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Merge mumps into trunk
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@@ -1,4 +1,4 @@
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<!--Converted with LaTeX2HTML 2012 (1.2)
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original version by: Nikos Drakos, CBLU, University of Leeds
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@@ -25,7 +25,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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</HEAD>
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<BODY >
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<!--Navigation Panel-->
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<DIV CLASS="navigation"><!--Navigation Panel-->
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<A NAME="tex2html195"
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HREF="node12.html">
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<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
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@@ -48,7 +49,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<B> <A NAME="tex2html194"
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HREF="node2.html">Contents</A></B>
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<BR>
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<BR>
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<BR></DIV>
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<!--End of Navigation Panel-->
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<H1><A NAME="SECTION00060000000000000000"></A><A NAME="sec:background"></A>
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@@ -57,7 +58,7 @@ Multi-level Domain Decomposition Background
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</H1>
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<P>
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<I>Domain Decomposition</I> (DD) preconditioners, coupled with Krylov iterative
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<SPAN CLASS="textit">Domain Decomposition</SPAN> (DD) preconditioners, coupled with Krylov iterative
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solvers, are widely used in the parallel solution of large and sparse linear systems.
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These preconditioners are based on the divide and conquer technique: the matrix
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to be preconditioned is divided into submatrices, a ``local'' linear system
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@@ -73,7 +74,7 @@ solution of the original problem from the local solutions
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HREF="node25.html#dd2_96">22</A>].
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<P>
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<I>Additive Schwarz</I> preconditioners are DD preconditioners using overlapping
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<SPAN CLASS="textit">Additive Schwarz</SPAN> preconditioners are DD preconditioners using overlapping
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submatrices, i.e. with some common rows, to couple the local information
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related to the submatrices (see, e.g., [<A
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HREF="node25.html#dd2_96">22</A>]).
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@@ -89,7 +90,7 @@ in a coarse space, which globally couples the information related to the single
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submatrices.
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<P>
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<I>Two-level Schwarz</I> preconditioners are obtained
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<SPAN CLASS="textit">Two-level Schwarz</SPAN> preconditioners are obtained
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by combining basic (one-level) Schwarz preconditioners with a coarse-level
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correction. In this context, the one-level preconditioner is often
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called `smoother'. Different two-level preconditioners are obtained by varying the
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@@ -97,7 +98,7 @@ choice of the smoother and of the coarse-level correction, and the
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way they are combined [<A
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HREF="node25.html#dd2_96">22</A>]. The same reasoning can be applied starting
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from the coarse-level system, i.e. a coarse-space correction can be built
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from this system, thus obtaining <I>multi-level</I> preconditioners.
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from this system, thus obtaining <SPAN CLASS="textit">multi-level</SPAN> preconditioners.
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<P>
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It is worth noting that optimal preconditioners do not necessarily correspond
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@@ -123,8 +124,8 @@ interpolation [<A
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<P>
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MLD2P4 uses a pure algebraic approach for building the sequence of coarse matrices
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starting from the original matrix. The algebraic approach is based on the <I>smoothed
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aggregation</I> algorithm [<A
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starting from the original matrix. The algebraic approach is based on the <SPAN CLASS="textit">smoothed
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aggregation</SPAN> algorithm [<A
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HREF="node25.html#BREZINA_VANEK">1</A>,<A
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HREF="node25.html#VANEK_MANDEL_BREZINA">26</A>]. A decoupled version
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of this algorithm is implemented, where the smoothed aggregation is applied locally
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@@ -144,14 +145,15 @@ is referred to [<A
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<!--Table of Child-Links-->
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<UL>
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<UL CLASS="ChildLinks">
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<LI><A NAME="tex2html197"
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HREF="node12.html">Multi-level Schwarz Preconditioners</A>
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<LI><A NAME="tex2html198"
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HREF="node13.html">Smoothed Aggregation</A>
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</UL>
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<!--End of Table of Child-Links-->
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<HR>
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<DIV CLASS="navigation"><HR>
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<!--Navigation Panel-->
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<A NAME="tex2html195"
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HREF="node12.html">
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@@ -173,7 +175,7 @@ is referred to [<A
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<B> Previous:</B> <A NAME="tex2html186"
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HREF="node10.html">Example and test programs</A>
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<B> <A NAME="tex2html194"
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HREF="node2.html">Contents</A></B>
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HREF="node2.html">Contents</A></B> </DIV>
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<!--End of Navigation Panel-->
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</BODY>
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