fdurastante/amg4psblas
1
0
Fork 0
mirror of https://github.com/sfilippone/amg4psblas.git synced 2026-10-06 22:55:12 +00:00
Code Issues Packages Projects Releases Wiki Activity

mld2p4-2:

Browse Source 
docs/html/userhtml.html
 docs/mld2p4-2.1-guide.pdf
 docs/src/abstract.tex
 docs/src/background.tex
 docs/src/bibliography.tex
 docs/src/building.tex
 docs/src/distribution.tex
 docs/src/gettingstarted.tex
 docs/src/overview.tex
 docs/src/userguide.tex
 docs/src/userinterface.tex
 mlprec/impl/mld_ccprecset.F90
 mlprec/impl/mld_cprecset.F90
 mlprec/impl/mld_csp_renum.f90
 mlprec/impl/mld_dcprecset.F90
 mlprec/impl/mld_dprecset.F90
 mlprec/impl/mld_dsp_renum.f90
 mlprec/impl/mld_scprecset.F90
 mlprec/impl/mld_sprecset.F90
 mlprec/impl/mld_ssp_renum.f90
 mlprec/impl/mld_z_onelev_impl.f90
 mlprec/impl/mld_zcprecset.F90
 mlprec/impl/mld_zprecset.F90
 mlprec/impl/mld_zsp_renum.f90
 mlprec/mld_base_prec_type.F90

Take out SUB_REN.
Update docs.
This commit is contained in:
Salvatore Filippone
2017-04-18 13:48:34 +00:00
parent 4304f1e2c9
commit 816047d48c
163 changed files with 7987 additions and 9042 deletions
Download Patch File Download Diff File Expand all files Collapse all files
docs/html/node14.html
+87 -105
View File
@@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds
<BODY >
<!--Navigation Panel-->
<A NAME="tex2html237"
<A NAME="tex2html248"
HREF="node15.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
<A NAME="tex2html233"
<A NAME="tex2html244"
HREF="userhtml.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
<A NAME="tex2html227"
<A NAME="tex2html238"
HREF="node13.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
<A NAME="tex2html235"
<A NAME="tex2html246"
HREF="node2.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html238"
<B> Next:</B> <A NAME="tex2html249"
HREF="node15.html">Examples</A>
<B> Up:</B> <A NAME="tex2html234"
<B> Up:</B> <A NAME="tex2html245"
HREF="userhtml.html">userhtml</A>
<B> Previous:</B> <A NAME="tex2html228"
<B> Previous:</B> <A NAME="tex2html239"
HREF="node13.html">Smoothed Aggregation</A>
&nbsp; <B> <A NAME="tex2html236"
&nbsp; <B> <A NAME="tex2html247"
HREF="node2.html">Contents</A></B>
<BR>
<BR>
@@ -58,8 +58,8 @@ Getting Started
<P>
We describe the basics for building and applying MLD2P4 one-level and multi-level
Schwarz preconditioners with the Krylov solvers included in PSBLAS [<A
HREF="node27.html#PSBLASGUIDE">16</A>].
(i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS [<A
HREF="node28.html#PSBLASGUIDE">16</A>].
The following steps are required:
<OL>
@@ -73,77 +73,56 @@ The following steps are required:
</LI>
<LI><I>Allocate and initialize the preconditioner data structure, according to
a preconditioner type chosen by the user</I>. This is performed by the routine
<code>mld_precinit</code>, which also sets defaults for each preconditioner
type selected by the user. The defaults associated to each preconditioner
type are given in Table&nbsp;<A HREF="#tab:precinit">1</A>, where the strings used by
<code>mld_precinit</code> to identify the preconditioner types are also given.
<code>init</code>, which also sets defaults for each preconditioner
type selected by the user. The preconditioner types and the defaults associated
with them are given in Table&nbsp;<A HREF="#tab:precinit">1</A>, where the strings used by
<code>init</code> to identify the preconditioner types are also given.
Note that these strings are valid also if uppercase letters are substituted by
corresponding lowercase ones.
</LI>
<LI><I>Modify the aggregation parameters.</I> This is performed by
the routine <code>mld_precset</code>.
This routine must be called only if the user wants to modify the default values
of the parameters associated to the aggregation hierarchy construction.
Examples of use of <code>mld_precset</code> are given in
Section&nbsp;<A HREF="node15.html#sec:examples">5.1</A>; a complete list of all the
preconditioner parameters and their allowed and default values is provided in
Section&nbsp;<A HREF="node16.html#sec:userinterface">6</A>, Tables&nbsp;<A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">6</A>.
</LI>
<LI><I>Build the aggregation hierarchy for a given matrix.</I> This is performed by
the routine <code>mld_hierarchy_bld</code>.
</LI>
<LI><I>Modify the selected preconditioner type, by properly setting
preconditioner parameters.</I> This is performed by the routine <code>mld_precset</code>.
preconditioner parameters.</I> This is performed by the routine <code>set</code>.
This routine must be called only if the user wants to modify the default values
of the parameters associated to the selected preconditioner type, to obtain a variant
of the preconditioner. Examples of use of <code>mld_precset</code> are given in
of the parameters associated with the selected preconditioner type, to obtain a variant
of that preconditioner. Examples of use of <code>set</code> are given in
Section&nbsp;<A HREF="node15.html#sec:examples">5.1</A>; a complete list of all the
preconditioner parameters and their allowed and default values is provided in
Section&nbsp;<A HREF="node16.html#sec:userinterface">6</A>, Tables&nbsp;<A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">6</A>.
Section&nbsp;<A HREF="node16.html#sec:userinterface">6</A>, Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>.
</LI>
<LI><I>Build the preconditioner for a given matrix.</I> This is performed by
the routine <code>mld_smoothers_bld</code>.
<LI><I>Build the preconditioner for a given matrix</I>. If the selected preconditioner
is multi-level, then two steps must be performed, as specified next.
<DL COMPACT>
<DT>4.1</DT>
<DD><I>Build the aggregation hierarchy for a given matrix.</I> This is
performed by the routine <code>hierarchy_bld</code>.
</DD>
<DT>4.2</DT>
<DD><I>Build the preconditioner for a given matrix.</I> This is performed
by the routine <code>smoothers_bld</code>.
</DD>
</DL>
If the selected preconditioner is one-level, it is built in a single step,
performed by the routine <code>bld</code>.
</LI>
<LI><I>Apply the preconditioner at each iteration of a Krylov solver.</I>
This is performed by the routine <code>mld_precaply</code>. When using the PSBLAS Krylov solvers,
this step is completely transparent to the user, since <code>mld_precaply</code> is called
This is performed by the routine <code>aply</code>. When using the PSBLAS Krylov solvers,
this step is completely transparent to the user, since <code>aply</code> is called
by the PSBLAS routine implementing the Krylov solver (<code>psb_krylov</code>).
</LI>
<LI><I>Free the preconditioner data structure</I>. This is performed by
the routine <code>mld_</code> <code>precfree</code>. This step is complementary to step 1 and should
the routine <code>free</code>. This step is complementary to step 1 and should
be performed when the preconditioner is no more used.
</LI>
</OL>
A detailed description of the above routines is given in Section&nbsp;<A HREF="node16.html#sec:userinterface">6</A>.
<P>
All the previous routines are available as methods of the preconditioner object.
A detailed description of them is given in Section&nbsp;<A HREF="node16.html#sec:userinterface">6</A>.
Examples showing the basic use of MLD2P4 are reported in Section&nbsp;<A HREF="node15.html#sec:examples">5.1</A>.
<P>
Note that the Fortran 95 module <code>mld_prec_mod</code>, containing the definition of the
preconditioner data type and the interfaces to the routines of MLD2P4,
must be used in any program calling such routines.
The modules <code>psb_base_mod</code>, for the sparse matrix and communication descriptor
data types, and <code>psb_krylov_mod</code>, for interfacing with the
Krylov solvers, must be also used (see Section&nbsp;<A HREF="node15.html#sec:examples">5.1</A>).
<P>
<BR><B>Remark 1.</B> The coarsest-level solver used by the default two-level
preconditioner has been chosen by taking into account that, on parallel
machines, it often leads to the smallest execution time when applied to
linear systems coming from finite-difference discretizations of basic
elliptic PDE problems, considered as standard tests for multi-level Schwarz
preconditioners [<A
HREF="node27.html#aaecc_07">3</A>,<A
HREF="node27.html#apnum_07">4</A>]. However, this solver does
not necessarily correspond to the smallest number of iterations of the
preconditioned Krylov method, which is usually obtained by applying
a direct solver to the coarsest-level system, e.g. based on the LU
factorization (see Section&nbsp;<A HREF="node16.html#sec:userinterface">6</A>
for the coarsest-level solvers available in MLD2P4).
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="949"></A>
<DIV ALIGN="CENTER"><A NAME="962"></A>
<TABLE>
<CAPTION><STRONG>Table 1:</STRONG>
Preconditioner types, corresponding strings and default choices.
@@ -152,90 +131,93 @@ Preconditioner types, corresponding strings and default choices.
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><SMALL>TYPE</SMALL></TD>
<TD ALIGN="LEFT"><SMALL>STRING</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=221><SMALL>DEFAULT PRECONDITIONER</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><SMALL>STRING</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232><SMALL>DEFAULT PRECONDITIONER</SMALL></TD>
</TR>
<TR><TD ALIGN="LEFT">No preconditioner</TD>
<TD ALIGN="LEFT"><code>'NOPREC'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=221>Considered only to use the PSBLAS
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'NOPREC'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Considered only to use the PSBLAS
Krylov solvers with no preconditioner.</TD>
</TR>
<TR><TD ALIGN="LEFT">Diagonal</TD>
<TD ALIGN="LEFT"><code>'DIAG'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=221>--</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'DIAG'</code> or <code>'JACOBI'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Diagonal preconditioner.
For any zero diagonal entry of the matrix to be preconditioned,
the corresponding entry of he preconditioner is set to&nbsp;1.</TD>
</TR>
<TR><TD ALIGN="LEFT">Block Jacobi</TD>
<TD ALIGN="LEFT"><code>'BJAC'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=221>Block Jacobi with ILU(0) on the local blocks.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'BJAC'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Block-Jacobi with ILU(0) on the local blocks.</TD>
</TR>
<TR><TD ALIGN="LEFT">Additive Schwarz</TD>
<TD ALIGN="LEFT"><code>'AS'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=221>Restricted Additive Schwarz (RAS),
with overlap 1 and ILU(0) on the local blocks.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'AS'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Restricted Additive Schwarz (RAS),
with overlap&nbsp;1 and ILU(0) on the local blocks.</TD>
</TR>
<TR><TD ALIGN="LEFT">Multilevel</TD>
<TD ALIGN="LEFT"><code>'ML'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=221>Multi-level hybrid preconditioner (additive on the
same level and multiplicative through the levels),
with pre- and post-smoothing.
Target aggregation size: cubic
root of the size at the finest
level. Smoother: RAS with overlap 1 and ILU(0)
on the local blocks.
Aggregation: decoupled smoothed aggregation with
threshold <IMG
WIDTH="45" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img88.png"
ALT="$\theta = 0$">.
Coarsest matrix: distributed among the processors.
Coarsest-level solver:
4 sweeps of the block-Jacobi solver,
with LU or ILU factorization of the blocks
(MUMPS, or UMFPACK for the double precision versions and
SuperLU for the single precision ones, if the packages
have been installed; ILU(0), otherwise).</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'ML'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>V-cycle with one hybrid forward Gauss-Seidel
(GS) sweep as pre-smoother and one hybrid backward
GS sweep as post-smoother, basic smoothed aggregation
as coarsening algorithm, and LU (plus triangular solve)
as coarsest-level solver. See the default values in
Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>
for further details of the preconditioner.</TD>
</TR>
</TABLE>
</DIV>
<P>
</TD></TR>
</DIV></TD></TR>
</TABLE>
</DIV><P></P>
<BR>
<P>
Note that the module <code>mld_prec_mod</code>, containing the definition of the
preconditioner data type and the interfaces to the routines of MLD2P4,
must be used in any program calling such routines.
The modules <code>psb_base_mod</code>, for the sparse matrix and communication descriptor
data types, and <code>psb_krylov_mod</code>, for interfacing with the
Krylov solvers, must be also used (see Section&nbsp;<A HREF="node15.html#sec:examples">5.1</A>).
<BR>
<P>
<B>Remark 1.</B> Coarsest-level solvers based on the LU factorization,
such as those implemented in UMFPACK, MUMPS, SuperLU, and SuperLU_Dist,
usually lead to smaller numbers of preconditioned Krylov
iterations than inexact solvers, when the linear system comes from
a standard discretization of basic scalar elliptic PDE problems. However,
this does not necessarily correspond to the smallest execution time
on parallel computers.
<P>
<BR><HR>
<!--Table of Child-Links-->
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL>
<LI><A NAME="tex2html239"
<LI><A NAME="tex2html250"
HREF="node15.html">Examples</A>
</UL>
<!--End of Table of Child-Links-->
<HR>
<!--Navigation Panel-->
<A NAME="tex2html237"
<A NAME="tex2html248"
HREF="node15.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
<A NAME="tex2html233"
<A NAME="tex2html244"
HREF="userhtml.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
<A NAME="tex2html227"
<A NAME="tex2html238"
HREF="node13.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
<A NAME="tex2html235"
<A NAME="tex2html246"
HREF="node2.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html238"
<B> Next:</B> <A NAME="tex2html249"
HREF="node15.html">Examples</A>
<B> Up:</B> <A NAME="tex2html234"
<B> Up:</B> <A NAME="tex2html245"
HREF="userhtml.html">userhtml</A>
<B> Previous:</B> <A NAME="tex2html228"
<B> Previous:</B> <A NAME="tex2html239"
HREF="node13.html">Smoothed Aggregation</A>
&nbsp; <B> <A NAME="tex2html236"
&nbsp; <B> <A NAME="tex2html247"
HREF="node2.html">Contents</A></B>
<!--End of Navigation Panel-->