fdurastante/amg4psblas
1
0
Fork 0
mirror of https://github.com/sfilippone/amg4psblas.git synced 2026-10-07 07:04:59 +00:00
Code Issues Packages Projects Releases Wiki Activity

mld2p4:

Browse Source 
Further doc fixes.
This commit is contained in:
Salvatore Filippone
2008-07-24 06:05:46 +00:00
parent 4dda0494a7
commit 78805bf653
130 changed files with 10569 additions and 7036 deletions
Download Patch File Download Diff File Expand all files Collapse all files
docs/html/node10.html
+13 -15
View File
@@ -1,4 +1,4 @@
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
original version by: Nikos Drakos, CBLU, University of Leeds
@@ -25,8 +25,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds
</HEAD>
<BODY >
<DIV CLASS="navigation"><!--Navigation Panel-->
<!--Navigation Panel-->
<A NAME="tex2html180"
HREF="node11.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
@@ -53,7 +52,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds
&nbsp; <B> <A NAME="tex2html179"
HREF="node2.html">Contents</A></B>
<BR>
<BR></DIV>
<BR>
<!--End of Navigation Panel-->
<H1><A NAME="SECTION00060000000000000000"></A><A NAME="sec:background"></A>
@@ -62,7 +61,7 @@ Multi-level Domain Decomposition Background
</H1>
<P>
<SPAN CLASS="textit">Domain Decomposition</SPAN> (DD) preconditioners, coupled with Krylov iterative
<I>Domain Decomposition</I> (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
@@ -78,7 +77,7 @@ solution of the original problem from the local solutions
HREF="node24.html#dd2_96">20</A>].
<P>
<SPAN CLASS="textit">Additive Schwarz</SPAN> preconditioners are DD preconditioners using overlapping
<I>Additive Schwarz</I> 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="node24.html#dd2_96">20</A>]).
@@ -94,7 +93,7 @@ in a coarse space, which globally couples the information related to the single
submatrices.
<P>
<SPAN CLASS="textit">Two-level Schwarz</SPAN> preconditioners are obtained
<I>Two-level Schwarz</I> 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
@@ -102,7 +101,7 @@ choice of the smoother and of the coarse-level correction, and the
way they are combined [<A
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.
from this system, thus obtaining <I>multi-level</I> preconditioners.
<P>
It is worth noting that optimal preconditioners do not necessarily correspond
@@ -128,8 +127,8 @@ interpolation [<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
starting from the original matrix. The algebraic approach is based on the <I>smoothed
aggregation</I> algorithm [<A
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
@@ -148,15 +147,14 @@ is referred to [<A
<!--Table of Child-Links-->
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL CLASS="ChildLinks">
<UL>
<LI><A NAME="tex2html182"
HREF="node11.html">Multi-level Schwarz Preconditioners</A>
<LI><A NAME="tex2html183"
HREF="node12.html">Smoothed Aggregation</A>
</UL>
<!--End of Table of Child-Links-->
<DIV CLASS="navigation"><HR>
<HR>
<!--Navigation Panel-->
<A NAME="tex2html180"
HREF="node11.html">
@@ -182,11 +180,11 @@ is referred to [<A
<B> Previous:</B> <A NAME="tex2html171"
HREF="node9.html">Example and test programs</A>
&nbsp; <B> <A NAME="tex2html179"
HREF="node2.html">Contents</A></B> </DIV>
HREF="node2.html">Contents</A></B>
<!--End of Navigation Panel-->
<ADDRESS>
Salvatore Filippone
2008-07-23
2008-07-24
</ADDRESS>
</BODY>
</HTML>