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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>1.5 Correspondence: operator-module</TITLE><LINK REL=STYLESHEET TYPE="text/css" HREF="./Modulef.css" TITLE="Modulef CSS"><meta name="description" value="1.5 Correspondence: operator-module"><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=tex2html422 HREF="node9.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/previous_motif.gif" ALT="previous"></A><A NAME=tex2html426 HREF="node5.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/up_motif.gif" ALT="up"></A><A NAME=tex2html428 HREF="node11.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/next_motif.gif" ALT="next"></A><A NAME=tex2html430 HREF="node2.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/contents_motif.gif" ALT="contents"></A><A HREF="../Guide5-18/node10.html"><IMG BORDER=0 SRC="../icons/zoom18.gif" ALIGN=BOTTOM ALT="[BIG]"></A><A HREF="../Guide5-14/node10.html"><IMG BORDER=0 SRC="../icons/zoom14.gif" ALIGN=BOTTOM ALT="[Normal]"></A><A HREF="../Guide5-10/node10.html"><IMG BORDER=0 SRC="../icons/zoom10.gif" ALIGN=BOTTOM ALT="[small]"></A><BR><B> Next: </B> <A NAME=tex2html429 HREF="node11.html">Part II: The modules</A><B>Up: </B> <A NAME=tex2html427 HREF="node5.html">1 Solution of linear systems</A><B> Prev: </B> <A NAME=tex2html423 HREF="node9.html">1.4 Solution by domain decomposition</A><B><A HREF="node2.html" >Contents</A></B><HR SIZE=3 WIDTH="75%"><H1><A NAME=SECTION03150000000000000000>1.5 Correspondence: operator-module</A></H1><P><P><P>The solution of a linear system consists of several steps which can be decomposed into several mathematical operators:<P><UL><LI> construction of the matrix and right-hand-side,<LI> solution.</UL><P>The construction of the matrix can be decomposed into:<UL><LI> compute the pointers defining the matrix structure,<LI> matrix assembly,<LI> assemble the right-hand-side,<LI> impose boundary conditions.</UL><P> depending on the method chosen, direct or iterative, the solution can also be decomposed into several operators:<P><UL><LI> Direct methods: <UL><LI> matrix factorization, <LI> forward-and-backward substitution. </UL><LI> Iterative methods: <UL><LI> construction of the preconditioner, <LI> iterative algorithm. </UL></UL><P>For the particular case of the domain decomposition method, all the above operators are used, as this algorithmperforms iterations on the unknowns on the sub-domain interfaces, the unknowns insidethe sub-domains being recomputed at each iteration by a direct method.<P>This sequence can be summarized as follows:<UL><LI> For each sub-domain: <UL><LI> assembly and factorization of the matrix of the Dirichlet problem, <LI> assembly and factorization of the matrix of the Neumann problem, <LI> construction of the right-hand-side. </UL> <LI> For the global solution: <UL><LI> construction of the preconditioner, <LI> conjugate gradient solution algorithm on the interface, consisting at each iteration of a Dirichlet forward-and-ackward substitution and a Neumann forward-and-backward substitution on each sub-domain. </UL></UL><P><P><P>As a function of the type of method chosen, on the one hand, and the matrix characteristics, on the other hand, there are several modules in library <b> RESO</b> corresponding to each operator:<P><UL><LI> Computation of pointers<A NAME=1242> </A>: <UL><LI> <b> PREPAC<A NAME=1244> </A></b> for a MUA structure, <LI> <b> PREPAF<A NAME=1245> </A></b> for a frontal method, <LI> <b> PREPGC<A NAME=1246> </A></b> for a AMAT structure.<P> </UL><LI> Matrix assembly<A NAME=1248> </A>: <UL><LI> <b> ASSAMA<A NAME=1250> </A></b> for a AMAT structure, <LI> <b> ASMAPS<A NAME=1251> </A></b> for a MUA structure in secondary memory, <LI> <b> ASSMUA<A NAME=1252> </A></b> for a MUA structure in main memory. </UL><LI> Assembly of the right-hand-side vector<A NAME=1254> </A>: <UL><LI> <b> ASEMBV<A NAME=1256> </A></b> for a B structure in main memory, <LI> <b> ASMBMS<A NAME=1257> </A></b> for a B structure in secondary memory. </UL><LI> Applying the boundary conditions<A NAME=1259> </A>: <UL><LI> <b> CLIMGC<A NAME=1261> </A></b> for a AMAT structure, <LI> <b> CLIMPC<A NAME=1262> </A></b> for a MUA structure in main memory, <LI> <b> CLIMPS<A NAME=1263> </A></b> for a MUA structure in secondary memory. </UL><LI> Solution by a direct method: <UL><LI> Factorization<A NAME=1266> </A>: <UL><LI> <b> CHOLPC<A NAME=1268> </A></b> for positive definite symmetric matrices (structure MUA symmetric in main memory), <LI> <b> CHOLPS<A NAME=1269> </A></b> for positive definite symmetric matrices (structure MUA symmetric in secondary memory), <LI> <b> CROUPC<A NAME=1270> </A></b> for symmetric matrices (structure MUA symmetric in main memory), <LI> <b> GAUSPC<A NAME=1271> </A></b> for regular matrices (structure MUA non-symmetric in main memory). </UL> <LI> Solution by forward-and-backward substitution<A NAME=1273> </A>: <UL><LI> <b> DRCHPC<A NAME=1275> </A></b> for positive definite symmetric matrices (structure MUA symmetric in main memory), <LI> <b> DRCHPS<A NAME=1276> </A></b> for positive definite symmetric matrices (structure MUA symmetric in secondary memory), <LI> <b> DRCRPC<A NAME=1277> </A></b> for symmetric matrices (structure MUA symmetric in main memory), <LI> <b> DRGAPC<A NAME=1278> </A></b> for regular matrices (structure MUA non-symmetric in main memory). </UL> <LI> Special case of the frontal method<A NAME=1280> </A>: <UL><LI> <b> FRONT<A NAME=1282> </A></b>: this model performs the tasks consisting of the assembly of the matrix and RHS, imposing the boundary conditions, the factorization of the matrix and, lastly, the solution of the system, whatever the properties of the matrix. </UL></UL><LI> Solution by an iterative method: <UL><LI> Construction of the preconditioner<A NAME=1286> </A>: <UL><LI> <b> CONDLU<A NAME=1288> </A></b> incomplete factorization of regular matrices (structure <BR>[4] AMAT non-symmetric in main memory), <LI> <b> FANIGC<A NAME=1289> </A></b> incomplete factorization of positive definite symmetric matrices (structure AMAT symmetric in main memory). </UL> <LI> Iterative algorithm<A NAME=1291> </A>: <UL><LI> <b> DGRADA<A NAME=1293> </A></b> iterations of double conjugate gradient<A NAME=1294> </A> and preconditioned for regular matrices (structure AMAT in main memory) <LI> <b> ICHRGC<A NAME=1295> </A></b> conjugate gradient iterations preconditioned by incomplete factorization<A NAME=1296> </A> of Cholesky or Crout, for positive definite symmetric matrices (structure AMAT in main memory) <LI> <b> GCDIAG<A NAME=1297> </A></b> conjugate gradient iterations with a diagonal preconditioning <A NAME=1298> </A> for positive definite symmetric matrices (structure AMAT in main memory), <LI> <b> SSORGC<A NAME=1299> </A></b> conjugate gradient iterations with a SSOR preconditioning<A NAME=1300> </A>, for positive definite symmetric matrices (structure AMAT in main memory), <LI> <b> SIMPGC<A NAME=1301> </A></b> <b> non</b> preconditioned conjugate gradient iterations for positive definite symmetric matrices (structure AMAT in main memory). </UL></UL></UL><P>For the case of a domain decomposition method,we need to use specific operators (super modules that use the preceding algorithms):<P><UL><LI> <b> PRSDOM<A NAME=1307> </A></b>: this program creates, using D.S. NOPO of different sub-domains as well as D.S. MILI and FORC, the operators required by the conjugate gradient algorithm, <LI> <b> SDOMVR<A NAME=1308> </A></b>: this program contains the conjugate gradient algorithm for the Schur matrix complement<A NAME=1309> </A> in single precision, <LI> <b> SDOMVD<A NAME=1310> </A></b>: this program contains the conjugate gradient algorithm for the Schur matrix complement in double precision.</UL><HR SIZE=3 WIDTH="75%"><IMG SRC="../icons/smallmod.gif" WIDTH=211 HEIGHT=50 ALIGN=BOTTOM ALT="Modulef"><A NAME=tex2html422 HREF="node9.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/previous_motif.gif" ALT="previous"></A><A NAME=tex2html426 HREF="node5.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/up_motif.gif" ALT="up"></A><A NAME=tex2html428 HREF="node11.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/next_motif.gif" ALT="next"></A><A NAME=tex2html430 HREF="node2.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/contents_motif.gif" ALT="contents"></A><A HREF="../Guide5-18/node10.html"><IMG BORDER=0 SRC="../icons/zoom18.gif" ALIGN=BOTTOM ALT="[BIG]"></A><A HREF="../Guide5-14/node10.html"><IMG BORDER=0 SRC="../icons/zoom14.gif" ALIGN=BOTTOM ALT="[Normal]"></A><A HREF="../Guide5-10/node10.html"><IMG BORDER=0 SRC="../icons/zoom10.gif" ALIGN=BOTTOM ALT="[small]"></A><BR><B> Next: </B> <A NAME=tex2html429 HREF="node11.html">Part II: The modules</A><B>Up: </B> <A NAME=tex2html427 HREF="node5.html">1 Solution of linear systems</A><B> Prev: </B> <A NAME=tex2html423 HREF="node9.html">1.4 Solution by domain decomposition</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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