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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>2.10 Norm and residues</TITLE><LINK REL=STYLESHEET TYPE="text/css" HREF="./Modulef.css" TITLE="Modulef CSS"><meta name="description" value="2.10 Norm and residues"><meta name="keywords" value="Guide6"><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=tex2html727 HREF="node20.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/previous_motif.gif" ALT="previous"></A><A NAME=tex2html731 HREF="node11.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/up_motif.gif" ALT="up"></A><A NAME=tex2html733 HREF="node22.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/next_motif.gif" ALT="next"></A><A NAME=tex2html735 HREF="node2.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/contents_motif.gif" ALT="contents"></A><A HREF="../Guide6-18/node21.html"><IMG BORDER=0 SRC="../icons/zoom18.gif" ALIGN=BOTTOM ALT="[BIG]"></A><A HREF="../Guide6-14/node21.html"><IMG BORDER=0 SRC="../icons/zoom14.gif" ALIGN=BOTTOM ALT="[Normal]"></A><A HREF="../Guide6-10/node21.html"><IMG BORDER=0 SRC="../icons/zoom10.gif" ALIGN=BOTTOM ALT="[small]"></A><BR><B> Next: </B> <A NAME=tex2html734 HREF="node22.html">3 Manipulation of structures and miscellaneous</A><B>Up: </B> <A NAME=tex2html732 HREF="node11.html">2 Manipulation of solutions</A><B> Prev: </B> <A NAME=tex2html728 HREF="node20.html">2.9 Extrema of a D.S. B</A><B><A HREF="node2.html" >Contents</A></B><HR SIZE=3 WIDTH="75%"><H1><A NAME=SECTION033100000000000000000>2.10 Norm and residues</A></H1><P><P><P><H2><A NAME=SECTION033101000000000000000>2.10.1 Norm corresponding to D.S. B</A></H2><P><P><P>Comparing the exact solution with the calculated solution consists of computing, at each node:<P><UL><LI> the difference <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img24.gif"><LI> the relative difference <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img25.gif"><LI> the percentage <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img26.gif"></UL><P>where <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img27.gif"> is the exact solution and <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img28.gif"> is the calculated solution, and printing, for each degreeof freedom:<P><UL><LI> the <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img29.gif"> error norm<DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img30.gif"></DIV><LI> the <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img29.gif"> relative error norm<DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img31.gif"></DIV><LI> the <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img32.gif"> relative error norm<DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img33.gif"></DIV><LI> the maximum error<DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img34.gif"></DIV></UL><P>by indicating in addition the number and coordinates of the node where the maximum occurs.<P><P><P>Preprocessor <b> NORMXX</b> compares the calculated solution with the exact solutionfor those cases where the solution to a problem is known analytically. It callsmodule NORME:<P><PRE> SUBROUTINE NORME (M,XM,DM,NFMAIL,NIMAIL,NFCOOR,NICOOR,NFB,NIB, + NFBS,NIBS,INDICB,NSM,FONINT,SOLEX,DSOLEX)C ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++C AIM : IPRINT THE EXACT SOLUTION, THE CALCULATED SOLUTION,C --- THE ABSOLUTE AND RELATIVE DIFFERENCES BETWEEN THEM,C THE L1,L2 ERRORS AND MAXC ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++</PRE><P>where<P><UL><LI> M, XM and DM designates the super array,<LI> NFMAIL, NIMAIL are the file number and level of structure <b> MAIL</b>,<LI> NFCOOR, NICOOR are the file number and level of structure <b> COOR</b>,<LI> NFB, NIB are the file number and level of structure <b> B</b>,<LI> NFBS, NIBS are the file number and level of structure <b> B</b> on exit,<LI> INDICB is the save option: <BR> 1 : the error is stored in NFBS (used in this case), 0 if not,<LI> NSM is the number of the load case to consider (between 1 and NDSM),<LI> FONINT is a logical set to .TRUE. if functions SOLEX or DSOLEX are input asinterpreted functions, and set to .FALSE. if they are input in the classical manner,<LI> SOLEX, DSOLEX are the functions used to input the exact solution (in single or double precision).</UL><P><P><P>Depending on the value of FONINT, functions SOLEX or DSOLEX must be written using the following format:<P><PRE> FUNCTION SOLEX(I,X,Y,Z) DOUBLE PRECISION FUNCTION DSOLEX(I,X,Y,Z)</PRE><P>where I is the degree of freedom number of the node with coordinates X, Y and Z.<P><P><P><H2><A NAME=SECTION033102000000000000000>2.10.2 Norm corresponding to D.S. TAE</A></H2><P><P><P>Preprocessor <b> NORMXX</b> compares the calculated stresses with the exact solutionfor those cases where the stresses of elasticity problem is known analytically, using thesame method of computation as for a D.S. <b> B</b> as seen above. It calls module NORTAE:<P><PRE> SUBROUTINE NORTAE(M,XM,DM,NFTAE,NITAE,NFTAES,NITAES,INDICB, + FONINT,SOLEX,DSOLEX,NSM,NC1)C ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++C AIM : PRINT THE EXACT SOLUTION THE CALCULATED SOLUTION,C --- THE ABSOLUTE AND RELATIVE DIFFERENCES BETWEEN THEM,C THE L1,L2 ERRORS AND MAX FOR A SOLUTION GIVEN BY TAESC ..................................................................</PRE><P>where<P><UL><LI> M, XM and DM designates the super array,<LI> NFTAE, NITAE are the file number and level of structure <b> TAE</b>,<LI> NFTAES, NITAES are the file number and level of structure <b> TAES</b> on exit,<LI> INDICB is the save option: <BR> 1 : the error is stored in NFTAES (used in this case), 0 if not,<LI> NSM is the number of the load case to consider (between 1 and NDSM),<LI> FONINT is a logical set to .TRUE. if functions SOLEX or DSOLEX are input asinterpreted functions, and set to .FALSE. if they are input in the classical manner,<LI> SOLEX, DSOLEX are the functions used to input the exact solution (in single or double precision).</UL><P><P><P>Depending on the value of FONINT, functions SOLEX or DSOLEX must be written using the following format:<P><PRE> FUNCTION SOLEX(I,X,Y,Z) DOUBLE PRECISION FUNCTION DSOLEX(I,X,Y,Z)</PRE><P>where I is the component number of the stresses treated, and X, Y and Z are the coordinates of the computational point of this stress.<P><P><P><H2><A NAME=SECTION033103000000000000000>2.10.3 Energy norm corresponding to D.S. B</A></H2><P><P><P>Preprocessor <b> NORMXX</b> calculates the energy norm between the exact solution and the solution obtainedwhen solving the problem, for those cases where the solution to a problem is known analytically.<P><DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img35.gif"></DIV><P>It calls module ENERGI:<P><PRE> SUBROUTINE ENERGI (M,XM,DM,NFMAIL,NIMAIL,NFCOOR,NICOOR,NFB,NIB, + NFTAE,NITAE,NSM,FONINT,SOLEX,DSOLEX)C ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++C AIM : CALCULATE THE ENERGY ERROR NORMC --- |A ( U-UH ; U-UH )|C ..................................................................</PRE><P>where<P><UL><LI> M, XM and DM designates the super array,<LI> NFMAIL, NIMAIL are the file number and level of structure <b> MAIL</b>,<LI> NFCOOR, NICOOR are the file number and level of structure <b> COOR</b>,<LI> NFB, NIB are the file number and level of structure <b> B</b>,<LI> NFTAE, NITAE are the file number and level of structure <b> TAE</b>,<LI> NSM is the number of the load case to consider (between 1 and NDSM),<LI> FONINT is a logical set to .TRUE. if functions SOLEX or DSOLEX are input asinterpreted functions, and set to .FALSE. if they are input in the classical manner,<LI> SOLEX, DSOLEX are the functions used to input the exact solution (in single or double precision).</UL><P><P><P>Depending on the value of FONINT, functions SOLEX or DSOLEX must be written using the following format:<P><PRE> FUNCTION SOLEX(I,X,Y,Z) DOUBLE PRECISION FUNCTION DSOLEX(I,X,Y,Z)</PRE><P>where I is the number of the degree of freedom of the node with coordinates X, Y et Z.<P><P><P><H2><A NAME=SECTION033104000000000000000>2.10.4 Solution error for D.S. B</A></H2><P><P><P>Module ERREUR calculates the solution error for a linear system from thesolution of this system and the element matrices and right-hand-side vectors.For clamped degrees of freedom, the result of this computation indicates the reaction.<P><PRE> SUBROUTINE ERREUR(M,NFTAE,NITAE,NFB,NIB,NFNDL1,NINDL1,NFBER, + NIBER,NTBER,NOT1,NOT2)C +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++C AIM : COMPUTE THE ERROR VECTOR.C ---C +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++</PRE><P>where<P><UL><LI> M is the super array,<LI> NFTAE, NITAE are the file number and level of structure <b> TAE</b> of element arrays,<LI> NFB, NIB are the file number and level of structure <b> B</b>, the computed solution,<LI> NFNDL1, NINDL1 are the file number and level of the eventual structure <b> NDL1</b>,<LI> NFBER, NIBER and NTBER are the file number, level and the number of arrays to associate with the output structure, <b> B</b>, the solution error,<LI> NOT1 is the number of the element array containing the stiffness matrices,<LI> NOT2 is the number of the element array containing the right-hand-side vectors.</UL><P>If NTBER is non-zero, the associated descriptive arrays must be input (see above).<P><HR SIZE=3 WIDTH="75%"><IMG SRC="../icons/smallmod.gif" WIDTH=211 HEIGHT=50 ALIGN=BOTTOM ALT="Modulef"><A NAME=tex2html727 HREF="node20.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/previous_motif.gif" ALT="previous"></A><A NAME=tex2html731 HREF="node11.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/up_motif.gif" ALT="up"></A><A NAME=tex2html733 HREF="node22.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/next_motif.gif" ALT="next"></A><A NAME=tex2html735 HREF="node2.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/contents_motif.gif" ALT="contents"></A><A HREF="../Guide6-18/node21.html"><IMG BORDER=0 SRC="../icons/zoom18.gif" ALIGN=BOTTOM ALT="[BIG]"></A><A HREF="../Guide6-14/node21.html"><IMG BORDER=0 SRC="../icons/zoom14.gif" ALIGN=BOTTOM ALT="[Normal]"></A><A HREF="../Guide6-10/node21.html"><IMG BORDER=0 SRC="../icons/zoom10.gif" ALIGN=BOTTOM ALT="[small]"></A><BR><B> Next: </B> <A NAME=tex2html734 HREF="node22.html">3 Manipulation of structures and miscellaneous</A><B>Up: </B> <A NAME=tex2html732 HREF="node11.html">2 Manipulation of solutions</A><B> Prev: </B> <A NAME=tex2html728 HREF="node20.html">2.9 Extrema of a D.S. 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