mld2p4: final fixes for 1.1 release.

stopcriterion
Salvatore Filippone 16 years ago
parent 5e0cfebc6d
commit 73dac6d963

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@ -74,13 +74,13 @@ 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">20</A>].
HREF="node25.html#dd2_96">21</A>].
<P>
<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">20</A>]).
HREF="node25.html#dd2_96">21</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
@ -99,7 +99,7 @@ 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">20</A>]. The same reasoning can be applied starting
HREF="node25.html#dd2_96">21</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 <I>multi-level</I> preconditioners.
@ -123,24 +123,25 @@ 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">22</A>].
HREF="node25.html#StubenGMD69_99">23</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 <I>smoothed
aggregation</I> algorithm [<A
HREF="node25.html#BREZINA_VANEK">1</A>,<A
HREF="node25.html#VANEK_MANDEL_BREZINA">24</A>]. A decoupled version
HREF="node25.html#VANEK_MANDEL_BREZINA">25</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">23</A>]. In the next two subsections we provide
HREF="node25.html#TUMINARO_TONG">24</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
HREF="node25.html#para_04">2</A>,<A
HREF="node25.html#aaecc_07">3</A>,<A
HREF="node25.html#apnum_07">4</A>,,<A
HREF="node25.html#dd2_96">20</A>].
HREF="node25.html#apnum_07">4</A>,<A
HREF="node25.html#MLD2P4_TOMS">8</A>,<A
HREF="node25.html#dd2_96">21</A>].
<P>
<BR><HR>

@ -299,7 +299,7 @@ ILU(<IMG
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img35.png"
ALT="$p,t$">) [<A
HREF="node25.html#Saad_book">19</A>, Chapter 10].
HREF="node25.html#Saad_book">20</A>, Chapter 10].
<P>
A variant of the classical AS preconditioner that outperforms it
@ -307,7 +307,7 @@ 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">13</A>]. It
HREF="node25.html#EFSTATHIOU">14</A>]. It
is obtained by zeroing the components of <IMG
WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img32.png"
@ -391,7 +391,7 @@ of <IMG
SRC="img10.png"
ALT="$W$"> increases [<A
HREF="node25.html#dd1_94">7</A>,<A
HREF="node25.html#dd2_96">20</A>]. To reduce the dependency
HREF="node25.html#dd2_96">21</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
@ -646,12 +646,12 @@ 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">20</A>, Chapter 3]).
HREF="node25.html#dd2_96">21</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">20</A>, Chapter 3].
HREF="node25.html#dd2_96">21</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 @@ and the corresponding basic preconditioner at each level <IMG
SRC="img65.png"
ALT="$A_1=A$">, while the related restriction operator is
denoted by <IMG
WIDTH="23" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
WIDTH="22" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img66.png"
ALT="$R_l$">.
@ -724,14 +724,14 @@ $w = y_1$;
}$
-->
<IMG
WIDTH="429" HEIGHT="435" ALIGN="BOTTOM" BORDER="0"
WIDTH="430" HEIGHT="435" ALIGN="BOTTOM" BORDER="0"
SRC="img67.png"
ALT="\framebox{
\begin{minipage}{.85\textwidth} {\small
\begin{tabbing}
\quad \=\quad...
...= y_l+r_l$\\
\textbf{endfor} [1mm]
\textbf{endfor} \ [1mm]
$w = y_1$;
\end{tabbing}}
\end{minipage}}">

@ -70,7 +70,7 @@ 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">24</A>].
HREF="node25.html#VANEK_MANDEL_BREZINA">25</A>].
The basic idea of this algorithm is to build a coarse set of vertices
<IMG
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
@ -120,7 +120,7 @@ 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">24</A>], a modification of
HREF="node25.html#VANEK_MANDEL_BREZINA">25</A>], a modification of
this algorithm has been actually considered,
in which each aggregate <IMG
WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
@ -159,7 +159,7 @@ for a given <!-- MATH
ALT="$\theta \in [0,1]$">.
Since this algorithm has a sequential nature, a <I>decoupled</I> version of
it has been chosen, where each processor <IMG
WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
WIDTH="10" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img74.png"
ALT="$i$"> independently applies the algorithm to
the set of vertices <IMG
@ -178,7 +178,7 @@ 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">23</A>].
HREF="node25.html#TUMINARO_TONG">24</A>].
<P>
The prolongator <IMG
@ -189,7 +189,7 @@ The prolongator <IMG
$P \in \Re^{n \times n_C}$
-->
<IMG
WIDTH="89" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
WIDTH="90" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
SRC="img77.png"
ALT="$P \in \Re^{n \times n_C}$">, defined as
<BR>
@ -257,7 +257,7 @@ 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">22</A>].
HREF="node25.html#StubenGMD69_99">23</A>].
A simple choice for <IMG
WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img83.png"
@ -286,7 +286,7 @@ where the value of <IMG
SRC="img85.png"
ALT="$\omega$"> can be chosen
using some estimate of the spectral radius of <IMG
WIDTH="51" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img86.png"
ALT="$D^{-1}A$"> [<A
HREF="node25.html#BREZINA_VANEK">1</A>].

@ -63,7 +63,7 @@ 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">14</A>].
HREF="node25.html#PSBLASGUIDE">15</A>].
The following steps are required:
<OL>

@ -79,7 +79,7 @@ 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">14</A>].
HREF="node25.html#PSBLASGUIDE">15</A>].
<P>
The setup and application of the default multi-level
@ -165,7 +165,7 @@ Figure&nbsp;<A HREF="#fig:ex_3lh">3</A> shows how to set a three-level hybrid Sc
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">8</A>].
HREF="node25.html#UMFPACK">9</A>].
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

@ -90,7 +90,7 @@ i.e.
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img21.png"
ALT="$v$"> and <IMG
WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img88.png"
ALT="$w$"> involved in
the preconditioner application <IMG

@ -198,7 +198,7 @@ Parameters defining the one-level preconditioner used as smoother.
<TR><TD ALIGN="LEFT"><code>mld_sub_ovr_</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="img89.png"
ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">1</TD>
@ -240,7 +240,7 @@ Parameters defining the one-level preconditioner used as smoother.
<TR><TD ALIGN="LEFT"><code>mld_sub_fillin_</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="img89.png"
ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">0</TD>
@ -252,7 +252,7 @@ Parameters defining the one-level preconditioner used as smoother.
<TR><TD ALIGN="LEFT"><code>mld_sub_iluthrs_</code></TD>
<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="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img89.png"
ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">0</TD>
@ -332,7 +332,7 @@ Parameters defining the aggregation algorithm.
smoothed aggregation should be computed:
either via an estimate of the spectral radius of
<IMG
WIDTH="51" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img86.png"
ALT="$D^{-1}A$">, or explicily
specified by the user.</TD>
@ -342,7 +342,7 @@ Parameters defining the aggregation algorithm.
<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=198>How to estimate the spectral radius of <IMG
WIDTH="51" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img86.png"
ALT="$D^{-1}A$">.
Currently only the infinity norm estimate
@ -371,7 +371,7 @@ Parameters defining the aggregation algorithm.
SRC="img94.png"
ALT="$\rho(D^{-1}A)$"> of
<IMG
WIDTH="51" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img86.png"
ALT="$D^{-1}A$">.</TD>
</TR>
@ -441,7 +441,7 @@ level.</CAPTION>
<TR><TD ALIGN="LEFT"><code>mld_coarse_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="img95.png"
ALT="$&gt; 0$"></TD>
<TD ALIGN="LEFT">4</TD>
@ -451,7 +451,7 @@ level.</CAPTION>
<TR><TD ALIGN="LEFT"><code>mld_coarse_fillin_</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="img89.png"
ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">0</TD>
@ -463,7 +463,7 @@ level.</CAPTION>
<TR><TD ALIGN="LEFT"><code>mld_coarse_iluthrs_</code></TD>
<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="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img89.png"
ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">0</TD>

@ -84,7 +84,7 @@ the user through the routines <code>mld_precinit</code> and <code>mld_precset</c
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">14</A>].</TD>
HREF="node25.html#PSBLASGUIDE">15</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>
@ -92,7 +92,7 @@ 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">14</A>].</TD>
HREF="node25.html#PSBLASGUIDE">15</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><I>x</I><code>prec_type), intent(inout)</code>.</TD>

@ -72,14 +72,14 @@ This routine computes <!-- MATH
$y = op(M^{-1})\, x$
-->
<IMG
WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
WIDTH="117" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img96.png"
ALT="$y = op(M^{-1}) x$">, where <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img59.png"
ALT="$M$"> is a previously built
preconditioner, stored into <code>p</code>, and <IMG
WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img97.png"
ALT="$op$">
denotes the preconditioner itself or its transpose, according to
@ -109,7 +109,7 @@ and hence it is completely transparent to the user.
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img98.png"
ALT="$x$">. Note that <I>type</I> and
<I>kind_parameter</I> must be chosen according
@ -120,7 +120,7 @@ and hence it is completely transparent to the user.
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img99.png"
ALT="$y$">. Note that <I>type</I> and
<I>kind_parameter</I> must be chosen according

@ -72,7 +72,7 @@ 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">14</A>].
HREF="node25.html#PSBLASGUIDE">15</A>].
<P>

@ -73,7 +73,8 @@ Proceedings of PARA&nbsp;04 Workshop on State of the Art
in Scientific Computing, Lecture Notes in Computer Science,
Springer, 2005, 593-602.
<P></P><DT><A NAME="aaecc_07">3</A>
<DD> A.&nbsp;Buttari, P.&nbsp;D'Ambra, D.&nbsp;di&nbsp;Serafino, S.&nbsp;Filippone,
<DD>
A.&nbsp;Buttari, P.&nbsp;D'Ambra, D.&nbsp;di&nbsp;Serafino, S.&nbsp;Filippone,
<EM>2LEV-D2P4: a package of high-performance preconditioners
for scientific and engineering applications</EM>,
Applicable Algebra in Engineering, Communications and Computing,
@ -101,95 +102,101 @@ T.&nbsp;Chan and T.&nbsp;Mathew,
<EM>Domain Decomposition Algorithms</EM>,
in A.&nbsp;Iserles, editor, Acta Numerica 1994, 61-143.
Cambridge University Press.
<P></P><DT><A NAME="UMFPACK">8</A>
<P></P><DT><A NAME="MLD2P4_TOMS">8</A>
<DD>
P.&nbsp;D'Ambra, D.&nbsp;di&nbsp;Serafino, S.&nbsp;Filippone,
<I>MLD2P4: a Package of Parallel Multilevel
Algebraic Domain Decomposition Preconditioners
in Fortran 95</I>, ICAR-CNR Technical Report RT-ICAR-NA-09-01, 2009.
<P></P><DT><A NAME="UMFPACK">9</A>
<DD>
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">9</A>
<P></P><DT><A NAME="SUPERLU">10</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">10</A>
<P></P><DT><A NAME="blas3">11</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">11</A>
<P></P><DT><A NAME="blas2">12</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">12</A>
<P></P><DT><A NAME="BLACS">13</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">13</A>
<P></P><DT><A NAME="EFSTATHIOU">14</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">14</A>
<P></P><DT><A NAME="PSBLASGUIDE">15</A>
<DD>
S.&nbsp;Filippone, A.&nbsp;Buttari,
<EM>PSBLAS-2.3 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library</EM>, 2008,
available from <TT>http://www.ce.uniroma2.it/psblas/</TT>.
<P></P><DT><A NAME="psblas_00">15</A>
<P></P><DT><A NAME="psblas_00">16</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">16</A>
<P></P><DT><A NAME="MPI2">17</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">17</A>
<P></P><DT><A NAME="blas1">18</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">18</A>
<P></P><DT><A NAME="SUPERLUDIST">19</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">19</A>
<P></P><DT><A NAME="Saad_book">20</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">20</A>
<P></P><DT><A NAME="dd2_96">21</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">21</A>
<P></P><DT><A NAME="MPI1">22</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">22</A>
<P></P><DT><A NAME="StubenGMD69_99">23</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">23</A>
<P></P><DT><A NAME="TUMINARO_TONG">24</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">24</A>
<P></P><DT><A NAME="VANEK_MANDEL_BREZINA">25</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>,

@ -67,7 +67,7 @@ Mathematics Department, Macquarie University, Sydney.
The command line arguments were: <BR>
<STRONG>latex2html</STRONG> <TT>-noaddress -dir ../../html userhtml.tex</TT>
<P>
The translation was initiated by Salvatore Filippone on 2009-03-13
The translation was initiated by Salvatore Filippone on 2009-03-16
<BR><HR>
</BODY>

@ -63,7 +63,7 @@ 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 <I>multi-level Schwarz preconditioners</I>&nbsp;[<A
HREF="node25.html#dd2_96">20</A>],
HREF="node25.html#dd2_96">21</A>],
to be used in the iterative solutions of sparse linear systems:
<BR>
<DIV ALIGN="RIGHT">
@ -102,7 +102,7 @@ explicitly using any information on the geometry of the original problem (e.g. t
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">24</A>].
HREF="node25.html#VANEK_MANDEL_BREZINA">25</A>].
</LI>
</UL>
@ -120,7 +120,7 @@ real and the complex case, that can be used through a single interface.
MLD2P4 has been designed to implement scalable and easy-to-use multilevel preconditioners
in the context of the <I>PSBLAS (Parallel Sparse BLAS)
computational framework</I>&nbsp;[<A
HREF="node25.html#psblas_00">15</A>].
HREF="node25.html#psblas_00">16</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
@ -133,10 +133,10 @@ 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
recent PSBLAS 2.0 version&nbsp;[<A
HREF="node25.html#PSBLASGUIDE">14</A>]. The inter-process comunication required
HREF="node25.html#PSBLASGUIDE">15</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">21</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
HREF="node25.html#MPI1">22</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
machine where PSBLAS and MPI implementations are available.
<P>

@ -64,9 +64,9 @@ The following base libraries are needed:
<DL>
<DT><STRONG>BLAS</STRONG></DT>
<DD>[<A
HREF="node25.html#blas3">10</A>,<A
HREF="node25.html#blas2">11</A>,<A
HREF="node25.html#blas1">17</A>] Many vendors provide optimized versions
HREF="node25.html#blas3">11</A>,<A
HREF="node25.html#blas2">12</A>,<A
HREF="node25.html#blas1">18</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>)
@ -81,13 +81,13 @@ The following base libraries are needed:
</DD>
<DT><STRONG>MPI</STRONG></DT>
<DD>[<A
HREF="node25.html#MPI2">16</A>,<A
HREF="node25.html#MPI1">21</A>] A version of MPI is available on most
HREF="node25.html#MPI2">17</A>,<A
HREF="node25.html#MPI1">22</A>] A version of MPI is available on most
high-performance computing systems; only version 1.1 is required.
</DD>
<DT><STRONG>BLACS</STRONG></DT>
<DD>[<A
HREF="node25.html#BLACS">12</A>] The Basic Linear Algebra Communication Subprograms
HREF="node25.html#BLACS">13</A>] The Basic Linear Algebra Communication Subprograms
are available in source form from <code>http://www.netlib.org/blacs</code>;
some vendors include them in their parallel computing
support libraries.
@ -95,8 +95,8 @@ The following base libraries are needed:
</DD>
<DT><STRONG>PSBLAS</STRONG></DT>
<DD>[<A
HREF="node25.html#PSBLASGUIDE">14</A>,<A
HREF="node25.html#psblas_00">15</A>] Parallel Sparse BLAS is
HREF="node25.html#PSBLASGUIDE">15</A>,<A
HREF="node25.html#psblas_00">16</A>] Parallel Sparse BLAS is
available from
<BR><code>http://www.ce.uniroma2.it/psblas</code>; version 2.3.1
(or later) is required. Indeed, all the prerequisites

@ -68,7 +68,7 @@ for multilevel preconditioners may change to reflect their presence.
<DL>
<DT><STRONG>UMFPACK</STRONG></DT>
<DD>[<A
HREF="node25.html#UMFPACK">8</A>]
HREF="node25.html#UMFPACK">9</A>]
A sparse direct factorization package available from
<BR> <code>http://www.cise.ufl.edu/research/sparse/umfpack/</code>;
provides serial factorization and triangular system solution for double
@ -77,7 +77,7 @@ for multilevel preconditioners may change to reflect their presence.
</DD>
<DT><STRONG>SuperLU</STRONG></DT>
<DD>[<A
HREF="node25.html#SUPERLU">9</A>]
HREF="node25.html#SUPERLU">10</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,
@ -85,7 +85,7 @@ for multilevel preconditioners may change to reflect their presence.
</DD>
<DT><STRONG>SuperLU_Dist</STRONG></DT>
<DD>[<A
HREF="node25.html#SUPERLUDIST">18</A>]
HREF="node25.html#SUPERLUDIST">19</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.

File diff suppressed because one or more lines are too long

@ -85,7 +85,7 @@
TOPFILE = userguide.tex
HTMLFILE = userhtml.tex
SECFILE = title.tex abstract.tex overview.tex distribution.tex \
SECFILE = abstract.tex overview.tex distribution.tex \
building.tex background.tex gettingstarted.tex userinterface.tex \
errors.tex bibliography.tex license.tex
FIGDIR = figures

@ -28,7 +28,8 @@ Proceedings of PARA~04 Workshop on State of the Art
in Scientific Computing, Lecture Notes in Computer Science,
Springer, 2005, 593--602.
%
\bibitem{aaecc_07} A.~Buttari, P.~D'Ambra, D.~di~Serafino, S.~Filippone,
\bibitem{aaecc_07}
A.~Buttari, P.~D'Ambra, D.~di~Serafino, S.~Filippone,
{\em 2LEV-D2P4: a package of high-performance preconditioners
for scientific and engineering applications},
Applicable Algebra in Engineering, Communications and Computing,
@ -70,12 +71,11 @@ T.~Chan and T.~Mathew,
in A.~Iserles, editor, Acta Numerica 1994, 61--143.
Cambridge University Press.
%
%% \bibitem{MLD2P4_TOMS}
%% P.~D'Ambra, D.~di~Serafino, S.~Filippone,
%% \emph{MLD2P4: a Package of Parallel Multilevel
%% Algebraic Domain Decomposition Preconditioners
%% in Fortran 95},
%% COMPLETARE.
\bibitem{MLD2P4_TOMS}
P.~D'Ambra, D.~di~Serafino, S.~Filippone,
\emph{MLD2P4: a Package of Parallel Multilevel
Algebraic Domain Decomposition Preconditioners
in Fortran 95}, ICAR-CNR Technical Report RT-ICAR-NA-09-01, 2009.
%
\bibitem{UMFPACK}
T.A.~Davis,

@ -1,72 +0,0 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Contents: The title page
% $Id: title.tex 1999 2007-10-29 15:25:27Z sfilippo $
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\ifcase\pdfoutput % We're not running pdftex
{\Large\bfseries MLD2P4\\[.8ex] User's and Reference Guide}\\
\emph{\large A guide for the Multi-Level Domain Decomposition \\[.6ex]
Parallel Preconditioners Package
based on PSBLAS}
{\bfseries Pasqua D'Ambra}\\
ICAR-CNR, Naples, Italy\\[3ex]
{\bfseries Daniela di Serafino}\\
Second University of Naples, Italy\\[3ex]
{\bfseries Salvatore Filippone} \\
University of Rome ``Tor Vergata'', Italy
%\\[10ex]
%\today
Software version: 1.0\\
%\today
July 24, 2008
\or
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{\Huge\bfseries MLD2P4\\[.8ex] User's and Reference Guide
}
\noindent\rule[-1ex]{\textwidth}{5pt}\\[2.5ex]
\hfill\emph{\Large A guide for the Multi-Level Domain Decomposition \\[.6ex]
Parallel Preconditioners Package
based on PSBLAS}
\end{minipage}}
\vspace{\stretch{1}}
\noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth}
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{\large\bfseries Pasqua D'Ambra}\\
\large ICAR-CNR, Naples, Italy\\[3ex]
{\large\bfseries Daniela di Serafino}\\
\large Second University of Naples, Italy\\[3ex]
{\large\bfseries Salvatore Filippone} \\
\large University of Rome ``Tor Vergata'', Italy
%\\[10ex]
%\today
\end{minipage}}
\vspace{\stretch{1}}
\noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth}
\flushright
\large Software version: 1.0\\
%\today
\large July 24, 2008
\end{minipage}}
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