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mld2p4:

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Further docs fixes.
This commit is contained in:
Salvatore Filippone
2008-07-23 09:08:06 +00:00
parent cf4061d09e
commit 5a8ed47797
34 changed files with 5454 additions and 5187 deletions
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+31 -31
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@@ -27,30 +27,30 @@ original version by: Nikos Drakos, CBLU, University of Leeds
<BODY >
<DIV CLASS="navigation"><!--Navigation Panel-->
<A NAME="tex2html186"
<A NAME="tex2html180"
HREF="node11.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
SRC="file:/usr/share/latex2html/icons/next.png"></A>
<A NAME="tex2html182"
<A NAME="tex2html176"
HREF="userhtml.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
SRC="file:/usr/share/latex2html/icons/up.png"></A>
<A NAME="tex2html176"
<A NAME="tex2html170"
HREF="node9.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
SRC="file:/usr/share/latex2html/icons/prev.png"></A>
<A NAME="tex2html184"
<A NAME="tex2html178"
HREF="node2.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
SRC="file:/usr/share/latex2html/icons/contents.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html187"
<B> Next:</B> <A NAME="tex2html181"
HREF="node11.html">Multi-level Schwarz Preconditioners</A>
<B> Up:</B> <A NAME="tex2html183"
<B> Up:</B> <A NAME="tex2html177"
HREF="userhtml.html">userhtml</A>
<B> Previous:</B> <A NAME="tex2html177"
<B> Previous:</B> <A NAME="tex2html171"
HREF="node9.html">Example and test programs</A>
&nbsp; <B> <A NAME="tex2html185"
&nbsp; <B> <A NAME="tex2html179"
HREF="node2.html">Contents</A></B>
<BR>
<BR></DIV>
@@ -73,15 +73,15 @@ into subdomains, e.g. in a PDE discretization, to (approximately) solving the
subproblems corresponding to the subdomains and to building an approximate
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">20</A>].
HREF="node24.html#Cai_Widlund_92">6</A>,<A
HREF="node24.html#dd1_94">7</A>,<A
HREF="node24.html#dd2_96">20</A>].
<P>
<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">20</A>]).
HREF="node24.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
@@ -100,7 +100,7 @@ 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">20</A>]. The same reasoning can be applied starting
HREF="node24.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 <SPAN CLASS="textit">multi-level</SPAN> preconditioners.
@@ -124,24 +124,24 @@ 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">22</A>].
HREF="node24.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 <SPAN CLASS="textit">smoothed
aggregation</SPAN> algorithm [<A
HREF="node30.html#BREZINA_VANEK">1</A>,<A
HREF="node30.html#VANEK_MANDEL_BREZINA">24</A>]. A decoupled version
HREF="node24.html#BREZINA_VANEK">1</A>,<A
HREF="node24.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">23</A>]. In the next two subsections we provide
HREF="node24.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">20</A>].
HREF="node24.html#para_04">2</A>,<A
HREF="node24.html#aaecc_07">3</A>,<A
HREF="node24.html#apnum_07">4</A>,<A
HREF="node24.html#dd2_96">20</A>].
<P>
<BR><HR>
@@ -149,39 +149,39 @@ is referred to [<A
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL CLASS="ChildLinks">
<LI><A NAME="tex2html188"
<LI><A NAME="tex2html182"
HREF="node11.html">Multi-level Schwarz Preconditioners</A>
<LI><A NAME="tex2html189"
<LI><A NAME="tex2html183"
HREF="node12.html">Smoothed Aggregation</A>
</UL>
<!--End of Table of Child-Links-->
<DIV CLASS="navigation"><HR>
<!--Navigation Panel-->
<A NAME="tex2html186"
<A NAME="tex2html180"
HREF="node11.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
SRC="file:/usr/share/latex2html/icons/next.png"></A>
<A NAME="tex2html182"
<A NAME="tex2html176"
HREF="userhtml.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
SRC="file:/usr/share/latex2html/icons/up.png"></A>
<A NAME="tex2html176"
<A NAME="tex2html170"
HREF="node9.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
SRC="file:/usr/share/latex2html/icons/prev.png"></A>
<A NAME="tex2html184"
<A NAME="tex2html178"
HREF="node2.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
SRC="file:/usr/share/latex2html/icons/contents.png"></A>
<BR>
<B> Next:</B> <A NAME="tex2html187"
<B> Next:</B> <A NAME="tex2html181"
HREF="node11.html">Multi-level Schwarz Preconditioners</A>
<B> Up:</B> <A NAME="tex2html183"
<B> Up:</B> <A NAME="tex2html177"
HREF="userhtml.html">userhtml</A>
<B> Previous:</B> <A NAME="tex2html177"
<B> Previous:</B> <A NAME="tex2html171"
HREF="node9.html">Example and test programs</A>
&nbsp; <B> <A NAME="tex2html185"
&nbsp; <B> <A NAME="tex2html179"
HREF="node2.html">Contents</A></B> </DIV>
<!--End of Navigation Panel-->
<ADDRESS>