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New interfaces for building hierachy and preconditioner.
This commit is contained in:
Salvatore Filippone
2016-06-09 15:38:36 +00:00
parent d989714ee9
commit 86982461ad
35 changed files with 5859 additions and 5210 deletions
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docs/html/node13.html
+26 -26
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@@ -25,26 +25,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds
<BODY >
<!--Navigation Panel-->
<A NAME="tex2html221"
<A NAME="tex2html225"
HREF="node14.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
<A NAME="tex2html217"
<A NAME="tex2html221"
HREF="node11.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
<A NAME="tex2html213"
<A NAME="tex2html217"
HREF="node12.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
<A NAME="tex2html219"
<A NAME="tex2html223"
HREF="node2.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html222"
<B> Next:</B> <A NAME="tex2html226"
HREF="node14.html">Getting Started</A>
<B> Up:</B> <A NAME="tex2html218"
<B> Up:</B> <A NAME="tex2html222"
HREF="node11.html">Multi-level Domain Decomposition Background</A>
<B> Previous:</B> <A NAME="tex2html214"
<B> Previous:</B> <A NAME="tex2html218"
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
&nbsp; <B> <A NAME="tex2html220"
&nbsp; <B> <A NAME="tex2html224"
HREF="node2.html">Contents</A></B>
<BR>
<BR>
@@ -65,8 +65,8 @@ the coarse-level matrix <IMG
SRC="img44.png"
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">27</A>].
HREF="node27.html#BREZINA_VANEK">1</A>,<A
HREF="node27.html#VANEK_MANDEL_BREZINA">27</A>].
The basic idea of this algorithm is to build a coarse set of vertices
<IMG
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
@@ -114,8 +114,8 @@ Three main steps can be identified in the smoothed aggregation procedure:
<P>
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">27</A>], a modification of
HREF="node27.html#apnum_07">4</A>]. According to [<A
HREF="node27.html#VANEK_MANDEL_BREZINA">27</A>], a modification of
this algorithm has been actually considered,
in which each aggregate <IMG
WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
@@ -171,9 +171,9 @@ dependent on the number of processors and on the initial partitioning of the mat
Nevertheless, this algorithm has been chosen for the implementation in MLD2P4,
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">26</A>].
HREF="node27.html#aaecc_07">3</A>,<A
HREF="node27.html#apnum_07">4</A>,<A
HREF="node27.html#TUMINARO_TONG">26</A>].
<P>
The prolongator <IMG
@@ -251,8 +251,8 @@ P_C = S P,
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">25</A>].
HREF="node27.html#BREZINA_VANEK">1</A>,<A
HREF="node27.html#StubenGMD69_99">25</A>].
A simple choice for <IMG
WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img84.png"
@@ -284,30 +284,30 @@ using some estimate of the spectral radius of <IMG
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img87.png"
ALT="$D^{-1}A$"> [<A
HREF="node25.html#BREZINA_VANEK">1</A>].
HREF="node27.html#BREZINA_VANEK">1</A>].
<P>
<HR>
<!--Navigation Panel-->
<A NAME="tex2html221"
<A NAME="tex2html225"
HREF="node14.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
<A NAME="tex2html217"
<A NAME="tex2html221"
HREF="node11.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
<A NAME="tex2html213"
<A NAME="tex2html217"
HREF="node12.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
<A NAME="tex2html219"
<A NAME="tex2html223"
HREF="node2.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html222"
<B> Next:</B> <A NAME="tex2html226"
HREF="node14.html">Getting Started</A>
<B> Up:</B> <A NAME="tex2html218"
<B> Up:</B> <A NAME="tex2html222"
HREF="node11.html">Multi-level Domain Decomposition Background</A>
<B> Previous:</B> <A NAME="tex2html214"
<B> Previous:</B> <A NAME="tex2html218"
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
&nbsp; <B> <A NAME="tex2html220"
&nbsp; <B> <A NAME="tex2html224"
HREF="node2.html">Contents</A></B>
<!--End of Navigation Panel-->