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Chapters:
  1: Introduction
  2: Simple example
  3: Invocation
  4: Finer Control
  5: X-Y Plots
  6: Contour Plots
  7: Image Plots
  8: Examples
  9: Gri Commands
  10: Programming
  11: Environment
  12: Emacs Mode
  13: History
  14: Installation
  15: Gri Bugs
  16: Test Suite
  17: Gri in Press
  18: Acknowledgments
  19: License

Indices:
  Concepts
  Commands
  Variables
 		index.html#Top Examples.html#Examples Gri: running means Gri: handling data index.html#Top Gri: handling data

8.11: Finite Element Model mesh

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, `model.nodes' say, consists of a description of the x-y coordinates of the nodes (vertices) of the triangles. The second, `model.elements' 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 `model.nodes': 


1	1	1
2	2	1
3	1	2
4	3	1.5
5	2	2
6	1.5	3

Here is the corresponding file of the elements, called `model.elements' 


1	1	2	3
2	2	5	3
3	2	4	5
4	3	5	6

In each of these files, the first column is a reference number. Thus, `model.elements' indicates that the first triangle is defined by the nodes numbered `1', `2' and `3' as defined in `model.nodes'. More specifically, the triangle is defined by vertices at (x,y) locations (1,1), (2,1), and (1,2).

A Gri program, named `FEM.gri', to draw the nodes is the following. 


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

The work of interpreting the data files is done by the perlscript that follows, named `FEM.pl' 


#!/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";


# 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++;
}


# 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++;
}


# 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";
}

The resultant image is below. FEM image

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