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Merged MixedI8 in new branch (to be later merged into development)

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Salvatore Filippone
2018-12-10 11:42:40 +00:00
parent 5371e39c16
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@@ -61,7 +61,7 @@ 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 <SPAN CLASS="MATH"><IMG
WIDTH="46" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
WIDTH="45" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img15.png"
ALT="$1\dots n$"></SPAN> is isomorphic to the set of cell centers,
whereas the pattern of the associated linear system matrix is
@@ -72,7 +72,7 @@ by the discretization stencil.
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 <SPAN CLASS="MATH"><IMG
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img16.png"
ALT="$n$"></SPAN> and the allocation of the elements of the
index space to the various processes making up the MPI (virtual)
@@ -81,22 +81,22 @@ parallel machine.
<P>
The index space is partitioned among processes, and this creates a
mapping from the &ldquo;global&rdquo; numbering <SPAN CLASS="MATH"><IMG
WIDTH="46" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
WIDTH="45" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img15.png"
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"
WIDTH="9" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img4.png"
ALT="$i$"></SPAN> will own a certain subset
<!-- MATH
$1\dots n_{\hbox{row}_i}$
-->
<SPAN CLASS="MATH"><IMG
WIDTH="77" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
WIDTH="76" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img17.png"
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="13" ALIGN="BOTTOM" BORDER="0"
WIDTH="45" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img15.png"
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
@@ -106,7 +106,7 @@ library will translate into the appropriate &ldquo;local&rdquo; numbering.
<P>
For a given index space <SPAN CLASS="MATH"><IMG
WIDTH="46" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
WIDTH="45" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img15.png"
ALT="$1\dots n$"></SPAN> there are many possible associated
topologies, i.e. many different discretization stencils; thus the
@@ -115,7 +115,7 @@ 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 <SPAN CLASS="MATH"><IMG
WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
WIDTH="9" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img4.png"
ALT="$i$"></SPAN> will have
defined a set of &ldquo;halo&rdquo; (or &ldquo;ghost&rdquo;) indices
@@ -123,16 +123,16 @@ defined a set of &ldquo;halo&rdquo; (or &ldquo;ghost&rdquo;) indices
$n_{\hbox{row}_i}+1\dots n_{\hbox{col}_i}$
-->
<SPAN CLASS="MATH"><IMG
WIDTH="130" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
WIDTH="131" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img18.png"
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"
WIDTH="9" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img4.png"
ALT="$i$"></SPAN>; however the
variables associated with them are needed to complete computations
associated with the sparse matrix <SPAN CLASS="MATH"><IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img1.png"
ALT="$A$"></SPAN>, and thus they have to be
fetched from (neighbouring) processes. The descriptor of the index
@@ -173,8 +173,8 @@ follows:
<LI>Call the iterative method of choice, e.g. <code>psb_bicgstab</code>
</LI>
</OL>
This is the structure of the sample program
<code>test/pargen/psb_d_pde3d.f90</code>.
This is the structure of the sample programs in the directory
<code>test/pargen/</code>.
<P>
For a simulation in which the same discretization mesh is used over