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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>1.3 The non-symmetric model problem</TITLE><LINK REL=STYLESHEET TYPE="text/css" HREF="./Modulef.css" TITLE="Modulef CSS"><meta name="description" value="1.3 The non-symmetric model problem"><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=tex2html802 HREF="node42.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/previous_motif.gif" ALT="previous"></A><A NAME=tex2html806 HREF="node40.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/up_motif.gif" ALT="up"></A><A NAME=tex2html808 HREF="node44.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/next_motif.gif" ALT="next"></A><A NAME=tex2html810 HREF="node2.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/contents_motif.gif" ALT="contents"></A><A HREF="../Guide5-18/node43.html"><IMG BORDER=0 SRC="../icons/zoom18.gif" ALIGN=BOTTOM ALT="[BIG]"></A><A HREF="../Guide5-14/node43.html"><IMG BORDER=0 SRC="../icons/zoom14.gif" ALIGN=BOTTOM ALT="[Normal]"></A><A HREF="../Guide5-10/node43.html"><IMG BORDER=0 SRC="../icons/zoom10.gif" ALIGN=BOTTOM ALT="[small]"></A><BR><B> Next: </B> <A NAME=tex2html809 HREF="node44.html">References</A><B>Up: </B> <A NAME=tex2html807 HREF="node40.html">1 Examples</A><B> Prev: </B> <A NAME=tex2html803 HREF="node42.html">1.2 The symmetric model problem</A><B><A HREF="node2.html" >Contents</A></B><HR SIZE=3 WIDTH="75%"><H1><A NAME=SECTION05130000000000000000>1.3 The non-symmetric model problem</A></H1><P><P><P>The solution of partial differential equations by the finite element method oftenleads to linear systemswith positive definite symmetric matrices. To obtain a non-symmetric matrix,a particular scheme must intervenein the variational formulation, for example of the decentralizing type.This requires therefore a special treatment during the construction of the element matrices,or else a modification in the assembly of the matrix of the linear system to be solved.<P>To simplify this presentation,we assume that we construct the matrix and RHS of the linear system in the usual way. Under these conditions,the modules used are PREPAC, ASSMUA, ASEMBV, CLIMGC, GAUSPC and DRGAPC for a solution by a direct method, or PREPGC, ASSAMA, ASEMBV, CLIMGC, CONDLU and DGRADA for a solution by an iterative method.<P>The physical problem arises from the numerical simulation of the exploitationof a oil-field. The matrix is obtained by a finite difference type scheme at 7 points.It corresponds to a three-dimensional problem, the domain <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img84.gif"> is a cube, and thenodes of the mesh are distributed over a network in the three space directions.The example presented here contains 1000 unknowns, corresponding to the pressure calculated ateach of the nodes in the mesh (there are 10 nodes in each direction),The resulting matrix is strongly non-symmetric, and badly conditioned; this linear system is used byoil engineers to test the efficiency of their solution and preconditioning algorithms.<P>For more details about the variational formulation of this problem, as well as its finite element approximation and the different aspects of the computer implementation, consult [<A HREF="node44.html#magnifiquedocument">1</A>].Other numerical experiences, concerning the solution of this type of problem, are also found in [<A HREF="node44.html#magnifiquedocument">1</A>].<P><P><P><H2><A NAME=SECTION05131000000000000000>1.3.1 Solution by the Gauss method</A></H2><P><P><P>The solution of the model problem by a direct method is performed by calling program <b> GAUSXX</b>, using the following data:<P><PRE> mail $ FILE NAME 1 $ AND LEVEL OF THE D.S. MAIL 1 5 3 $ NDSM NTYP ND tae $ FILE NAME 1 $ AND LEVEL OF THE D.S. TAE 1 $ 1 IF BDCL IS USED , 0 IF NOT bdcl $ FILE NAME 1 $ AND LEVEL OF THE D.S. BDCL 0 $ 1 IF BOUNDARY CONDITIONS $ I.T.O. LINEAR RELATIONS EXIST mua $ FILE NAME 1 $ AND LEVEL OF THE D.S. MUA sd.amat $ FILE NAME 1 $ AND LEVEL OF THE D.S. AMAT sd.b $ FILE NAME 1 $ AND LEVEL OF THE D.S. B sd.b.out $ FILE NAME 1 $ AND LEVEL OF THE D.S. B 5 $ IMPREB</PRE><P>The corresponding results are given below:<P><PRE> M M OOO DDDD U U L EEEEE FFFFF MM MM O O D D U U L E F M M M O O D D U U L EEEE FFFF M M O O D D U U L E F M M OOO DDDD UUU LLLLL EEEEE F VERSION 93 DATE : 22/07/93 AUTEUR : pate ****************************************** EXECUTING THE GAUSS ****************************************** -- CREATE THE DATA =-= EXECUTE MODULE (DATA EXISTING) =-= END =-= ? - - ---e -- NAME OF DATA FILE ? dgaus.data ++ OPEN(10,FILE='dgaus.data',SPEC='OLD',RECL=0) -- PRINT PARAMETER FOR THE EXECUTION ? 5 ++ OPEN(11,FILE='mail',SPEC='OLD,UNFORMATTED',RECL=0) ++ OPEN(12,FILE='tae',SPEC='OLD,UNFORMATTED',RECL=0) ++ OPEN(13,FILE='bdcl',SPEC='OLD,UNFORMATTED',RECL=0) ++ OPEN(14,FILE='mua',SPEC='UNFORMATTED',RECL=0) ++ OPEN(15,FILE='sd.amat',SPEC='UNFORMATTED',RECL=0) &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& MODULE TAM : S.D.E. AMAT (NFAMAT ET NIAMAT) : 15 1 S.D.S. MUA (NFMUA ET NIMUA ) : 0 1 ++ OPEN(15,FILE='sd.b',SPEC='UNFORMATTED',RECL=0) ++ OPEN(16,FILE='sd.b.out',SPEC='UNFORMATTED',RECL=0) &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& MODULE GAUSPC : PRECISION (EPS) : 0.1000000E-05 RETURN OPTION (NENTRE) : 0 INPUT D.S. NDL1 (NFNDL1 AND NINDL1): 0 0 INPUT D.S. MUA (NFMUAE AND NIMUAE): 0 1 OUTPUT D.S. MUA (NFMUAS AND NIMUAS): 0 2 ** FACTORISATION EXECUTION TIME 0.260645E+01 S ** ** NUMBER OF UNKNOWS 1000 ** ** SIZE OF ARRAY MUA5 140960 ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& END OF MODULE GAUSPC &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& MODULE DRGAPC : PROCESSING OPTION (NIVEAU) : 2 PRESENCE OF BOUNDARY CONDITIONS IN L.R. (NCLRL) : 0 INPUT D.S. NDL1 (NFNDL1 AND NINDL1) : 0 0 INPUT D.S. MUA (NFMUAE AND NIMUAE) : 0 2 INPUT D.S. B (NFBE AND NIBE) : 15 1 INPUT D.S. BDCL (NFBDCL AND NIBDCL) : 13 1 OUTPUT D.S. B (NFBS AND NIBS) : 16 1 ** SOLUTION EXECUTION TIME 0.210832E+00 SECONDES ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& END OF MODULE DRGAPC &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& PRINT OUT OF D.S. B OF LEVEL 1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& TITLE : DATE AND USER'S NAME : 06/05/93 pate DATA STRUCTURE TYPE : B LEVEL AND STATE NUMBER : 1 1 NUMBER OF ASSOCIATED TABLES : 0 TABLE B 2 ---------- TYPE OF THE TABLE (NTYT) : 5 NUMBER OF INDICES AND THEIR MAX VALUES (NIND..) : 2 1 1000 OPTION (1: PAGES OF SAME SIZE , 0: IF NOT) (NCOD) : 1 NUMBER OF PAGES OF THE TABLE B4 (NBLOC) : 1 NUMBER OF NODES (NOE) : 1000 NUMBER OF TABLES B4 IN THIS D.S. (NBBLOC) : 1 CONSTANT NUMBER OF D.O.F. AT EACH NODE OR 0 (ND) : 1 NUMBER OF D.O.F. OR LENGHT OF A B4 PAGE (NTDL) : 1000 STORAGE OPTION FOR B4 (NCODSB) : -1 TABLE B 3 ---------- POINTER ON THE LAST ROW OF EACH PAGE OF B4 1 0 2 1000 TABLE B4(NDSM,NTDL) NUMBER : 1 ----------------------------------- TABLE B4(NDSM,NTDL) PAGINATED IN 1 OR MORE PAGES ------------------------------------------------ PAGE 1⌨️ 快捷键说明
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