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Chapters:
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<a href="Introduction.html">1: Introduction</a><br>
<a href="SimpleExample.html">2: Simple example</a><br>
<a href="InvokingGri.html">3: Invocation</a><br>
<a href="GettingMoreControl.html">4: Finer Control</a><br>
<a href="X-Y.html">5: X-Y Plots</a><br>
<a href="ContourPlots.html">6: Contour Plots</a><br>
<a href="Images.html">7: Image Plots</a><br>
<a href="Examples.html">8: Examples</a><br>
<a href="Commands.html">9: Gri Commands</a><br>
<a href="Programming.html">10: Programming</a><br>
<a href="Environment.html">11: Environment</a><br>
<a href="Emacs.html">12: Emacs Mode</a><br>
<a href="History.html">13: History</a><br>
<a href="Installation.html">14: Installation</a><br>
<a href="Bugs.html">15: Gri Bugs</a><br>
<a href="TestSuite.html">16: Test Suite</a><br>
<a href="Acknowledgments.html">17: Acknowledgments</a><br>
<a href="License.html">18: License</a><br>
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Indices:</br>
<a href="ConceptIndex.html"><i>Concepts</i></a><br>
<a href="CommandIndex.html"><i>Commands</i></a><br>
<a href="BuiltinIndex.html"><i>Variables</i></a><br>
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<h2>8.11: Finite Element Model mesh</h2>
Finite Element Models (used in fluid mechanics) employ non-rectangular
meshes, and plotting these meshes requires a few intermediate steps.
Consider the common case of triangular elements. Suppose two data files
exist describing the mesh, the first, `<font color="#82140F"><samp>model.nodes</samp></font>' say, consists
of a description of the x-y coordinates of the nodes (vertices) of the
triangles. The second, `<font color="#82140F"><samp>model.elements</samp></font>' say, consists of a
description of which triplet of nodes defines each triangle in the mesh.
Here, from a sample application, is a node file called
`<font color="#82140F"><samp>model.nodes</samp></font>':
<p>
<TABLE SUMMARY="Example" BORDER="0" BGCOLOR="#efefef" WIDTH="100%">
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<PRE>
<font color="#82140F">
1 1 1
2 2 1
3 1 2
4 3 1.5
5 2 2
6 1.5 3
</font></PRE>
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</TABLE>
<p>
Here is the corresponding file of the elements, called `<font color="#82140F"><samp>model.elements</samp></font>'
<p>
<TABLE SUMMARY="Example" BORDER="0" BGCOLOR="#efefef" WIDTH="100%">
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<PRE>
<font color="#82140F">
1 1 2 3
2 2 5 3
3 2 4 5
4 3 5 6
</font></PRE>
</TD>
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</TABLE>
<p>
In each of these files, the first column is a reference number. Thus,
`<font color="#82140F"><samp>model.elements</samp></font>' indicates that the first triangle is defined by
the nodes numbered `<font color="#82140F"><code>1</code></font>', `<font color="#82140F"><code>2</code></font>' and `<font color="#82140F"><code>3</code></font>' as defined in
`<font color="#82140F"><samp>model.nodes</samp></font>'. More specifically, the triangle is defined by
vertices at (x,y) locations (1,1), (2,1), and (1,2).
<p>
A Gri program, named `<font color="#82140F"><samp>FEM.gri</samp></font>', to draw the nodes is the following.
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<PRE>
<font color="#82140F">
set missing value -99.99
# Create data using perl-script ...
system FEM.pl model.nodes model.elements > tmp
# ... then plot it ...
open tmp
read columns x y
close
draw curve
# ... and, finally, clean up the temporary file
system rm tmp
</font></PRE>
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<p>
The work of interpreting the data files is done by the perlscript that
follows, named `<font color="#82140F"><samp>FEM.pl</samp></font>'
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#!/usr/bin/perl -w
$missing = -99.99; # missing value
$node_file = $ARGV[0];
$element_file = $ARGV[1];
open (NODE, $node_file)
or die "Cannot open '$node_file' file";
open (ELEM, $element_file)
or die "Cannot open '$element_file' file";
<p>
# Read in node information, creating arrays
# named $node_x[] and $node_y[]. Check that
# the first column (the index) makes sense.
$max_node = 1;
while(<NODE>) {
($index, $node_x[$max_node], $node_y[$max_node])
= split;
die "Node mismatch at index=$index"
if ($index != $max_node);
$max_node++;
}
<p>
# Read in triangle elements, into arrays
# $a[], $b[], and $c[]. Check that the
# first column (the index) makes sense.
$max_elem = 1;
while(<ELEM>) {
($index, $a[$max_elem], $b[$max_elem], $c[$max_elem])
= split;
die "Element mismatch at index=$index"
if ($index != $max_elem);
$max_elem++;
}
<p>
# Print out triangles suitable for plotting in gri.
for ($i = 1; $i < $max_elem; $i++) {
print $node_x[$a[$i]], " ", $node_y[$a[$i]], "\n";
print $node_x[$b[$i]], " ", $node_y[$b[$i]], "\n";
print $node_x[$c[$i]], " ", $node_y[$c[$i]], "\n";
# Repeat first, to close the triangle.
print $node_x[$a[$i]], " ", $node_y[$a[$i]], "\n";
print $missing, " ", $missing, "\n";
}
</font></PRE>
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The resultant image is below.
<IMG ALT="FEM image" SRC="FEM.png">
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