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<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 3.2 Final//FR"><!-- Converted with LaTeX2HTML 95.1 (Fri Jan 20 1995) --><!-- by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds --><!-- Modified Simulog 03/97 --><HTML><HEAD><TITLE>1.4 Solution by domain decomposition</TITLE><LINK REL=STYLESHEET TYPE="text/css" HREF="./Modulef.css" TITLE="Modulef CSS"><meta name="description" value="1.4 Solution by domain decomposition"><meta name="keywords" value="Guide5"><meta name="resource-type" value="document"><meta name="distribution" value="global"></HEAD><BODY BGCOLOR="#FFFFFF"><P> <IMG SRC="../icons/smallmod.gif" WIDTH=211 HEIGHT=50 ALIGN=BOTTOM ALT="Modulef"><A NAME=tex2html411 HREF="node8.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/previous_motif.gif" ALT="previous"></A><A NAME=tex2html417 HREF="node5.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/up_motif.gif" ALT="up"></A><A NAME=tex2html419 HREF="node10.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/next_motif.gif" ALT="next"></A><A NAME=tex2html421 HREF="node2.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/contents_motif.gif" ALT="contents"></A><A HREF="../Guide5-18/node9.html"><IMG BORDER=0 SRC="../icons/zoom18.gif" ALIGN=BOTTOM ALT="[BIG]"></A><A HREF="../Guide5-14/node9.html"><IMG BORDER=0 SRC="../icons/zoom14.gif" ALIGN=BOTTOM ALT="[Normal]"></A><A HREF="../Guide5-10/node9.html"><IMG BORDER=0 SRC="../icons/zoom10.gif" ALIGN=BOTTOM ALT="[small]"></A><BR><B> Next: </B> <A NAME=tex2html420 HREF="node10.html">1.5 Correspondence: operator-module</A><B>Up: </B> <A NAME=tex2html418 HREF="node5.html">1 Solution of linear systems</A><B> Prev: </B> <A NAME=tex2html412 HREF="node8.html">1.3 Solution by an iterative method</A><B><A HREF="node2.html" >Contents</A></B><HR SIZE=3 WIDTH="75%"><H1><A NAME=SECTION03140000000000000000>1.4 Solution by domain decomposition</A></H1><P><P><P>The numerical solution of large problems by domain decomposition techniques <A NAME=1215> </A> is very well adapted to current generation parallel computers. However, the efficiency of these techniques depend strongly on the algorithm chosen and its implementation.<P>The approach proposed in the MODULEF code divides the computational domain into non-structured sub-domains ofarbitrary form, and reduces the initial problem to an interface problem.The corresponding operator (the Steklov-Poincaré operator at the continuous level, the Schur complement matrixat the discrete level) is inverted by an preconditioned conjugate gradient algorithm<A NAME=1216> </A>.This algorithm requires, at each step, the solution of a Dirichlet and a Neumann problem on each sub-domain.<P>For a detailed description of the algorithm implemented in MODULEF, consult [<A HREF="node44.html#dd">2</A>].<P><DL COMPACT><DT>Note:<DD> The notion of <b> sub-domains</b> has, here, a different meaning to the the one generally used inMODULEF.In fact, here it is synonym to <b> sub-structure</b>, whereas in general, (COMACO, COMILI,COFORC) it is rather synonym to <b> material number</b>.<P> </DL><P><P><P><HR SIZE=3 WIDTH="75%"><IMG SRC="../icons/smallmod.gif" WIDTH=211 HEIGHT=50 ALIGN=BOTTOM ALT="Modulef"><A NAME=tex2html411 HREF="node8.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/previous_motif.gif" ALT="previous"></A><A NAME=tex2html417 HREF="node5.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/up_motif.gif" ALT="up"></A><A NAME=tex2html419 HREF="node10.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/next_motif.gif" ALT="next"></A><A NAME=tex2html421 HREF="node2.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/contents_motif.gif" ALT="contents"></A><A HREF="../Guide5-18/node9.html"><IMG BORDER=0 SRC="../icons/zoom18.gif" ALIGN=BOTTOM ALT="[BIG]"></A><A HREF="../Guide5-14/node9.html"><IMG BORDER=0 SRC="../icons/zoom14.gif" ALIGN=BOTTOM ALT="[Normal]"></A><A HREF="../Guide5-10/node9.html"><IMG BORDER=0 SRC="../icons/zoom10.gif" ALIGN=BOTTOM ALT="[small]"></A><BR><B> Next: </B> <A NAME=tex2html420 HREF="node10.html">1.5 Correspondence: operator-module</A><B>Up: </B> <A NAME=tex2html418 HREF="node5.html">1 Solution of linear systems</A><B> Prev: </B> <A NAME=tex2html412 HREF="node8.html">1.3 Solution by an iterative method</A><B><A HREF="node2.html" >Contents</A></B><BR> <HR><P><ADDRESS></ADDRESS></BODY></HTML>⌨️ 快捷键说明
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