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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>2.2 The algorithms</TITLE><LINK REL=STYLESHEET TYPE="text/css" HREF="./Modulef.css" TITLE="Modulef CSS"><meta name="description" value="2.2 The algorithms"><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=tex2html515 HREF="node17.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/previous_motif.gif" ALT="previous"></A><A NAME=tex2html519 HREF="node16.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/up_motif.gif" ALT="up"></A><A NAME=tex2html521 HREF="node19.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/next_motif.gif" ALT="next"></A><A NAME=tex2html523 HREF="node2.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/contents_motif.gif" ALT="contents"></A><A HREF="../Guide5-18/node18.html"><IMG BORDER=0 SRC="../icons/zoom18.gif" ALIGN=BOTTOM ALT="[BIG]"></A><A HREF="../Guide5-14/node18.html"><IMG BORDER=0 SRC="../icons/zoom14.gif" ALIGN=BOTTOM ALT="[Normal]"></A><A HREF="../Guide5-10/node18.html"><IMG BORDER=0 SRC="../icons/zoom10.gif" ALIGN=BOTTOM ALT="[small]"></A><BR><B> Next: </B> <A NAME=tex2html522 HREF="node19.html">3 The domain decomposition method</A><B>Up: </B> <A NAME=tex2html520 HREF="node16.html">2 Iterative methods</A><B> Prev: </B> <A NAME=tex2html516 HREF="node17.html">2.1 The modules</A><B><A HREF="node2.html" >Contents</A></B><HR SIZE=3 WIDTH="75%"><H1><A NAME=SECTION04220000000000000000>2.2 The algorithms</A></H1><P><P><P>It could be interesting to use the algorithms directly, in particular to write an efficient non-linear procedure. Two programs correspond to each module:one in single precision and one in double precision.In principle, the names of the two programs differ only in the last letter:R in single precision (library <b> RESR</b>), D in double (library <b> RESD</b>).<P><P><P><H2><A NAME=SECTION04221000000000000000>2.2.1 List of programs</A></H2><P><P><P><UL><LI> Matrix assembly<A NAME=1880> </A> <UL><LI> <b> ASGC1D</b> assembly of a symmetric or non-symmetric matrix in double precision, <LI> <b> ASGC1R</b> assembly of a symmetric or non-symmetric matrix in single precision. </UL><LI> Assembly of the right-hand-side<A NAME=1885> </A> <UL><LI> <b> ASSBPD</b> assembly of the RHS in double precision (structure B in secondary memory), <LI> <b> ASSEBD</b> assembly of the RHS in double precision (structure B in main memory), <LI> <b> ASSMBD</b> vectorial assembly of the RHS in double precision, <LI> <b> ASSBPR</b> assembly of the RHS in single precision (structure B in secondary memory), <LI> <b> ASSEBR</b> assembly of the RHS in single precision (structure B in main memory), <LI> <b> ASSMBR</b> vectorial assembly of the RHS in double precision. </UL><LI> Impose the boundary conditions<A NAME=1894> </A> <UL><LI> <b> CLGC1D</b> boundary conditions of type <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img61.gif"> = V in double precision, <LI> <b> CLGC2D</b> boundary conditions i.t.o. linear relations in double precision, <LI> <b> CLGC1R</b> boundary conditions of type <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img61.gif"> = V in single precision, <LI> <b> CLGC2R</b> boundary conditions i.t.o. linear relations in single precision. </UL><LI> Solution by iterative method<A NAME=1903> </A> <UL><LI> Incomplete factorization<A NAME=1905> </A> (computation of the preconditioning matrix) <UL><LI> <b> CDLL1D</b> incomplete Cholesky factorization in double precision, <LI> <b> CDLL2D</b> incomplete Crout factorization in double precision, <LI> <b> CDLU1D</b> incomplete Gauss factorization in double precision, <LI> <b> CDLL1R</b> incomplete Cholesky factorization in single precision, <LI> <b> CDLL2R</b> incomplete Crout factorization in single precision, <LI> <b> CDLU1R</b> incomplete Gauss factorization in single precision. </UL> <LI> Solution conjugate gradient iterations <UL><LI> <b> DGRA1D</b> accelerated double conjugate gradient with incomplete Gauss preconditioning in double precision, <LI> <b> ICHR1D</b> conjugate gradient with incomplete Cholesky/Crout preconditioning in double precision, <LI> <b> GCDIAD</b> conjugate gradient with diagonal preconditioning in double precision, <LI> <b> SIMGCD</b> conjugate gradient without preconditioning in double precision, <LI> <b> SSOR1D</b> conjugate gradient with SSOR preconditioning in double precision, <LI> <b> DGRA1R</b> accelerated double conjugate gradient with incomplete Gauss preconditioning in single precision, <LI> <b> ICHR1R</b> conjugate gradient with Cholesky/Crout preconditioning in single precision, <LI> <b> GCDIAR</b> conjugate gradient with diagonal preconditioning <A NAME=1923> </A> in single precision, <LI> <b> SIMGCR</b> conjugate gradient without preconditioning in single precision, <LI> <b> SSOR1R</b> conjugate gradient with SSOR preconditioning <A NAME=1926> </A> in single precision. </UL> <LI> Solution of a preconditioned linear system <UL><LI> <b> DRCHID</b> incomplete Cholesky preconditioning in double precision, <LI> <b> DRCRID</b> incomplete Crout preconditioning in double precision, <LI> <b> DGRA1D</b> incomplete Gauss preconditioning in double precision, <LI> <b> SSOR2D</b> preconditioning by matrix SSOR in double precision, <LI> <b> DRCHIR</b> incomplete Cholesky preconditioning in single precision, <LI> <b> DRCRIR</b> incomplete Crout preconditioning in single precision, <LI> <b> DGRA1R</b> incomplete Gauss preconditioning in single precision, <LI> <b> SSOR2R</b> preconditioning by matrix SSOR in single precision. </UL></UL></UL><HR SIZE=3 WIDTH="75%"><IMG SRC="../icons/smallmod.gif" WIDTH=211 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