mld2p4-2:

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Added aggregation ordering option to docs.
stopcriterion
Salvatore Filippone 9 years ago
parent 875443efe7
commit c592733a8e

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<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>
@ -77,70 +76,70 @@ Oct. 12, 2015
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<LI><A NAME="tex2html16"
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HREF="node1.html">Abstract</A>
<LI><A NAME="tex2html17"
HREF="node3.html">General Overview</A>
HREF="node2.html">Contents</A>
<LI><A NAME="tex2html18"
HREF="node4.html">Code Distribution</A>
HREF="node3.html">General Overview</A>
<LI><A NAME="tex2html19"
HREF="node4.html">Code Distribution</A>
<LI><A NAME="tex2html20"
HREF="node5.html">Configuring and Building MLD2P4</A>
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<LI><A NAME="tex2html20"
HREF="node6.html">Prerequisites</A>
<LI><A NAME="tex2html21"
HREF="node7.html">Optional third party libraries</A>
HREF="node6.html">Prerequisites</A>
<LI><A NAME="tex2html22"
HREF="node8.html">Configuration options</A>
HREF="node7.html">Optional third party libraries</A>
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<BR>
<LI><A NAME="tex2html25"
<LI><A NAME="tex2html26"
HREF="node11.html">Multi-level Domain Decomposition Background</A>
<UL>
<LI><A NAME="tex2html26"
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
<LI><A NAME="tex2html27"
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
<LI><A NAME="tex2html28"
HREF="node13.html">Smoothed Aggregation</A>
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<UL>
<LI><A NAME="tex2html31"
HREF="node17.html">Subroutine mld_precinit</A>
<LI><A NAME="tex2html32"
HREF="node18.html">Subroutine mld_precset</A>
HREF="node17.html">Subroutine mld_precinit</A>
<LI><A NAME="tex2html33"
HREF="node19.html">Subroutine mld_precbld</A>
HREF="node18.html">Subroutine mld_precset</A>
<LI><A NAME="tex2html34"
HREF="node20.html">Subroutine mld_precaply</A>
HREF="node19.html">Subroutine mld_precbld</A>
<LI><A NAME="tex2html35"
HREF="node21.html">Subroutine mld_precfree</A>
HREF="node20.html">Subroutine mld_precaply</A>
<LI><A NAME="tex2html36"
HREF="node21.html">Subroutine mld_precfree</A>
<LI><A NAME="tex2html37"
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@ -87,30 +86,29 @@ the user interface of MLD2P4.
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<H1><A NAME="SECTION00060000000000000000"></A><A NAME="sec:background"></A>
@ -58,7 +57,7 @@ Multi-level Domain Decomposition Background
</H1>
<P>
<SPAN CLASS="textit">Domain Decomposition</SPAN> (DD) preconditioners, coupled with Krylov iterative
<I>Domain Decomposition</I> (DD) preconditioners, coupled with Krylov iterative
solvers, are widely used in the parallel solution of large and sparse linear systems.
These preconditioners are based on the divide and conquer technique: the matrix
to be preconditioned is divided into submatrices, a ``local'' linear system
@ -71,13 +70,13 @@ solution of the original problem from the local solutions
[<A
HREF="node25.html#Cai_Widlund_92">6</A>,<A
HREF="node25.html#dd1_94">7</A>,<A
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>
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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].
<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&nbsp;[<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"
@ -288,26 +288,26 @@ using some estimate of the spectral radius of <IMG
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@ -59,7 +59,7 @@ 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="node25.html#PSBLASGUIDE">15</A>].
HREF="node25.html#PSBLASGUIDE">16</A>].
The following steps are required:
<OL>
@ -131,7 +131,7 @@ for the coarsest-level solvers available in MLD2P4).
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="924"></A>
<DIV ALIGN="CENTER"><A NAME="943"></A>
<TABLE>
<CAPTION><STRONG>Table 1:</STRONG>
Preconditioner types, corresponding strings and default choices.
@ -197,32 +197,32 @@ Preconditioner types, corresponding strings and default choices.
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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@ -24,31 +24,30 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<H2><A NAME="SECTION00071000000000000000"></A><A NAME="sec:examples"></A>
@ -76,7 +75,7 @@ in the directory <code>examples/fileread</code> of the MLD2P4 tree (see
Section&nbsp;<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>].
HREF="node25.html#PSBLASGUIDE">16</A>].
<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
<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&nbsp;[<A
HREF="node25.html#UMFPACK">9</A>].
Figure&nbsp;<A HREF="#fig:ex_3lhm">4</A> shows how to set a three-level preconditioner similar to the one of&nbsp;<A HREF="#fig:ex_3lh">3</A>, but the coarsest-level systems is solved with the multifrontal factorization from MUMPS&nbsp;[<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&nbsp;<A HREF="#fig:ex_3la">4</A> shows how to
Figure&nbsp;<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&nbsp;<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&nbsp;<A HREF="#fig:ex_3lh">3</A>-<A HREF="#fig:ex_3la">4</A> are
The code fragments shown in in Figures&nbsp;<A HREF="#fig:ex_3lh">3</A>&nbsp;<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&nbsp;<A HREF="#fig:ex_1l">5</A> shows the setup of a one-level
Finally, Figure&nbsp;<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>
<DIV ALIGN="CENTER">
</DIV>
<P>
<DIV ALIGN="CENTER">
</DIV></TD></TR>
</TABLE>
</DIV>
<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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<H1><A NAME="SECTION00080000000000000000"></A><A NAME="sec:userinterface"></A>
@ -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.
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HREF="node20.html">Subroutine mld_precaply</A>
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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>
<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>&nbsp;</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>
<P>
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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>&nbsp;</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>&nbsp;</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&nbsp;<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>&nbsp;</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&nbsp;int.&nbsp;num.&nbsp;<SPAN CLASS="MATH"><IMG
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>any&nbsp;int.&nbsp;num.&nbsp;<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&nbsp;int.&nbsp;num.&nbsp;<SPAN CLASS="MATH"><IMG
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<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&nbsp;real&nbsp;num.&nbsp;<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&nbsp;real&nbsp;num.&nbsp;<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&nbsp;int.&nbsp;num.&nbsp;<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&nbsp;real&nbsp;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&nbsp;real&nbsp;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&nbsp;nonnegative&nbsp;real&nbsp;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&nbsp;int.&nbsp;num.&nbsp;<SPAN CLASS="MATH"><IMG
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<IMG
WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img99.png"
ALT="$&gt; 0$"></SPAN></TD>
ALT="$&gt; 0$"></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&nbsp;int.&nbsp;num.&nbsp;<SPAN CLASS="MATH"><IMG
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<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&nbsp;real.&nbsp;num.&nbsp;<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&nbsp;real.&nbsp;num.&nbsp;<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>
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<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>&nbsp;</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>&nbsp;</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>&nbsp;</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.
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@ -53,64 +52,64 @@ Contents</A>
</H2>
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<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>
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HREF="node8.html">Configuration options</A>
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HREF="node10.html">Example and test programs</A>
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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>
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<BR>
<LI><A NAME="tex2html74"
<LI><A NAME="tex2html75"
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<UL>
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<BR>
<LI><A NAME="tex2html76"
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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>
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<LI><A NAME="tex2html83"
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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>&nbsp;</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>&nbsp;</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>&nbsp;</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>
@ -143,39 +142,39 @@ and hence it is completely transparent to the user.
<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"
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>&nbsp;</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.
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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>&nbsp;</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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<H2><A NAME="SECTION00086000000000000000"></A><A NAME="sec:precdescr"></A>
@ -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>
<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(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>&nbsp;</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>

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<H1><A NAME="SECTION00090000000000000000"></A><A NAME="sec:errors"></A>
@ -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
User's Guide [<A
HREF="node25.html#PSBLASGUIDE">15</A>].
HREF="node25.html#PSBLASGUIDE">16</A>].
<P>

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@ -102,35 +102,44 @@ T.A.&nbsp;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/&nbsp;davis/</TT>)<P></P><DT><A NAME="SUPERLU">10</A>
(See also <TT>http://www.cise.ufl.edu/&nbsp;davis/</TT>)
<P>
<P></P><DT><A NAME="MUMPS">10</A>
<DD>
P.R.&nbsp;Amestoy, C.&nbsp;Ashcraft, O.&nbsp;Boiteau, A.&nbsp;Buttari, J.&nbsp;L'Excellent, C.&nbsp;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.&nbsp;Demmel, S.C.&nbsp;Eisenstat, J.R.&nbsp;Gilbert, X.S.&nbsp;Li and J.W.H.&nbsp;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.&nbsp;J.&nbsp;Dongarra, J.&nbsp;Du Croz, I.&nbsp;S.&nbsp;Duff, S.&nbsp;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.&nbsp;J.&nbsp;Dongarra, J.&nbsp;Du Croz, S.&nbsp;Hammarling, R.&nbsp;J.&nbsp;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.&nbsp;J.&nbsp;Dongarra and R.&nbsp;C.&nbsp;Whaley,
<EM>A User's Guide to the BLACS v.&nbsp;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.&nbsp;Efstathiou, J.&nbsp;G.&nbsp;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.&nbsp;Filippone, A.&nbsp;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.&nbsp;Filippone, M.&nbsp;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.&nbsp;Gropp, S.&nbsp;Huss-Lederman, A.&nbsp;Lumsdaine, E.&nbsp;Lusk, B.&nbsp;Nitzberg, W.&nbsp;Saphir, M.&nbsp;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.&nbsp;L.&nbsp;Lawson, R.&nbsp;J.&nbsp;Hanson, D.&nbsp;Kincaid, F.&nbsp;T.&nbsp;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.&nbsp;S.&nbsp;Li, J.&nbsp;W.&nbsp;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.&nbsp;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.&nbsp;Smith, P.&nbsp;Bjorstad, W.&nbsp;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.&nbsp;Snir, S.&nbsp;Otto, S.&nbsp;Huss-Lederman, D.&nbsp;Walker, J.&nbsp;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.&nbsp;St&#252;ben,
<EM>Algebraic Multigrid (AMG): an Introduction with Applications</EM>,
in A.&nbsp;Sch&#252;ller, U.&nbsp;Trottenberg, C.&nbsp;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.&nbsp;S.&nbsp;Tuminaro, C.&nbsp;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.&nbsp;Vanek, J.&nbsp;Mandel and M.&nbsp;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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@ -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
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@ -1,4 +1,4 @@
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<H1><A NAME="SECTION00030000000000000000"></A><A NAME="sec:overview"></A>
@ -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>&nbsp;[<A
HREF="node25.html#dd2_96">22</A>],
</SMALL>PSBLAS (MLD2P4) provides <I>multi-level Schwarz preconditioners</I>&nbsp;[<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">
<!-- MATH
\begin{equation}
Ax=b,
\end{equation}
-->
<A NAME="system1"></A>
<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&nbsp;[<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&nbsp;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&nbsp;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>&nbsp;[<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>&nbsp;[<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&nbsp;[<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&nbsp;[<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&nbsp;<A HREF="node23.html#sec:errors">7</A>. The copyright terms conc
of MLD2P4 are reported in Appendix&nbsp;<A HREF="node24.html#sec:license">A</A>.
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<H1><A NAME="SECTION00040000000000000000"></A><A NAME="sec:distribution"></A>
@ -76,7 +75,7 @@ account when treating derived works.
The library defines a version string with the
constant
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
\verb|mld_version_string_|

@ -1,4 +1,4 @@
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<H1><A NAME="SECTION00050000000000000000"></A><A NAME="sec:building"></A>
@ -80,16 +79,16 @@ real and complex data, in both single and double precision.
<!--Table of Child-Links-->
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<LI><A NAME="tex2html122"
HREF="node6.html">Prerequisites</A>
<UL>
<LI><A NAME="tex2html123"
HREF="node7.html">Optional third party libraries</A>
HREF="node6.html">Prerequisites</A>
<LI><A NAME="tex2html124"
HREF="node8.html">Configuration options</A>
HREF="node7.html">Optional third party libraries</A>
<LI><A NAME="tex2html125"
HREF="node9.html">Bug reporting</A>
HREF="node8.html">Configuration options</A>
<LI><A NAME="tex2html126"
HREF="node9.html">Bug reporting</A>
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HREF="node10.html">Example and test programs</A>
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@ -61,9 +60,9 @@ The following base libraries are needed:
<DL>
<DT><STRONG>BLAS</STRONG></DT>
<DD>[<A
HREF="node25.html#blas3">11</A>,<A
HREF="node25.html#blas2">12</A>,<A
HREF="node25.html#blas1">19</A>] Many vendors provide optimized versions
HREF="node25.html#blas3">12</A>,<A
HREF="node25.html#blas2">13</A>,<A
HREF="node25.html#blas1">20</A>] Many vendors provide optimized versions
of the Basic Linear Algebra Subprograms; if no vendor version is
available for a given platform, the ATLAS software
(<code>http://math-atlas.sourceforge.net/</code>)
@ -78,15 +77,15 @@ The following base libraries are needed:
</DD>
<DT><STRONG>MPI</STRONG></DT>
<DD>[<A
HREF="node25.html#MPI2">18</A>,<A
HREF="node25.html#MPI1">23</A>] A version of MPI is available on most
HREF="node25.html#MPI2">19</A>,<A
HREF="node25.html#MPI1">24</A>] A version of MPI is available on most
high-performance computing systems;
</DD>
<DT><STRONG>PSBLAS</STRONG></DT>
<DD>[<A
HREF="node25.html#PSBLASGUIDE">15</A>,<A
HREF="node25.html#psblas_00">17</A>] Parallel Sparse BLAS is
HREF="node25.html#PSBLASGUIDE">16</A>,<A
HREF="node25.html#psblas_00">18</A>] Parallel Sparse BLAS is
available from
<BR><code>http://www.ce.uniroma2.it/psblas</code>; version
3.3 (or later) is required. Indeed, all the prerequisites
@ -99,31 +98,7 @@ usually this means that they should all be built with the same
compiler as MLD2P4.
<P>
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@ -74,7 +73,7 @@ for multilevel preconditioners may change to reflect their presence.
</DD>
<DT><STRONG>SuperLU</STRONG></DT>
<DD>[<A
HREF="node25.html#SUPERLU">10</A>]
HREF="node25.html#SUPERLU">11</A>]
A sparse direct factorization package available from
<BR> <code>http://crd.lbl.gov/~xiaoye/SuperLU/</code>; provides serial
factorization and triangular system solution for single and double precision,
@ -83,15 +82,16 @@ for multilevel preconditioners may change to reflect their presence.
</DD>
<DT><STRONG>SuperLU_Dist</STRONG></DT>
<DD>[<A
HREF="node25.html#SUPERLUDIST">20</A>]
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.
</DD>
<DT><STRONG>MUMPS</STRONG></DT>
<DD>[]
MUMPS (“Multifrontal Massively Parallel Solver”) is a sparse, direct factorization
<DD>[<A
HREF="node25.html#MUMPS">10</A>]
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
@ -100,30 +100,29 @@ for multilevel preconditioners may change to reflect their presence.
<P>
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<H2><A NAME="SECTION00053000000000000000">
@ -208,6 +207,10 @@ generated the file <code>Make.inc</code> which will then be used by all
Makefiles in the directory tree; this file will be copied in the
install directory under the name <code>Make.inc.MLD2P4</code>.
<P>
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.
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).
<P>
To build the library the user will now enter
<PRE>
@ -216,8 +219,30 @@ make
followed (optionally) by
<PRE>
make install
</PRE>
<BR><HR>
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<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>
@ -77,70 +76,70 @@ Oct. 12, 2015
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HREF="node1.html">Abstract</A>
<LI><A NAME="tex2html17"
HREF="node3.html">General Overview</A>
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<LI><A NAME="tex2html18"
HREF="node4.html">Code Distribution</A>
HREF="node3.html">General Overview</A>
<LI><A NAME="tex2html19"
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<LI><A NAME="tex2html20"
HREF="node5.html">Configuring and Building MLD2P4</A>
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<LI><A NAME="tex2html20"
HREF="node6.html">Prerequisites</A>
<LI><A NAME="tex2html21"
HREF="node7.html">Optional third party libraries</A>
HREF="node6.html">Prerequisites</A>
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HREF="node7.html">Optional third party libraries</A>
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<UL>
<LI><A NAME="tex2html26"
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
<LI><A NAME="tex2html27"
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
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<BR>
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<LI><A NAME="tex2html31"
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<UL>
<LI><A NAME="tex2html31"
HREF="node17.html">Subroutine mld_precinit</A>
<LI><A NAME="tex2html32"
HREF="node18.html">Subroutine mld_precset</A>
HREF="node17.html">Subroutine mld_precinit</A>
<LI><A NAME="tex2html33"
HREF="node19.html">Subroutine mld_precbld</A>
HREF="node18.html">Subroutine mld_precset</A>
<LI><A NAME="tex2html34"
HREF="node20.html">Subroutine mld_precaply</A>
HREF="node19.html">Subroutine mld_precbld</A>
<LI><A NAME="tex2html35"
HREF="node21.html">Subroutine mld_precfree</A>
HREF="node20.html">Subroutine mld_precaply</A>
<LI><A NAME="tex2html36"
HREF="node21.html">Subroutine mld_precfree</A>
<LI><A NAME="tex2html37"
HREF="node22.html">Subroutine mld_precdescr</A>
</UL>
<BR>
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