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 [<A
HREF="node25.html#Cai_Widlund_92">6</A>,<A HREF="node25.html#Cai_Widlund_92">6</A>,<A
HREF="node25.html#dd1_94">7</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> <P>
<I>Additive Schwarz</I> 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 submatrices, i.e. with some common rows, to couple the local information
related to the submatrices (see, e.g., [<A 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 The main motivation for choosing Additive Schwarz preconditioners is their
intrinsic parallelism. A drawback of these intrinsic parallelism. A drawback of these
preconditioners is that the number of iterations of the preconditioned solvers 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 called `smoother'. Different two-level preconditioners are obtained by varying the
choice of the smoother and of the coarse-level correction, and the choice of the smoother and of the coarse-level correction, and the
way they are combined [<A 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 the coarse-level system, i.e. a coarse-space correction can be built
from this system, thus obtaining <I>multi-level</I> preconditioners. 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 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 the fine and coarse levels by suitably choosing the coarse space and the coarse-to-fine
interpolation [<A interpolation [<A
HREF="node25.html#StubenGMD69_99">22</A>]. HREF="node25.html#StubenGMD69_99">23</A>].
<P> <P>
MLD2P4 uses a pure algebraic approach for building the sequence of coarse matrices 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 starting from the original matrix. The algebraic approach is based on the <I>smoothed
aggregation</I> algorithm [<A aggregation</I> algorithm [<A
HREF="node25.html#BREZINA_VANEK">1</A>,<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 of this algorithm is implemented, where the smoothed aggregation is applied locally
to each submatrix [<A 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 a brief description of the multi-level Schwarz preconditioners and of the smoothed
aggregation technique as implemented in MLD2P4. For further details the reader aggregation technique as implemented in MLD2P4. For further details the reader
is referred to [<A is referred to [<A
HREF="node25.html#para_04">2</A>,<A HREF="node25.html#para_04">2</A>,<A
HREF="node25.html#aaecc_07">3</A>,<A HREF="node25.html#aaecc_07">3</A>,<A
HREF="node25.html#apnum_07">4</A>,,<A HREF="node25.html#apnum_07">4</A>,<A
HREF="node25.html#dd2_96">20</A>]. HREF="node25.html#MLD2P4_TOMS">8</A>,<A
HREF="node25.html#dd2_96">21</A>].
<P> <P>
<BR><HR> <BR><HR>

@ -299,7 +299,7 @@ ILU(<IMG
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img35.png" SRC="img35.png"
ALT="$p,t$">) [<A ALT="$p,t$">) [<A
HREF="node25.html#Saad_book">19</A>, Chapter 10]. HREF="node25.html#Saad_book">20</A>, Chapter 10].
<P> <P>
A variant of the classical AS preconditioner that outperforms it 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 time on parallel distributed-memory computers is the so-called <I>Restricted AS
(RAS)</I> preconditioner&nbsp;[<A (RAS)</I> preconditioner&nbsp;[<A
HREF="node25.html#CAI_SARKIS">5</A>,<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 is obtained by zeroing the components of <IMG
WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img32.png" SRC="img32.png"
@ -391,7 +391,7 @@ of <IMG
SRC="img10.png" SRC="img10.png"
ALT="$W$"> increases [<A ALT="$W$"> increases [<A
HREF="node25.html#dd1_94">7</A>,<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 of the number of iterations on the degree of parallelism we may
introduce a global coupling among the overlapping partitions by defining introduce a global coupling among the overlapping partitions by defining
a coarse-space approximation <IMG 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> coarse-level system. The corresponding preconditioners, called <I>multi-level</I>
preconditioners, can significantly reduce the computational cost of preconditioning preconditioners, can significantly reduce the computational cost of preconditioning
with respect to the two-level case (see [<A 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 Additive and hybrid multilevel preconditioners
are obtained as direct extensions of the two-level counterparts. are obtained as direct extensions of the two-level counterparts.
For a detailed descrition of them, the reader is For a detailed descrition of them, the reader is
referred to [<A 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 The algorithm for the application of a multi-level hybrid
post-smoothed preconditioner <IMG post-smoothed preconditioner <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
@ -685,7 +685,7 @@ and the corresponding basic preconditioner at each level <IMG
SRC="img65.png" SRC="img65.png"
ALT="$A_1=A$">, while the related restriction operator is ALT="$A_1=A$">, while the related restriction operator is
denoted by <IMG denoted by <IMG
WIDTH="23" HEIGHT="32" ALIGN="MIDDLE" BORDER="0" WIDTH="22" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img66.png" SRC="img66.png"
ALT="$R_l$">. ALT="$R_l$">.
@ -724,14 +724,14 @@ $w = y_1$;
}$ }$
--> -->
<IMG <IMG
WIDTH="429" HEIGHT="435" ALIGN="BOTTOM" BORDER="0" WIDTH="430" HEIGHT="435" ALIGN="BOTTOM" BORDER="0"
SRC="img67.png" SRC="img67.png"
ALT="\framebox{ ALT="\framebox{
\begin{minipage}{.85\textwidth} {\small \begin{minipage}{.85\textwidth} {\small
\begin{tabbing} \begin{tabbing}
\quad \=\quad... \quad \=\quad...
...= y_l+r_l$\\ ...= y_l+r_l$\\
\textbf{endfor} [1mm] \textbf{endfor} \ [1mm]
$w = y_1$; $w = y_1$;
\end{tabbing}} \end{tabbing}}
\end{minipage}}"> \end{minipage}}">

@ -70,7 +70,7 @@ the coarse-level matrix <IMG
ALT="$A_C$">, MLD2P4 uses the <I>smoothed aggregation</I> ALT="$A_C$">, MLD2P4 uses the <I>smoothed aggregation</I>
algorithm described in [<A algorithm described in [<A
HREF="node25.html#BREZINA_VANEK">1</A>,<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 The basic idea of this algorithm is to build a coarse set of vertices
<IMG <IMG
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0" 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 To perform the coarsening step, we have implemented the aggregation algorithm sketched
in [<A in [<A
HREF="node25.html#apnum_07">4</A>]. According to [<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, this algorithm has been actually considered,
in which each aggregate <IMG in which each aggregate <IMG
WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0" WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
@ -159,7 +159,7 @@ for a given <!-- MATH
ALT="$\theta \in [0,1]$">. ALT="$\theta \in [0,1]$">.
Since this algorithm has a sequential nature, a <I>decoupled</I> version of Since this algorithm has a sequential nature, a <I>decoupled</I> version of
it has been chosen, where each processor <IMG 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" SRC="img74.png"
ALT="$i$"> independently applies the algorithm to ALT="$i$"> independently applies the algorithm to
the set of vertices <IMG the set of vertices <IMG
@ -178,7 +178,7 @@ since it has been shown to produce good results in practice
[<A [<A
HREF="node25.html#aaecc_07">3</A>,<A HREF="node25.html#aaecc_07">3</A>,<A
HREF="node25.html#apnum_07">4</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> <P>
The prolongator <IMG The prolongator <IMG
@ -189,7 +189,7 @@ The prolongator <IMG
$P \in \Re^{n \times n_C}$ $P \in \Re^{n \times n_C}$
--> -->
<IMG <IMG
WIDTH="89" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" WIDTH="90" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
SRC="img77.png" SRC="img77.png"
ALT="$P \in \Re^{n \times n_C}$">, defined as ALT="$P \in \Re^{n \times n_C}$">, defined as
<BR> <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 and hence to improve the convergence properties of the multi-level
Schwarz method [<A Schwarz method [<A
HREF="node25.html#BREZINA_VANEK">1</A>,<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 A simple choice for <IMG
WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img83.png" SRC="img83.png"
@ -286,7 +286,7 @@ where the value of <IMG
SRC="img85.png" SRC="img85.png"
ALT="$\omega$"> can be chosen ALT="$\omega$"> can be chosen
using some estimate of the spectral radius of <IMG 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" SRC="img86.png"
ALT="$D^{-1}A$"> [<A ALT="$D^{-1}A$"> [<A
HREF="node25.html#BREZINA_VANEK">1</A>]. HREF="node25.html#BREZINA_VANEK">1</A>].

@ -63,7 +63,7 @@ Getting Started
<P> <P>
We describe the basics for building and applying MLD2P4 one-level and multi-level We describe the basics for building and applying MLD2P4 one-level and multi-level
Schwarz preconditioners with the Krylov solvers included in PSBLAS [<A 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: The following steps are required:
<OL> <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>). 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 For details on the use of the PSBLAS routines, see the PSBLAS User's
Guide [<A Guide [<A
HREF="node25.html#PSBLASGUIDE">14</A>]. HREF="node25.html#PSBLASGUIDE">15</A>].
<P> <P>
The setup and application of the default multi-level 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 preconditioner, which uses block Jacobi with ILU(0) on the
local blocks as post-smoother, has a coarsest matrix replicated on the processors, 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 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 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 preconditioner parameters are set by calling <code>mld_precset</code>. Note that
the type of multilevel framework (i.e. multiplicative among the levels 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" WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img21.png" SRC="img21.png"
ALT="$v$"> and <IMG ALT="$v$"> and <IMG
WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img88.png" SRC="img88.png"
ALT="$w$"> involved in ALT="$w$"> involved in
the preconditioner application <IMG 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> <TR><TD ALIGN="LEFT"><code>mld_sub_ovr_</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD> <TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>any&nbsp;int.&nbsp;num.&nbsp;<IMG <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" SRC="img89.png"
ALT="$\ge 0$"></TD> ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">1</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> <TR><TD ALIGN="LEFT"><code>mld_sub_fillin_</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD> <TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<IMG <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" SRC="img89.png"
ALT="$\ge 0$"></TD> ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">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> <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"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;real&nbsp;num.&nbsp;<IMG <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" SRC="img89.png"
ALT="$\ge 0$"></TD> ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">0</TD> <TD ALIGN="LEFT">0</TD>
@ -332,7 +332,7 @@ Parameters defining the aggregation algorithm.
smoothed aggregation should be computed: smoothed aggregation should be computed:
either via an estimate of the spectral radius of either via an estimate of the spectral radius of
<IMG <IMG
WIDTH="51" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img86.png" SRC="img86.png"
ALT="$D^{-1}A$">, or explicily ALT="$D^{-1}A$">, or explicily
specified by the user.</TD> 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=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 <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" SRC="img86.png"
ALT="$D^{-1}A$">. ALT="$D^{-1}A$">.
Currently only the infinity norm estimate Currently only the infinity norm estimate
@ -371,7 +371,7 @@ Parameters defining the aggregation algorithm.
SRC="img94.png" SRC="img94.png"
ALT="$\rho(D^{-1}A)$"> of ALT="$\rho(D^{-1}A)$"> of
<IMG <IMG
WIDTH="51" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img86.png" SRC="img86.png"
ALT="$D^{-1}A$">.</TD> ALT="$D^{-1}A$">.</TD>
</TR> </TR>
@ -441,7 +441,7 @@ level.</CAPTION>
<TR><TD ALIGN="LEFT"><code>mld_coarse_sweeps_</code></TD> <TR><TD ALIGN="LEFT"><code>mld_coarse_sweeps_</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD> <TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<IMG <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" SRC="img95.png"
ALT="$&gt; 0$"></TD> ALT="$&gt; 0$"></TD>
<TD ALIGN="LEFT">4</TD> <TD ALIGN="LEFT">4</TD>
@ -451,7 +451,7 @@ level.</CAPTION>
<TR><TD ALIGN="LEFT"><code>mld_coarse_fillin_</code></TD> <TR><TD ALIGN="LEFT"><code>mld_coarse_fillin_</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD> <TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<IMG <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" SRC="img89.png"
ALT="$\ge 0$"></TD> ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">0</TD> <TD ALIGN="LEFT">0</TD>
@ -463,7 +463,7 @@ level.</CAPTION>
<TR><TD ALIGN="LEFT"><code>mld_coarse_iluthrs_</code></TD> <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"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;real.&nbsp;num.&nbsp;<IMG <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" SRC="img89.png"
ALT="$\ge 0$"></TD> ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">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, to the real/complex,
single/double precision version of MLD2P4 under use. single/double precision version of MLD2P4 under use.
See the PSBLAS User's Guide for details [<A 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>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD> <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> <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> <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 <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
details [<A details [<A
HREF="node25.html#PSBLASGUIDE">14</A>].</TD> HREF="node25.html#PSBLASGUIDE">15</A>].</TD>
</TR> </TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD> <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> <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
$y = op(M^{-1})\, x$ $y = op(M^{-1})\, x$
--> -->
<IMG <IMG
WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0" WIDTH="117" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img96.png" SRC="img96.png"
ALT="$y = op(M^{-1}) x$">, where <IMG ALT="$y = op(M^{-1}) x$">, where <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img59.png" SRC="img59.png"
ALT="$M$"> is a previously built ALT="$M$"> is a previously built
preconditioner, stored into <code>p</code>, and <IMG 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" SRC="img97.png"
ALT="$op$"> ALT="$op$">
denotes the preconditioner itself or its transpose, according to denotes the preconditioner itself or its transpose, according to
@ -109,7 +109,7 @@ and hence it is completely transparent to the user.
</TR> </TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD> <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG <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" SRC="img98.png"
ALT="$x$">. Note that <I>type</I> and ALT="$x$">. Note that <I>type</I> and
<I>kind_parameter</I> must be chosen according <I>kind_parameter</I> must be chosen according
@ -120,7 +120,7 @@ and hence it is completely transparent to the user.
</TR> </TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD> <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG <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" SRC="img99.png"
ALT="$y$">. Note that <I>type</I> and ALT="$y$">. Note that <I>type</I> and
<I>kind_parameter</I> must be chosen according <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 an error message should be printed. These options may be set by using
the PSBLAS error handling routines; for further details see the PSBLAS the PSBLAS error handling routines; for further details see the PSBLAS
User's Guide [<A User's Guide [<A
HREF="node25.html#PSBLASGUIDE">14</A>]. HREF="node25.html#PSBLASGUIDE">15</A>].
<P> <P>

@ -73,7 +73,8 @@ Proceedings of PARA&nbsp;04 Workshop on State of the Art
in Scientific Computing, Lecture Notes in Computer Science, in Scientific Computing, Lecture Notes in Computer Science,
Springer, 2005, 593-602. Springer, 2005, 593-602.
<P></P><DT><A NAME="aaecc_07">3</A> <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 <EM>2LEV-D2P4: a package of high-performance preconditioners
for scientific and engineering applications</EM>, for scientific and engineering applications</EM>,
Applicable Algebra in Engineering, Communications and Computing, Applicable Algebra in Engineering, Communications and Computing,
@ -101,95 +102,101 @@ T.&nbsp;Chan and T.&nbsp;Mathew,
<EM>Domain Decomposition Algorithms</EM>, <EM>Domain Decomposition Algorithms</EM>,
in A.&nbsp;Iserles, editor, Acta Numerica 1994, 61-143. in A.&nbsp;Iserles, editor, Acta Numerica 1994, 61-143.
Cambridge University Press. 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> <DD>
T.A.&nbsp;Davis, T.A.&nbsp;Davis,
<EM>Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal <EM>Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal
Method with a Column Pre-ordering Strategy</EM>, Method with a Column Pre-ordering Strategy</EM>,
ACM Transactions on Mathematical Software, 30, 2004, 196-199. ACM Transactions on Mathematical Software, 30, 2004, 196-199.
(See also <TT>http://www.cise.ufl.edu/&nbsp;davis/</TT>) (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> <DD>
J.W.&nbsp;Demmel, S.C.&nbsp;Eisenstat, J.R.&nbsp;Gilbert, X.S.&nbsp;Li and J.W.H.&nbsp;Liu, 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, A supernodal approach to sparse partial pivoting,
SIAM Journal on Matrix Analysis and Applications, 20, 3, 1999, 720-755. 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> <DD>
J.&nbsp;J.&nbsp;Dongarra, J.&nbsp;Du Croz, I.&nbsp;S.&nbsp;Duff, S.&nbsp;Hammarling, 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>, <I>A set of Level 3 Basic Linear Algebra Subprograms</I>,
ACM Transactions on Mathematical Software, 16, 1990, 1-17. 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> <DD>
J.&nbsp;J.&nbsp;Dongarra, J.&nbsp;Du Croz, S.&nbsp;Hammarling, R.&nbsp;J.&nbsp;Hanson, 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>, <I>An extended set of FORTRAN Basic Linear Algebra Subprograms</I>,
ACM Transactions on Mathematical Software, 14, 1988, 1-17. 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> <DD>
J.&nbsp;J.&nbsp;Dongarra and R.&nbsp;C.&nbsp;Whaley, J.&nbsp;J.&nbsp;Dongarra and R.&nbsp;C.&nbsp;Whaley,
<EM>A User's Guide to the BLACS v.&nbsp;1.1</EM>, <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 Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of
Tennessee, March 1995 (updated May 1997). Tennessee, March 1995 (updated May 1997).
<P></P><DT><A NAME="EFSTATHIOU">13</A> <P></P><DT><A NAME="EFSTATHIOU">14</A>
<DD> <DD>
E.&nbsp;Efstathiou, J.&nbsp;G.&nbsp;Gander, E.&nbsp;Efstathiou, J.&nbsp;G.&nbsp;Gander,
<EM>Why Restricted Additive Schwarz Converges Faster than Additive Schwarz</EM>, <EM>Why Restricted Additive Schwarz Converges Faster than Additive Schwarz</EM>,
BIT Numerical Mathematics, 43, 2003, 945-959. BIT Numerical Mathematics, 43, 2003, 945-959.
<P></P><DT><A NAME="PSBLASGUIDE">14</A> <P></P><DT><A NAME="PSBLASGUIDE">15</A>
<DD> <DD>
S.&nbsp;Filippone, A.&nbsp;Buttari, S.&nbsp;Filippone, A.&nbsp;Buttari,
<EM>PSBLAS-2.3 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library</EM>, 2008, <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>. 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> <DD>
S.&nbsp;Filippone, M.&nbsp;Colajanni, S.&nbsp;Filippone, M.&nbsp;Colajanni,
<EM>PSBLAS: A Library for Parallel Linear Algebra <EM>PSBLAS: A Library for Parallel Linear Algebra
Computation on Sparse Matrices</EM>, Computation on Sparse Matrices</EM>,
ACM Transactions on Mathematical Software, 26, 4, 2000, 527-550. 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> <DD>
W.&nbsp;Gropp, S.&nbsp;Huss-Lederman, A.&nbsp;Lumsdaine, E.&nbsp;Lusk, B.&nbsp;Nitzberg, W.&nbsp;Saphir, M.&nbsp;Snir, 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>, <EM>MPI: The Complete Reference. Volume 2 - The MPI-2 Extensions</EM>,
MIT Press, 1998. MIT Press, 1998.
<P></P><DT><A NAME="blas1">17</A> <P></P><DT><A NAME="blas1">18</A>
<DD> <DD>
C.&nbsp;L.&nbsp;Lawson, R.&nbsp;J.&nbsp;Hanson, D.&nbsp;Kincaid, F.&nbsp;T.&nbsp;Krogh, 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>, <I>Basic Linear Algebra Subprograms for FORTRAN usage</I>,
ACM Transactions on Mathematical Software, 5, 1979, 308-323. 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> <DD>
X.&nbsp;S.&nbsp;Li, J.&nbsp;W.&nbsp;Demmel, <EM>SuperLU_DIST: A Scalable Distributed-memory 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>, Sparse Direct Solver for Unsymmetric Linear Systems</EM>,
ACM Transactions on Mathematical Software, 29, 2, 2003, 110-140. 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> <DD>
Y.&nbsp;Saad, Y.&nbsp;Saad,
<I>Iterative methods for sparse linear systems</I>, 2nd edition, <I>Iterative methods for sparse linear systems</I>, 2nd edition,
SIAM, 2003 SIAM, 2003
<P> <P>
<P></P><DT><A NAME="dd2_96">20</A> <P></P><DT><A NAME="dd2_96">21</A>
<DD> <DD>
B.&nbsp;Smith, P.&nbsp;Bjorstad, W.&nbsp;Gropp, B.&nbsp;Smith, P.&nbsp;Bjorstad, W.&nbsp;Gropp,
<EM>Domain Decomposition: Parallel Multilevel Methods for Elliptic <EM>Domain Decomposition: Parallel Multilevel Methods for Elliptic
Partial Differential Equations</EM>, Partial Differential Equations</EM>,
Cambridge University Press, 1996. Cambridge University Press, 1996.
<P></P><DT><A NAME="MPI1">21</A> <P></P><DT><A NAME="MPI1">22</A>
<DD> <DD>
M.&nbsp;Snir, S.&nbsp;Otto, S.&nbsp;Huss-Lederman, D.&nbsp;Walker, J.&nbsp;Dongarra, 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, <EM>MPI: The Complete Reference. Volume 1 - The MPI Core</EM>, second edition,
MIT Press, 1998. MIT Press, 1998.
<P></P><DT><A NAME="StubenGMD69_99">22</A> <P></P><DT><A NAME="StubenGMD69_99">23</A>
<DD> <DD>
K.&nbsp;St&#252;ben, K.&nbsp;St&#252;ben,
<EM>Algebraic Multigrid (AMG): an Introduction with Applications</EM>, <EM>Algebraic Multigrid (AMG): an Introduction with Applications</EM>,
in A.&nbsp;Sch&#252;ller, U.&nbsp;Trottenberg, C.&nbsp;Oosterlee, editors, Multigrid, in A.&nbsp;Sch&#252;ller, U.&nbsp;Trottenberg, C.&nbsp;Oosterlee, editors, Multigrid,
Academic Press, 2000. Academic Press, 2000.
<P></P><DT><A NAME="TUMINARO_TONG">23</A> <P></P><DT><A NAME="TUMINARO_TONG">24</A>
<DD> <DD>
R.&nbsp;S.&nbsp;Tuminaro, C.&nbsp;Tong, R.&nbsp;S.&nbsp;Tuminaro, C.&nbsp;Tong,
<EM>Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines</EM>, <EM>Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines</EM>,
in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000. 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> <DD>
P.&nbsp;Vanek, J.&nbsp;Mandel and M.&nbsp;Brezina, P.&nbsp;Vanek, J.&nbsp;Mandel and M.&nbsp;Brezina,
<EM>Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems</EM>, <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> The command line arguments were: <BR>
<STRONG>latex2html</STRONG> <TT>-noaddress -dir ../../html userhtml.tex</TT> <STRONG>latex2html</STRONG> <TT>-noaddress -dir ../../html userhtml.tex</TT>
<P> <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> <BR><HR>
</BODY> </BODY>

@ -63,7 +63,7 @@ General Overview
<P> <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 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 </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: to be used in the iterative solutions of sparse linear systems:
<BR> <BR>
<DIV ALIGN="RIGHT"> <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 discretization of a PDE). The <I>smoothed aggregation</I> technique is applied
as algebraic coarsening strategy&nbsp;[<A as algebraic coarsening strategy&nbsp;[<A
HREF="node25.html#BREZINA_VANEK">1</A>,<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> </LI>
</UL> </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 MLD2P4 has been designed to implement scalable and easy-to-use multilevel preconditioners
in the context of the <I>PSBLAS (Parallel Sparse BLAS) in the context of the <I>PSBLAS (Parallel Sparse BLAS)
computational framework</I>&nbsp;[<A 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 PSBLAS is a library originally developed to address the parallel implementation of
iterative solvers for sparse linear system, by providing basic linear algebra iterative solvers for sparse linear system, by providing basic linear algebra
operators and data management facilities for distributed sparse matrices; it 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 package. On the other hand, the implementation of MLD2P4 has led to some
revisions and extentions of the PSBLAS kernels, leading to the revisions and extentions of the PSBLAS kernels, leading to the
recent PSBLAS 2.0 version&nbsp;[<A 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 by MLD2P4 is encapsulated into the PSBLAS routines, except few cases where
MPI&nbsp;[<A 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. machine where PSBLAS and MPI implementations are available.
<P> <P>

@ -64,9 +64,9 @@ The following base libraries are needed:
<DL> <DL>
<DT><STRONG>BLAS</STRONG></DT> <DT><STRONG>BLAS</STRONG></DT>
<DD>[<A <DD>[<A
HREF="node25.html#blas3">10</A>,<A HREF="node25.html#blas3">11</A>,<A
HREF="node25.html#blas2">11</A>,<A HREF="node25.html#blas2">12</A>,<A
HREF="node25.html#blas1">17</A>] Many vendors provide optimized versions HREF="node25.html#blas1">18</A>] Many vendors provide optimized versions
of the Basic Linear Algebra Subprograms; if no vendor version is of the Basic Linear Algebra Subprograms; if no vendor version is
available for a given platform, the ATLAS software available for a given platform, the ATLAS software
(<code>http://math-atlas.sourceforge.net/</code>) (<code>http://math-atlas.sourceforge.net/</code>)
@ -81,13 +81,13 @@ The following base libraries are needed:
</DD> </DD>
<DT><STRONG>MPI</STRONG></DT> <DT><STRONG>MPI</STRONG></DT>
<DD>[<A <DD>[<A
HREF="node25.html#MPI2">16</A>,<A HREF="node25.html#MPI2">17</A>,<A
HREF="node25.html#MPI1">21</A>] A version of MPI is available on most HREF="node25.html#MPI1">22</A>] A version of MPI is available on most
high-performance computing systems; only version 1.1 is required. high-performance computing systems; only version 1.1 is required.
</DD> </DD>
<DT><STRONG>BLACS</STRONG></DT> <DT><STRONG>BLACS</STRONG></DT>
<DD>[<A <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>; are available in source form from <code>http://www.netlib.org/blacs</code>;
some vendors include them in their parallel computing some vendors include them in their parallel computing
support libraries. support libraries.
@ -95,8 +95,8 @@ The following base libraries are needed:
</DD> </DD>
<DT><STRONG>PSBLAS</STRONG></DT> <DT><STRONG>PSBLAS</STRONG></DT>
<DD>[<A <DD>[<A
HREF="node25.html#PSBLASGUIDE">14</A>,<A HREF="node25.html#PSBLASGUIDE">15</A>,<A
HREF="node25.html#psblas_00">15</A>] Parallel Sparse BLAS is HREF="node25.html#psblas_00">16</A>] Parallel Sparse BLAS is
available from available from
<BR><code>http://www.ce.uniroma2.it/psblas</code>; version 2.3.1 <BR><code>http://www.ce.uniroma2.it/psblas</code>; version 2.3.1
(or later) is required. Indeed, all the prerequisites (or later) is required. Indeed, all the prerequisites

@ -68,7 +68,7 @@ for multilevel preconditioners may change to reflect their presence.
<DL> <DL>
<DT><STRONG>UMFPACK</STRONG></DT> <DT><STRONG>UMFPACK</STRONG></DT>
<DD>[<A <DD>[<A
HREF="node25.html#UMFPACK">8</A>] HREF="node25.html#UMFPACK">9</A>]
A sparse direct factorization package available from A sparse direct factorization package available from
<BR> <code>http://www.cise.ufl.edu/research/sparse/umfpack/</code>; <BR> <code>http://www.cise.ufl.edu/research/sparse/umfpack/</code>;
provides serial factorization and triangular system solution for double provides serial factorization and triangular system solution for double
@ -77,7 +77,7 @@ for multilevel preconditioners may change to reflect their presence.
</DD> </DD>
<DT><STRONG>SuperLU</STRONG></DT> <DT><STRONG>SuperLU</STRONG></DT>
<DD>[<A <DD>[<A
HREF="node25.html#SUPERLU">9</A>] HREF="node25.html#SUPERLU">10</A>]
A sparse direct factorization package available from A sparse direct factorization package available from
<BR> <code>http://crd.lbl.gov/~xiaoye/SuperLU/</code>; provides serial <BR> <code>http://crd.lbl.gov/~xiaoye/SuperLU/</code>; provides serial
factorization and triangular system solution for single and double precision, factorization and triangular system solution for single and double precision,
@ -85,7 +85,7 @@ for multilevel preconditioners may change to reflect their presence.
</DD> </DD>
<DT><STRONG>SuperLU_Dist</STRONG></DT> <DT><STRONG>SuperLU_Dist</STRONG></DT>
<DD>[<A <DD>[<A
HREF="node25.html#SUPERLUDIST">18</A>] HREF="node25.html#SUPERLUDIST">19</A>]
A sparse direct factorization package available A sparse direct factorization package available
from the same site as SuperLU; provides parallel factorization and from the same site as SuperLU; provides parallel factorization and
triangular system solution for double precision real and complex data. 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 TOPFILE = userguide.tex
HTMLFILE = userhtml.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 \ building.tex background.tex gettingstarted.tex userinterface.tex \
errors.tex bibliography.tex license.tex errors.tex bibliography.tex license.tex
FIGDIR = figures FIGDIR = figures

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