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Document DESC%CNV method and MOLD arguments to CDASB and PREC%BUILD

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Salvatore Filippone
2017-12-14 17:09:59 +00:00
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<!--Converted with LaTeX2HTML 2012 (1.2)
original version by: Nikos Drakos, CBLU, University of Leeds
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
* with significant contributions from:
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
<!--Converted with LaTeX2HTML 2017.2 (Released Jan 23, 2017) -->
<HTML>
<HEAD>
<TITLE>Application structure</TITLE>
@@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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@@ -25,30 +21,31 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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@@ -63,10 +60,10 @@ library objects are created and exist with reference to a discretized
space to which there corresponds an index space and a matrix sparsity
pattern. As an example, consider a cell-centered finite-volume
discretization of the Navier-Stokes equations on a simulation domain;
the index space <IMG
the index space <SPAN CLASS="MATH"><IMG
WIDTH="46" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img15.png"
ALT="$1\dots n$"> is isomorphic to the set of cell centers,
ALT="$1\dots n$"></SPAN> is isomorphic to the set of cell centers,
whereas the pattern of the associated linear system matrix is
isomorphic to the adjacency graph imposed on the discretization mesh
by the discretization stencil.
@@ -74,70 +71,70 @@ by the discretization stencil.
<P>
Thus the first order of business is to establish an index space, and
this is done with a call to <code>psb_cdall</code> in which we specify the
size of the index space <IMG
size of the index space <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img16.png"
ALT="$n$"> and the allocation of the elements of the
ALT="$n$"></SPAN> and the allocation of the elements of the
index space to the various processes making up the MPI (virtual)
parallel machine.
<P>
The index space is partitioned among processes, and this creates a
mapping from the ``global'' numbering <IMG
mapping from the &ldquo;global&rdquo; numbering <SPAN CLASS="MATH"><IMG
WIDTH="46" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img15.png"
ALT="$1\dots n$"> to a numbering
``local'' to each process; each process <IMG
ALT="$1\dots n$"></SPAN> to a numbering
&ldquo;local&rdquo; to each process; each process <SPAN CLASS="MATH"><IMG
WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img4.png"
ALT="$i$"> will own a certain subset
ALT="$i$"></SPAN> will own a certain subset
<!-- MATH
$1\dots n_{\hbox{row}_i}$
-->
<IMG
<SPAN CLASS="MATH"><IMG
WIDTH="77" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img17.png"
ALT="$1\dots n_{\hbox{row}_i}$">, each element of which corresponds to a certain
element of <IMG
ALT="$1\dots n_{\hbox{row}_i}$"></SPAN>, each element of which corresponds to a certain
element of <SPAN CLASS="MATH"><IMG
WIDTH="46" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img15.png"
ALT="$1\dots n$">. The user does not set explicitly this mapping;
ALT="$1\dots n$"></SPAN>. The user does not set explicitly this mapping;
when the application needs to indicate to which element of the index
space a certain item is related, such as the row and column index of a
matrix coefficient, it does so in the ``global'' numbering, and the
library will translate into the appropriate ``local'' numbering.
matrix coefficient, it does so in the &ldquo;global&rdquo; numbering, and the
library will translate into the appropriate &ldquo;local&rdquo; numbering.
<P>
For a given index space <IMG
For a given index space <SPAN CLASS="MATH"><IMG
WIDTH="46" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img15.png"
ALT="$1\dots n$"> there are many possible associated
ALT="$1\dots n$"></SPAN> there are many possible associated
topologies, i.e. many different discretization stencils; thus the
description of the index space is not completed until the user has
defined a sparsity pattern, either explicitly through <code>psb_cdins</code>
or implicitly through <code>psb_spins</code>. The descriptor is finalized
with a call to <code>psb_cdasb</code> and a sparse matrix with a call to
<code>psb_spasb</code>. After <code>psb_cdasb</code> each process <IMG
<code>psb_spasb</code>. After <code>psb_cdasb</code> each process <SPAN CLASS="MATH"><IMG
WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img4.png"
ALT="$i$"> will have
defined a set of ``halo'' (or ``ghost'') indices
ALT="$i$"></SPAN> will have
defined a set of &ldquo;halo&rdquo; (or &ldquo;ghost&rdquo;) indices
<!-- MATH
$n_{\hbox{row}_i}+1\dots n_{\hbox{col}_i}$
-->
<IMG
<SPAN CLASS="MATH"><IMG
WIDTH="130" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img18.png"
ALT="$n_{\hbox{row}_i}+1\dots n_{\hbox{col}_i}$">, denoting elements of the index
space that are <I>not</I> assigned to process <IMG
ALT="$n_{\hbox{row}_i}+1\dots n_{\hbox{col}_i}$"></SPAN>, denoting elements of the index
space that are <SPAN CLASS="textit">not</SPAN> assigned to process <SPAN CLASS="MATH"><IMG
WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img4.png"
ALT="$i$">; however the
ALT="$i$"></SPAN>; however the
variables associated with them are needed to complete computations
associated with the sparse matrix <IMG
associated with the sparse matrix <SPAN CLASS="MATH"><IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$">, and thus they have to be
ALT="$A$"></SPAN>, and thus they have to be
fetched from (neighbouring) processes. The descriptor of the index
space is built exactly for the purpose of properly sequencing the
communication steps required to achieve this objective.
@@ -171,7 +168,7 @@ follows:
</LI>
<LI>Choose the preconditioner to be used with <code>prec%init</code> and
build it with <code>prec%build</code><A NAME="tex2html5"
HREF="footnode.html#foot278"><SUP>3</SUP></A>.
HREF="footnode.html#foot278"><SUP><SPAN CLASS="arabic">3</SPAN></SUP></A>.
</LI>
<LI>Call the iterative method of choice, e.g. <code>psb_bicgstab</code>
</LI>
@@ -249,34 +246,35 @@ from optimal.
<!--Table of Child-Links-->
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HREF="node7.html">User-defined index mappings</A>
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<B> Next:</B> <A NAME="tex2html266"
HREF="node7.html">User-defined index mappings</A>
<B> Up:</B> <A NAME="tex2html261"
<B> Up:</B> <A NAME="tex2html262"
HREF="node3.html">General overview</A>
<B> Previous:</B> <A NAME="tex2html255"
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