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Configure minro fix: require psblas 2.3
Doc fixes: dual version of title for pdf/html, fixed tables.
This commit is contained in:
Salvatore Filippone
2008-07-23 08:51:18 +00:00
parent b7445f740c
commit 3f302b360c
65 changed files with 2450 additions and 2042 deletions
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+43 -41
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@@ -1,4 +1,4 @@
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
original version by: Nikos Drakos, CBLU, University of Leeds
@@ -25,34 +25,35 @@ original version by: Nikos Drakos, CBLU, University of Leeds
</HEAD>
<BODY >
<!--Navigation Panel-->
<A NAME="tex2html187"
<DIV CLASS="navigation"><!--Navigation Panel-->
<A NAME="tex2html186"
HREF="node11.html">
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SRC="file:/usr/share/latex2html/icons/up.png"></A>
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<BR>
<B> Next:</B> <A NAME="tex2html188"
<B> Next:</B> <A NAME="tex2html187"
HREF="node11.html">Multi-level Schwarz Preconditioners</A>
<B> Up:</B> <A NAME="tex2html184"
<B> Up:</B> <A NAME="tex2html183"
HREF="userhtml.html">userhtml</A>
<B> Previous:</B> <A NAME="tex2html178"
<B> Previous:</B> <A NAME="tex2html177"
HREF="node9.html">Example and test programs</A>
&nbsp; <B> <A NAME="tex2html186"
HREF="node1.html">Contents</A></B>
<BR>
&nbsp; <B> <A NAME="tex2html185"
HREF="node2.html">Contents</A></B>
<BR>
<BR></DIV>
<!--End of Navigation Panel-->
<H1><A NAME="SECTION00060000000000000000"></A><A NAME="sec:background"></A>
@@ -61,7 +62,7 @@ Multi-level Domain Decomposition Background
</H1>
<P>
<I>Domain Decomposition</I> (DD) preconditioners, coupled with Krylov iterative
<SPAN CLASS="textit">Domain Decomposition</SPAN> (DD) preconditioners, coupled with Krylov iterative
solvers, are widely used in the parallel solution of large and sparse linear systems.
These preconditioners are based on the divide and conquer technique: the matrix
to be preconditioned is divided into submatrices, a ``local'' linear system
@@ -74,13 +75,13 @@ solution of the original problem from the local solutions
[<A
HREF="node30.html#Cai_Widlund_92">6</A>,<A
HREF="node30.html#dd1_94">7</A>,<A
HREF="node30.html#dd2_96">15</A>].
HREF="node30.html#dd2_96">20</A>].
<P>
<I>Additive Schwarz</I> preconditioners are DD preconditioners using overlapping
<SPAN CLASS="textit">Additive Schwarz</SPAN> preconditioners are DD preconditioners using overlapping
submatrices, i.e. with some common rows, to couple the local information
related to the submatrices (see, e.g., [<A
HREF="node30.html#dd2_96">15</A>]).
HREF="node30.html#dd2_96">20</A>]).
The main motivation for choosing Additive Schwarz preconditioners is their
intrinsic parallelism. A drawback of these
preconditioners is that the number of iterations of the preconditioned solvers
@@ -93,15 +94,15 @@ in a coarse space, which globally couples the information related to the single
submatrices.
<P>
<I>Two-level Schwarz</I> preconditioners are obtained
<SPAN CLASS="textit">Two-level Schwarz</SPAN> preconditioners are obtained
by combining basic (one-level) Schwarz preconditioners with a coarse-level
correction. In this context, the one-level preconditioner is often
called `smoother'. Different two-level preconditioners are obtained by varying the
choice of the smoother and of the coarse-level correction, and the
way they are combined [<A
HREF="node30.html#dd2_96">15</A>]. The same reasoning can be applied starting
HREF="node30.html#dd2_96">20</A>]. The same reasoning can be applied starting
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 <SPAN CLASS="textit">multi-level</SPAN> preconditioners.
<P>
It is worth noting that optimal preconditioners do not necessarily correspond
@@ -123,68 +124,69 @@ are considered. The algebraic approach builds coarse-space corrections using onl
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
interpolation [<A
HREF="node30.html#StubenGMD69_99">17</A>].
HREF="node30.html#StubenGMD69_99">22</A>].
<P>
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
aggregation</I> algorithm [<A
starting from the original matrix. The algebraic approach is based on the <SPAN CLASS="textit">smoothed
aggregation</SPAN> algorithm [<A
HREF="node30.html#BREZINA_VANEK">1</A>,<A
HREF="node30.html#VANEK_MANDEL_BREZINA">19</A>]. A decoupled version
HREF="node30.html#VANEK_MANDEL_BREZINA">24</A>]. A decoupled version
of this algorithm is implemented, where the smoothed aggregation is applied locally
to each submatrix [<A
HREF="node30.html#TUMINARO_TONG">18</A>]. In the next two subsections we provide
HREF="node30.html#TUMINARO_TONG">23</A>]. In the next two subsections we provide
a brief description of the multi-level Schwarz preconditioners and of the smoothed
aggregation technique as implemented in MLD2P4. For further details the user
is referred to [<A
HREF="node30.html#para_04">2</A>,<A
HREF="node30.html#aaecc_07">3</A>,<A
HREF="node30.html#apnum_07">4</A>,<A
HREF="node30.html#dd2_96">15</A>].
HREF="node30.html#dd2_96">20</A>].
<P>
<BR><HR>
<!--Table of Child-Links-->
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL>
<LI><A NAME="tex2html189"
<UL CLASS="ChildLinks">
<LI><A NAME="tex2html188"
HREF="node11.html">Multi-level Schwarz Preconditioners</A>
<LI><A NAME="tex2html190"
<LI><A NAME="tex2html189"
HREF="node12.html">Smoothed Aggregation</A>
</UL>
<!--End of Table of Child-Links-->
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SRC="file:/usr/share/latex2html/icons/next.png"></A>
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HREF="userhtml.html">
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SRC="file:/usr/share/latex2html/icons/up.png"></A>
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HREF="node9.html">
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SRC="file:/usr/share/latex2html/icons/contents.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html188"
<B> Next:</B> <A NAME="tex2html187"
HREF="node11.html">Multi-level Schwarz Preconditioners</A>
<B> Up:</B> <A NAME="tex2html184"
<B> Up:</B> <A NAME="tex2html183"
HREF="userhtml.html">userhtml</A>
<B> Previous:</B> <A NAME="tex2html178"
<B> Previous:</B> <A NAME="tex2html177"
HREF="node9.html">Example and test programs</A>
&nbsp; <B> <A NAME="tex2html186"
HREF="node1.html">Contents</A></B>
&nbsp; <B> <A NAME="tex2html185"
HREF="node2.html">Contents</A></B> </DIV>
<!--End of Navigation Panel-->
<ADDRESS>
Salvatore Filippone
2008-07-22
2008-07-23
</ADDRESS>
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