
|
||||
HREF="node25.html#dd2_96">23</A>],
|
||||
to be used in the iterative solutions of sparse linear systems:
|
||||
<BR>
|
||||
<DIV ALIGN="RIGHT" CLASS="mathdisplay">
|
||||
<DIV ALIGN="RIGHT">
|
||||
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||||
<!-- MATH
|
||||
\begin{equation}
|
||||
Ax=b,
|
||||
\end{equation}
|
||||
-->
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||||
<A NAME="system1"></A>
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||||
<TABLE WIDTH="100%" ALIGN="CENTER">
|
||||
<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="system1"></A><IMG
|
||||
WIDTH="58" HEIGHT="30" BORDER="0"
|
||||
@@ -78,35 +76,35 @@ Ax=b,
|
||||
ALT="\begin{displaymath}
|
||||
Ax=b,
|
||||
\end{displaymath}"></TD>
|
||||
<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
|
||||
(<SPAN CLASS="arabic">1</SPAN>)</TD></TR>
|
||||
<TD WIDTH=10 ALIGN="RIGHT">
|
||||
(1)</TD></TR>
|
||||
</TABLE>
|
||||
<BR CLEAR="ALL"></DIV><P></P>
|
||||
where <SPAN CLASS="MATH"><IMG
|
||||
where <IMG
|
||||
WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img2.png"
|
||||
ALT="$A$"></SPAN> is a square, real or complex, sparse matrix with a symmetric
|
||||
ALT="$A$"> is a square, real or complex, sparse matrix with a symmetric
|
||||
sparsity pattern. These preconditioners have the following general features:
|
||||
|
||||
<UL>
|
||||
<LI>both <SPAN CLASS="textit">additive and hybrid multilevel</SPAN> variants are implemented,
|
||||
<LI>both <I>additive and hybrid multilevel</I> variants are implemented,
|
||||
i.e. variants that are additive among the levels and inside each level, and variants
|
||||
that are multiplicative among the levels and additive inside each level;
|
||||
the basic Additive Schwarz (AS) preconditioners are obtained by considering only one level;
|
||||
</LI>
|
||||
<LI>a <SPAN CLASS="textit">purely algebraic</SPAN> approach is used to
|
||||
<LI>a <I>purely algebraic</I> approach is used to
|
||||
generate a sequence of coarse-level corrections to a basic AS preconditioner, without
|
||||
explicitly using any information on the geometry of the original problem (e.g. the
|
||||
discretization of a PDE). The <SPAN CLASS="textit">smoothed aggregation</SPAN> technique is applied
|
||||
discretization of a PDE). The <I>smoothed aggregation</I> technique is applied
|
||||
as algebraic coarsening strategy [<A
|
||||
HREF="node25.html#BREZINA_VANEK">1</A>,<A
|
||||
HREF="node25.html#VANEK_MANDEL_BREZINA">26</A>].
|
||||
HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>].
|
||||
</LI>
|
||||
</UL>
|
||||
|
||||
<P>
|
||||
Version 2.0 of the package is written in <SPAN CLASS="textit">Fortran 2003</SPAN>, following an
|
||||
<SPAN CLASS="textit">object-oriented design</SPAN> through the exploitation of features
|
||||
Version 2.0 of the package is written in <I>Fortran 2003</I>, following an
|
||||
<I>object-oriented design</I> through the exploitation of features
|
||||
such as abstract data type creation, functional overloading and
|
||||
dynamic memory management. The parallel implementation is based on a Single Program Multiple Data
|
||||
(SPMD) paradigm for distributed-memory architectures. Single and
|
||||
@@ -116,10 +114,10 @@ interface.
|
||||
|
||||
<P>
|
||||
MLD2P4 has been designed to implement scalable and easy-to-use
|
||||
multilevel preconditioners in the context of the <SPAN CLASS="textit">PSBLAS
|
||||
(Parallel Sparse BLAS) computational framework</SPAN> [<A
|
||||
HREF="node25.html#psblas_00">17</A>,<A
|
||||
HREF="node25.html#PSBLAS3">16</A>].
|
||||
multilevel preconditioners in the context of the <I>PSBLAS
|
||||
(Parallel Sparse BLAS) computational framework</I> [<A
|
||||
HREF="node25.html#psblas_00">18</A>,<A
|
||||
HREF="node25.html#PSBLAS3">17</A>].
|
||||
PSBLAS is a library originally developed to address the parallel implementation of
|
||||
iterative solvers for sparse linear system, by providing basic linear algebra
|
||||
operators and data management facilities for distributed sparse matrices; it
|
||||
@@ -132,10 +130,10 @@ portability, modularity ed extensibility in the development of the preconditione
|
||||
package. On the other hand, the implementation of MLD2P4 has led to some
|
||||
revisions and extentions of the PSBLAS kernels, leading to the
|
||||
PSBLAS 2.0 version [<A
|
||||
HREF="node25.html#PSBLASGUIDE">15</A>]. The inter-process comunication required
|
||||
HREF="node25.html#PSBLASGUIDE">16</A>]. The inter-process comunication required
|
||||
by MLD2P4 is encapsulated into the PSBLAS routines, except few cases where
|
||||
MPI [<A
|
||||
HREF="node25.html#MPI1">23</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
|
||||
HREF="node25.html#MPI1">24</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
|
||||
machine where PSBLAS and MPI implementations are available.
|
||||
|
||||
<P>
|
||||
@@ -172,30 +170,29 @@ in Section <A HREF="node23.html#sec:errors">7</A>. The copyright terms conc
|
||||
of MLD2P4 are reported in Appendix <A HREF="node24.html#sec:license">A</A>.
|
||||
|
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|
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|
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HREF="node9.html">Bug reporting</A>
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<DT><STRONG>BLAS</STRONG></DT>
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|
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<DT><STRONG>MPI</STRONG></DT>
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<DD>[<A
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high-performance computing systems;
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<DT><STRONG>PSBLAS</STRONG></DT>
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HREF="node25.html#PSBLASGUIDE">16</A>,<A
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HREF="node25.html#psblas_00">18</A>] Parallel Sparse BLAS is
|
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available from
|
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<BR><code>http://www.ce.uniroma2.it/psblas</code>; version
|
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3.3 (or later) is required. Indeed, all the prerequisites
|
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<DT><STRONG>SuperLU</STRONG></DT>
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<DD>[<A
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HREF="node25.html#SUPERLU">10</A>]
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HREF="node25.html#SUPERLU">11</A>]
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A sparse direct factorization package available from
|
||||
<BR> <code>http://crd.lbl.gov/~xiaoye/SuperLU/</code>; provides serial
|
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factorization and triangular system solution for single and double precision,
|
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<DT><STRONG>SuperLU_Dist</STRONG></DT>
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<DD>[<A
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HREF="node25.html#SUPERLUDIST">20</A>]
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HREF="node25.html#SUPERLUDIST">21</A>]
|
||||
A sparse direct factorization package available
|
||||
from the same site as SuperLU; provides parallel factorization and
|
||||
triangular system solution for double precision real and complex data.
|
||||
We have tested version 3.3 and 4.2.
|
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</DD>
|
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<DT><STRONG>MUMPS</STRONG></DT>
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<DD>[]
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MUMPS (“Multifrontal Massively Parallel Solver”) is a sparse, direct factorization
|
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<DD>[<A
|
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HREF="node25.html#MUMPS">10</A>]
|
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MUMPS (“MUltifrontal Massively Parallel Solver”) is a sparse, direct factorization
|
||||
package available from
|
||||
<BR> <code>http://mumps.enseeiht.fr/</code>.
|
||||
It implements a direct method based on a multifrontal approach which performs
|
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@@ -100,30 +100,29 @@ for multilevel preconditioners may change to reflect their presence.
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<P>
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</DD>
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<P>
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In order to use the MUMPS solver based on multifrontal factorization, the user has to add MUMPS flags, include directories and libraries in the Make.inc file.
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The necessary MUMPS libraries are <code>-ldmumps, -lsmumps -lzmumps -lzmumps -mumps_common -lpord</code>. The flag <code>-DHAVE_MUMPS_</code> is mandatory too. Since MUMPS uses openmp and ScaLAPACK, <code>LINKOPT=-fonemp</code> must be added as well, along with the ScaLAPACK flags, include directories and library (which can be set using the configure script).
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|
||||
<!--End of Navigation Panel-->
|
||||
<BIG CLASS="XXLARGE"><B>MLD2P4
|
||||
<FONT SIZE="+2"><B>MLD2P4
|
||||
<BR>
|
||||
<BR>
|
||||
User's and Reference Guide</B></BIG>
|
||||
<BR><SPAN CLASS="textit"><BIG CLASS="LARGE">A guide for the Multi-Level Domain Decomposition
|
||||
User's and Reference Guide</B></FONT>
|
||||
<BR><I><FONT SIZE="+1">A guide for the Multi-Level Domain Decomposition
|
||||
Parallel Preconditioners Package
|
||||
based on PSBLAS</BIG></SPAN>
|
||||
based on PSBLAS</FONT></I>
|
||||
<BR>
|
||||
<BR>
|
||||
<BR>
|
||||
@@ -62,9 +61,9 @@ University of Rome ``Tor Vergata'', Italy
|
||||
<BR>
|
||||
<BR>
|
||||
<BR>
|
||||
Software version: 2.0
|
||||
Software version: 2.1
|
||||
<BR>
|
||||
Oct. 12, 2015
|
||||
Mar. 31, 2016
|
||||
|
||||
<BR>
|
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|
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@@ -77,70 +76,70 @@ Oct. 12, 2015
|
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<!--Table of Child-Links-->
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<A NAME="CHILD_LINKS"></A>
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<UL CLASS="ChildLinks">
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<LI><A NAME="tex2html15"
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HREF="node1.html">Abstract</A>
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<UL>
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<LI><A NAME="tex2html16"
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HREF="node2.html">Contents</A>
|
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HREF="node1.html">Abstract</A>
|
||||
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|
||||
HREF="node3.html">General Overview</A>
|
||||
HREF="node2.html">Contents</A>
|
||||
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HREF="node4.html">Code Distribution</A>
|
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HREF="node3.html">General Overview</A>
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|
||||
HREF="node4.html">Code Distribution</A>
|
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<LI><A NAME="tex2html20"
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||||
HREF="node5.html">Configuring and Building MLD2P4</A>
|
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<UL>
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<LI><A NAME="tex2html20"
|
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HREF="node6.html">Prerequisites</A>
|
||||
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|
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HREF="node7.html">Optional third party libraries</A>
|
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HREF="node6.html">Prerequisites</A>
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HREF="node8.html">Configuration options</A>
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HREF="node7.html">Optional third party libraries</A>
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HREF="node9.html">Bug reporting</A>
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HREF="node8.html">Configuration options</A>
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HREF="node9.html">Bug reporting</A>
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|
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|
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<LI><A NAME="tex2html26"
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|
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<UL>
|
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|
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HREF="node12.html">Multi-level Schwarz Preconditioners</A>
|
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|
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HREF="node12.html">Multi-level Schwarz Preconditioners</A>
|
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<LI><A NAME="tex2html28"
|
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|
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<BR>
|
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|
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<LI><A NAME="tex2html29"
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<UL>
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|
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<LI><A NAME="tex2html30"
|
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HREF="node15.html">Examples</A>
|
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</UL>
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<BR>
|
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<LI><A NAME="tex2html30"
|
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<LI><A NAME="tex2html31"
|
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HREF="node16.html">User Interface</A>
|
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<UL>
|
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<LI><A NAME="tex2html31"
|
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HREF="node17.html">Subroutine mld_precinit</A>
|
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<LI><A NAME="tex2html32"
|
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HREF="node18.html">Subroutine mld_precset</A>
|
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HREF="node17.html">Subroutine mld_precinit</A>
|
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<LI><A NAME="tex2html33"
|
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HREF="node19.html">Subroutine mld_precbld</A>
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HREF="node18.html">Subroutine mld_precset</A>
|
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<LI><A NAME="tex2html34"
|
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HREF="node20.html">Subroutine mld_precaply</A>
|
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HREF="node19.html">Subroutine mld_precbld</A>
|
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<LI><A NAME="tex2html35"
|
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