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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>3.1 Test 4: Thermal Problem</TITLE><LINK REL=STYLESHEET TYPE="text/css" HREF="./Modulef.css" TITLE="Modulef CSS"><meta name="description" value="3.1 Test 4: Thermal Problem"><meta name="keywords" value="Guide1"><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=tex2html457 HREF="node21.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/previous_motif.gif" ALT="previous"></A><A NAME=tex2html463 HREF="node21.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/up_motif.gif" ALT="up"></A><A NAME=tex2html465 HREF="node23.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/next_motif.gif" ALT="next"></A><A NAME=tex2html467 HREF="node2.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/contents_motif.gif" ALT="contents"></A><A HREF="../Guide1-18/node22.html"><IMG BORDER=0 SRC="../icons/zoom18.gif" ALIGN=BOTTOM ALT="[BIG]"></A><A HREF="../Guide1-14/node22.html"><IMG BORDER=0 SRC="../icons/zoom14.gif" ALIGN=BOTTOM ALT="[Normal]"></A><A HREF="../Guide1-10/node22.html"><IMG BORDER=0 SRC="../icons/zoom10.gif" ALIGN=BOTTOM ALT="[small]"></A><BR><B> Next: </B> <A NAME=tex2html466 HREF="node23.html">3.2 Test 5: Elasticity Problem</A><B>Up: </B> <A NAME=tex2html464 HREF="node21.html">3 Batch tests</A><B> Prev: </B> <A NAME=tex2html458 HREF="node21.html">3 Batch tests</A><B><A HREF="node2.html" >Contents</A></B><HR SIZE=3 WIDTH="75%"><H1><A NAME=SECTION04310000000000000000>3.1 Test 4: Thermal Problem</A></H1><P><P><P><H2><A NAME=SECTION04311000000000000000>3.1.1 Description</A></H2><P><P><P>Calculate the temperature distribution in a two-dimensional domain.<P><P><A NAME=2637> </A><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img214.gif"><BR><STRONG>Figure 3.1:</STRONG> <i> Two-dimensional heat problem</i><A NAME=fig11> </A><BR><P><P><P><P><H2><A NAME=SECTION04312000000000000000>3.1.2 The boundary value problem</A></H2><P><P><P>Find <b>u(x)</b> which satisfies:<P><DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img215.gif"></DIV><P>where <DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img216.gif"></DIV><P>This problem allows one exact solution:<DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img217.gif"></DIV><P>The type of finite element utilized in order to solve this problem: <b> TRIA 2P3D</b> (straight P3 Hermitian triangle)<P><P><A NAME=2647> </A><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img218.gif"><BR><STRONG>Figure 3.2:</STRONG> <i> Suggested mesh (<b> TRNOXX</b>)</i><A NAME=fig12> </A><BR><P><P><P><P><H2><A NAME=SECTION04313000000000000000>3.1.3 Execution of the test</A></H2><P><P><P><b> Step 1:</b> Mesh<P><TABLE COLS=3 RULES=GROUPS><COL ALIGN=LEFT><COL ALIGN=LEFT><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Execute program: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> D4NOXX</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Modules used: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> APNOPO</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> ... 2D mesh generator [<A HREF="node65.html#mod_104"><A NAME=tex2html37 HREF="../Guide3/welcome.html">MODULEF User Guide - 3</A></A>] </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> TRIHER</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> ... construction of mesh using Voronoi's polyhedra theory </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> REGMA2</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> ... regularization of mesh </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> GIBBS</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> ... renumbering </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Libraries: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP COLSPAN=2> <b> NOP2</b>, <b> NOPO</b>, <b> UTSD </b>, <b> UTII</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Input data file: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> D4NOPO.D</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Output data structure: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T4NOPO</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR></TABLE><P><P><P><b> Step2:</b> Interpolation [<A HREF="node65.html#mod_13">13</A>]<P><TABLE COLS=2 RULES=GROUPS><COL ALIGN=LEFT><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Execute program: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> D4COXX</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Module used: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> COMACO</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Libraries: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> THER</b>, <b> COSD</b>, <b> UTSD</b>, <b> UTII</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Element type: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> TRIA 2P3D</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Output data structures: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T4MAIL</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T4COOR</b> </TD></TR></TABLE><P><P><P><b> Step 3:</b> Description of the data [<A HREF="node65.html#mod_14">14</A>]<P><TABLE COLS=3 RULES=GROUPS><COL ALIGN=LEFT><COL ALIGN=LEFT><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Call preprocessor: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> FOMIXX</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Data File: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> D4FOMI.D</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> ... in library <b> TESD</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Output data structures: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T4FORC</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T4MILI</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR></TABLE><P><b> Step 4:</b> Calculation, assembly of the element arrays, description of boundary conditions and solution<P><P><P><TABLE COLS=3 RULES=GROUPS><COL ALIGN=LEFT><COL ALIGN=LEFT><COL ALIGN=JUSTIFY WIDTH="0.33"><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Execute program: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> D4ARXX</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="33%"></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="33%"></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Modules used: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> CONDL1</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="33%"> ... construction of pointers on the degrees of freedom associated with each node [<A HREF="node65.html#mod_20">20</A>] </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> COBDC1</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="33%"> ... description of boundary conditions </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> PREPAC</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="33%"> ... allocation of pointers </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> THEASS</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="33%"> ... calculates element arrays and assembly</TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> CLIMPC</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="33%"> ... introduction of boundary conditions </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> CHOLPC</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="33%"> ... factorization by Cholesky </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> DRCHPC</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="33%"> ... forward and backward substitution </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Libraries: </TD><TD VALIGN=BASELINE ALIGN=LEFT COLSPAN=2> <b> COSD</b>, <b> THER</b>, <b> RESB</b>, <b> RESO</b>, <b> RESR</b>, <b> UTSD</b>, <b> UTII</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="33%"></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Output data structure: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T4B</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="33%"></TD></TR></TABLE><P><b> Remark:</b> The finite element <b> TRIA 2P3D</b> utilizes the direct access file <b> POBA</b>. In this test thename of the file is <b> POBA</b>. In order to change the name of this file it is necessary to modify the variable <b> NOMPOB</b> in program <b> D4ARXX</b>. The file <b> POBA</b> is created, once the tape is loaded,by program <b> POBAXX</b> in <b> PPAL</b> (see Part <A HREF="node25.html#part3"> iii</A>).<P>The user function <b> VALCLR</b> allows for non-constant boundary conditions. This function is found at the end of program <b> D4ARXX</b> in file <b> D4ARXX.F</b> in library <b> TEST</b>. <BR><P><P><P>The number of words necessary to store the matrix : 5903<P>The number of words necessary to store the corresponding right-hand-side (RHS) vector : 365<P><P><P><H2><A NAME=SECTION04314000000000000000>3.1.4 Memory usage and Execution time</A></H2><P><P><P>The super array <b> M</b> is dimensioned equal to 45 000 words in all the programs.<P><P><P><TABLE COLS=3 BORDER FRAME=BOX RULES=GROUPS><COLGROUP><COL ALIGN=LEFT><COLGROUP><COL ALIGN=RIGHT><COLGROUP><COL ALIGN=RIGHT><TBODY><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Step </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> Dimension of </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> Execution time </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> the super array <b> LM</b> </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> (DPS8 Multics) </TD></TR></TBODY><TBODY><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Mesh </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 6 000 </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Interpolation </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 4 600 </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 3.38 </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Preparation </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 5 000 </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 52.18 </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Solution </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 10 000 </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 8.54 </TD></TR></TBODY></TABLE><P><P><P><H2><A NAME=SECTION04315000000000000000>3.1.5 Results</A></H2><P><P><P>The complete output of the D.S. <b> B</b>, containing the temperature and the temperature derivativein <b>x</b> and <b>y</b> at each node in the mesh, is found in the file <b> S4B.D</b> in library <b> TESD</b>.<P>The remainder of this section contains a partial or total printout of the various output D.S. of the different programs. These data structures can be viewed by calling preprocessor <b> IMAGXX</b> andspecifying the names of the files containing the desired data structures.<P><P><P>⌨️ 快捷键说明
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