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Added entrywise inversion and documentation for vec-vec operation

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cirdans-home
2019-11-21 13:56:22 +01:00
parent db7b882e9c
commit b3c4971146
340 changed files with 24932 additions and 20314 deletions
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@@ -23,26 +23,26 @@
<BODY >
<DIV CLASS="navigation"><!--Navigation Panel-->
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@@ -62,21 +62,21 @@ PDE.
Each point of the discretization mesh will have (at least) one
associated equation/variable, and therefore one index. We say that
point <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> <EM>depends</EM> on point <SPAN CLASS="MATH"><IMG
WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
WIDTH="11" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img5.png"
ALT="$j$"></SPAN> if the equation for a
variable associated with <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> contains a term in <SPAN CLASS="MATH"><IMG
WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
WIDTH="11" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img5.png"
ALT="$j$"></SPAN>, or equivalently
if <SPAN CLASS="MATH"><IMG
WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
WIDTH="53" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img6.png"
ALT="$a_{ij} \ne0$"></SPAN>.
After the partition of the discretization mesh into <EM>sub-domains</EM>
@@ -123,25 +123,25 @@ Overlap points do not usually exist in the basic data
distributions; however they are a feature of Domain Decomposition
Schwarz preconditioners which are the subject of related research
work&nbsp;[<A
HREF="node134.html#2007c">4</A>,<A
HREF="node134.html#2007d">3</A>].
HREF="node137.html#2007c">4</A>,<A
HREF="node137.html#2007d">3</A>].
<P>
We denote the sets of internal, boundary and halo points for a given
subdomain by <SPAN CLASS="MATH"><IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img7.png"
ALT="$\cal I$"></SPAN>, <SPAN CLASS="MATH"><IMG
WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img8.png"
ALT="$\cal B$"></SPAN> and <SPAN CLASS="MATH"><IMG
WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img9.png"
ALT="$\cal H$"></SPAN>.
Each subdomain is assigned to one process; each process usually
owns one subdomain, although the user may choose to assign more than
one subdomain to a process. If 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> owns one
subdomain, the number of rows in the local sparse matrix is
@@ -149,7 +149,7 @@ subdomain, the number of rows in the local sparse matrix is
$|{\cal I}_i| + |{\cal B}_i|$
-->
<SPAN CLASS="MATH"><IMG
WIDTH="70" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img10.png"
ALT="$\vert{\cal I}_i\vert + \vert{\cal B}_i\vert$"></SPAN>, and the number of local columns
(i.e. those for which there exists at least one non-zero entry in the
@@ -157,7 +157,7 @@ local rows) is <!-- MATH
$|{\cal I}_i| + |{\cal B}_i| +|{\cal H}_i|$
-->
<SPAN CLASS="MATH"><IMG
WIDTH="118" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
WIDTH="118" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img11.png"
ALT="$\vert{\cal I}_i\vert + \vert{\cal B}_i\vert +\vert{\cal H}_i\vert$"></SPAN>.
@@ -170,7 +170,7 @@ Point classfication.</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<IMG
WIDTH="318" HEIGHT="283" ALIGN="BOTTOM" BORDER="0"
WIDTH="318" HEIGHT="285" ALIGN="BOTTOM" BORDER="0"
SRC="img13.png"
ALT="\includegraphics[scale=0.65]{figures/points.eps}">
<!-- MATH
@@ -195,26 +195,26 @@ points in the literature.
<DIV CLASS="navigation"><HR>
<!--Navigation Panel-->
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<BR>
<B> Next:</B> <A NAME="tex2html243"
<B> Next:</B> <A NAME="tex2html249"
HREF="node5.html">Library contents</A>
<B> Up:</B> <A NAME="tex2html239"
<B> Up:</B> <A NAME="tex2html245"
HREF="node3.html">General overview</A>
<B> Previous:</B> <A NAME="tex2html233"
<B> Previous:</B> <A NAME="tex2html239"
HREF="node3.html">General overview</A>
&nbsp; <B> <A NAME="tex2html241"
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