📄 node17.html
字号:
<!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>2.1 Introductory Example</TITLE><LINK REL=STYLESHEET TYPE="text/css" HREF="./Modulef.css" TITLE="Modulef CSS"><meta name="description" value="2.1 Introductory Example"><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=tex2html403 HREF="node16.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/previous_motif.gif" ALT="previous"></A><A NAME=tex2html409 HREF="node16.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/up_motif.gif" ALT="up"></A><A NAME=tex2html411 HREF="node18.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/next_motif.gif" ALT="next"></A><A NAME=tex2html413 HREF="node2.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/contents_motif.gif" ALT="contents"></A><A HREF="../Guide1-18/node17.html"><IMG BORDER=0 SRC="../icons/zoom18.gif" ALIGN=BOTTOM ALT="[BIG]"></A><A HREF="../Guide1-14/node17.html"><IMG BORDER=0 SRC="../icons/zoom14.gif" ALIGN=BOTTOM ALT="[Normal]"></A><A HREF="../Guide1-10/node17.html"><IMG BORDER=0 SRC="../icons/zoom10.gif" ALIGN=BOTTOM ALT="[small]"></A><BR><B> Next: </B> <A NAME=tex2html412 HREF="node18.html">2.2 Test 1: Thermal Problem</A><B>Up: </B> <A NAME=tex2html410 HREF="node16.html">2 Conversational tests</A><B> Prev: </B> <A NAME=tex2html404 HREF="node16.html">2 Conversational tests</A><B><A HREF="node2.html" >Contents</A></B><HR SIZE=3 WIDTH="75%"><H1><A NAME=SECTION04210000000000000000>2.1 Introductory Example</A></H1> <A NAME=seccon_int> </A><P><P><P>In this section we give an introductory example of how a problem is solved with the aid ofthe conversational programs in the MODULEF library.<P>Consider the following boundary value problem:<P><DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img132.gif"></DIV>where the domain, <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img11.gif">, and the boundaries, <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img133.gif"> and <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img134.gif">, are described in figure <A HREF="node17.html#figex1">2.1</A><P><P><A NAME=1474> </A><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img135.gif"><BR><STRONG>Figure 2.1:</STRONG> <i> An introductory example</i><A NAME=figex1> </A><BR><P><P>The exact solution to the above problem is given by:<DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img136.gif"></DIV><P>We solve this problem utilizing straight and curved finite elements of degree 2 (elements <b> TRIA 2P2D</b>and <b> TRIA 2P2C</b> of the <b> THER</b> library).<P>Following the steps in section <A HREF="node15.html#secint_op">1.1.3</A>, we will create all the relevant data files interactively,execute the modules corresponding to the various steps, and finally complete this example by investigating the accuracy of the numerical solution compared to the exact solution and conclude with a plot of the isovalues.<P><DL COMPACT><P><P><DT>Step 1:<DD> <b> Mesh of the domain </b> <BR><P>The preprocessor <b> APNOXX</b> is utilized to create the data and run the 2D mesh generator module,<b> APNOPO</b>. A call to <b> APNOXX</b> generatesa main menu with three options:<P><OL><LI> Create a data file,<LI> Execute the module if the data file exists, and<LI> END to exit from module.</OL><P>A formatted data file is created interactively by respondingto the "CREATE option on the main menu, i.e., by typing the letter "C" on your keyboard.<P><b> Remember:</b> CAPITALS only!<P>You will now be confronted with various questions and prompts, to which you must respond by entering the appropriate keyword, data, etc. You can also specify howmuch screen output you would like when executing the module (for debugging purposes for example) by choosing a value of <b> IMPRE</b> between 0 and 10, where0 indicates no output, and 10 indicates maximum output. Additional information is obtained by entering a " Y " to the " HELP " prompt. The input parameters pertaining to the example under consideration areindicated in brackets.<P> A copy of the entire process, i.e., creation of data files and execution and results, is included in each step in order to facilitate getting acquainted with the various MODULEF modules.<P>The input is described in detail below:<P><UL><LI> Firstly, you are requested to enter a job title, maximum 72 characters between single quotes (ex: 'TEST EXAMPLE').<P><LI> The name of the data file must be entered (ex: <b> NOPO.DATA</b>).<P><LI> The curved line <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img134.gif"> is defined with the aid of a function parser, i.e., by specifying " Y " to the prompt<P> <DIV ALIGN=center>" ARE YOU USING FUNCTION PARSERS (YES-NO-?) ? ". </DIV><P> Additional information is output by entering " ? ".<P> <P><P> The first data values to be specified are:<P> <DL COMPACT><DT>IMPRE<DD> the output parameter, where (0 <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img137.gif"> <b> IMPRE</b> <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img137.gif"> 10), and <DT>NFONC<DD> the number of curves to be defined (ex: 1).<P> </DL><P> A curve is defined by a number (from 1 to 99) which is associated with each curve equation. These curve numbers serve as line, or side, reference numbers (for keywords <b> LIGN</b>, and <b> RETR</b>, respectively). Therefore, in this example, the curve is designated by reference number 2, and the straight lines by reference number 1.<P> <P><P> Each curve must then be defined as follows:<P> <DL COMPACT><DT>the curve number<DD> (ex: 2), and <DT>the equation of the curve<DD> including no blanks and ending with ";"<BR>[4] (ex: X**2+Y**2-0.25;).<P> </DL> <P><P><LI> The remaining information is specified by specifying certain keywords which constitutes the mesh generating process. In order to obtain a listing of all the available keywords, type a " ? " after the " KEYWORD ? " prompt.<P><LI> The characteristic points are generated by specifying the keyword <b> POIN</b>: <BR> <TABLE COLS=2><COL ALIGN=RIGHT><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP><TABLE COLS=1><COL ALIGN=JUSTIFY WIDTH="6cm"><TR><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="170">We first specify: <DL COMPACT><DT>IMPRE:<DD> the output parameter, and then <DT>NPOINT:<DD> the number of points characterizing the mesh (ex: 6). </DL> Each point is described by its: <DL COMPACT><DT>NOREF:<DD> reference number (ex: 1), <DT>X:<DD> x-coordinate, and <DT>Y:<DD> y-coordinate. </DL></TD></TR></TABLE></TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP><TABLE COLS=1><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP><P><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img138.gif"><P></TD></TR></TABLE></TD></TR></TABLE><P><LI> The characteristic lines are generated by entering the keyword <b> LIGN</b>:<P> As before, we specify:<P> <DL COMPACT><DT>IMPRE:<DD> the output parameter, and then <DT>NDLM:<DD> the number of lines characterizing the mesh (ex: 6). <BR><P> </DL><P> Each line is defined by specifying:<P> <DL COMPACT><DT>NOELIG:<DD> number of nodes including extremities, <DT>NEXTR1:<DD> point number at extremity 1, <DT>NEXTR2:<DD> point number at extremity 2, <BR> (<b> Note:</b> The line must be described in the trigonometric direction, i.e., to define the curve in the present example, <b> NEXTR1</b> = 6 and <b> NEXTR2</b> = 5.) <BR><P> <DT>NOREFL:<DD> reference number of the line <BR> (ex: <b> NOREFL</b> = 1 for lines 1, 2, 3, 4 and 6, and <b> NOREFL</b> = 2 for line 5), <BR> <DT>NFFRON:<DD> <BR> if <b> NFFRON</b> <b>></b> 0 then the line is described by a function parser, or by function <b> FFRONT</b> <BR> (ex: <b> NFFRON</b> = 10 for line 5), or <BR><P> if <b> NFFRON</b> = 0 then the line is a straight line connecting <b> NEXTR1</b> to <b> NEXTR2</b> <BR> (ex: <b> NFFRON</b> = 0 for lines 1, 2, 3, 4, and 6), or <BR><P> if <b> NFFRON</b> = -1 then the intermediary points are entered manually, or <BR><P> if <b> NFFRON</b> = -2 , then the line is the portion of a circle centered at the origin and passing through points <b> NEXTR1</b> and <b> NEXTR2</b>, or <BR> if <b> NFFRON</b> = -3 then the line is the portion of a circle centered at a specified point and passing through points <b> NEXTR1</b> and <b> NEXTR2</b>, and<P> <DT>RAISON:<DD> is the ratio of geometric progression between the generated points on the line (ex: 1, i.e., the points are equidistant)<P> </DL><P> <P><P> <b> Note:</b> Additional information is obtained by entering a " Y " to the " HELP " prompt.<P> <P><P><LI> The mesh generator <b> QUAC</b> is used:<P> Keywords <b> POIN</b> and <b> LIGN</b> must have been executed before. <BR><P> <P><P> The four sides of the quadrangle are defined by: <TABLE COLS=2><COL ALIGN=RIGHT><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP><TABLE COLS=1><COL ALIGN=JUSTIFY WIDTH="4cm"><TR><TD VALIGN=BASELINE ALIGN=LEFT WIDTH="113"> <DL COMPACT><DT>side 1:<DD> line 1 <DT>side 2:<DD> line 2 <DT>side 3:<DD> line 3 <DT>side 4:<DD> lines 4, 5 and 6. </DL></TD></TR></TABLE></TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP><TABLE COLS=1><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP><P><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img139.gif"><P></TD></TR></TABLE></TD></TR></TABLE><P> <b> Note:</b> The number of points per line is equal on opposite sides.<P> The following data must be entered:<P> <DL COMPACT><DT>IMPRE:<DD> the print parameter, <DT>NIVEAU:<DD> the level (an integer between 0 and 35) of the resulting D.S. <b> NOPO</b> storing the mesh (NOdes and POints) (ex: 1), <DT>NUDSD:<DD> the number of the sub-domain to be meshed (ex: 1), <DT>NBRELI:<DD> the number of lines on the contour of this sub-domain (ex: 6), and <DT>NS1L:<DD> the direction of the first line of the contour (ex: 1): <BR> <b> NS1L</b> = 1 : from <b> NEXTR1</b> to <b> NEXTR2</b>, and <BR> <b> NS1L</b> = -1 : otherwise. <BR><P> </DL><P> A list of the lines that form the contour is entered as follows:<P> <DL COMPACT><DT>NOLI(I):<DD> number of the I<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img140.gif"> line of the contour, in an anti-clockwise direction <BR> (ex: 1, 2, 3, 4, 5, 6).<P> </DL><P> And lastly the following data values must be specified:<P> <DL COMPACT><DT>IMAX:<DD> the number of points on the 1<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img141.gif"> side. This number defines the four sides of the quadrangle. (ex: 5), and <DT>NQUAD:<DD> (ex: -1) <BR> = 1: mesh by quadrangles, <BR> = 0; mesh by triangles, <BR> = -1: triangles with particular treatment at the corners, <BR> = -2: as above, but a more regular mesh, etc.<P> </DL><P> <P><P><LI> The keyword <b> ADPO</b> generates non-vertex nodes.<P> This keyword can only be activated after all the previous ones.<P> The following data must be input:⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -