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<html>
<head>
<title>
TEST_MESH - Sample 2D Meshes.
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_MESH <br> Sample 2D Meshes
</h1>
<hr>
<p>
<b>TEST_MESH</b>
is a FORTRAN90 library which
defines a few
simple triangular meshes of 2D regions.
</p>
<p>
Alan George and Joseph Liu generated the original set of 9 meshes.
They used them to generate refined meshes, made by subdividing
every triangle the same number of times. Then the node-connectivity
matrix of the refined mesh was used to define a positive definite
symmetric sparse matrix problem.
</p>
<p>
Of course, the meshes can be of interest for other reasons.
For instance, it is possible to output the mesh information
as a <b>poly</b> file. This format can be input to the
<a href = "../../g_src/showme/showme.html">
SHOWME</a> program for display, or to
<b>TRIANGLE</b>.
</p>
<p>
The program is set up to allow a user to easily access a particular
mesh by specifying its number, or to access all the examples,
by going through the master routines whose names begin with the
prefix <b>MESH00_</b>.
</p>
<p>
The user can easily handle problems of various size by first calling
the routines that give the sizes of various arrays, then using
the FORTRAN90 <b>ALLOCATE</b> command to set up enough space for the
array, and then calling the library routine that fills up the array
with information.
</p>
<p>
The meshes include:
<ol>
<li>
the Square, 4 nodes, 2 elements.
</li>
<li>
The Graded L, 22 nodes, 30 elements.
</li>
<li>
The Plus-Shaped Domain, 28 nodes, 26 elements.
</li>
<li>
The H-Shaped Domain, 40 nodes, 38 elements.
</li>
<li>
The Hollow Square (Small Hole), 12 nodes, 12 elements.
</li>
<li>
The Hollow Square (Large Hole), 32 nodes, 32 elements.
</li>
<li>
The 3-Hole Problem, 44 nodes, 56 elements.
</li>
<li>
The 6-Hole Problem, 46 nodes, 56 elements.
</li>
<li>
The Pinched Hole Problem, 8 nodes, 7 elements.
</li>
</ol>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../datasets/hbsmc/hbsmc.html">
HBSMC</a>,
a dataset directory which
contains the Harwell-Boeing Sparse Matrix Collection.
The meshes described here naturally give rise to adjacency
matrices. These matrices are typically sparse (mostly zero)
and irregular. Versions of these matrices, derived from the
meshes in this collection are available in HBSMC.
</p>
<p>
<a href = "../../f_src/mesh_bandwidth/mesh_bandwidth.html">
MESH_BANDWIDTH</a>,
a FORTRAN90 program which
returns the geometric bandwidth associated with a mesh of
elements of any order and in a space of arbitrary dimension.
</p>
<p>
<a href = "../../f_src/sparsepak/sparsepak.html">
SPARSEPAK</a>,
a FORTRAN90 library which
contains a version of a direct solver for sparse systems,
developed by George and Liu.
</p>
<p>
<a href = "../../f_src/test_triangulation/test_triangulation.html">
TEST_TRIANGULATION</a>,
a FORTRAN90 library which
defines a set of test regions for triangulation.
</p>
<p>
<a href = "../../c_src/triangle/triangle.html">
TRIANGLE</a>,
a C program which
can be used to
operate on meshes in the <b>TEST_MESH</b> library, producing the
Voronoi diagram, or determining a refined Delaunay triangulation,
constrained to include the original edges of the mesh.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Alan George, Joseph Liu,<br>
Computer Solution of Large Sparse Positive Definite Matrices,<br>
Prentice Hall, 1981,<br>
ISBN: 0131652745,<br>
LC: QA188.G46.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_mesh.f90">test_mesh.f90</a>, the source code.
</li>
<li>
<a href = "test_mesh.sh">test_mesh.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_mesh_prb.f90">test_mesh_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "test_mesh_prb.sh">test_mesh_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "test_mesh_prb_output.txt">test_mesh_prb_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
<b>TEST_MESH</b> includes a routine, <b>MESH00_EPS</b>, which
can create an
<a href = "../../data/eps/eps.html">
EPS file</a> containing an image of the mesh. EPS files you may
copy include:
<ul>
<li>
<a href = "mesh01_nodes.png">mesh01_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nodes in mesh #1.
</li>
<li>
<a href = "mesh01_elements.png">mesh01_elements.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the elements in mesh #1.
</li>
<li>
<a href = "mesh02_nodes.png">mesh02_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nodes in mesh #2.
</li>
<li>
<a href = "mesh02_elements.png">mesh02_elements.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the elements in mesh #2.
</li>
<li>
<a href = "mesh03_nodes.png">mesh03_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nodes in mesh #3.
</li>
<li>
<a href = "mesh03_elements.png">mesh03_elements.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the elements in mesh #3.
</li>
<li>
<a href = "mesh04_nodes.png">mesh04_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nodes in mesh #4.
</li>
<li>
<a href = "mesh04_elements.png">mesh04_elements.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the elements in mesh #4.
</li>
<li>
<a href = "mesh05_nodes.png">mesh05_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nodes in mesh #5.
</li>
<li>
<a href = "mesh05_elements.png">mesh05_elements.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the elements in mesh #5.
</li>
<li>
<a href = "mesh06_nodes.png">mesh06_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nodes in mesh #6.
</li>
<li>
<a href = "mesh06_elements.png">mesh06_elements.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the elements in mesh #6.
</li>
<li>
<a href = "mesh07_nodes.png">mesh07_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nodes in mesh #7.
</li>
<li>
<a href = "mesh07_elements.png">mesh07_elements.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the elements in mesh #7.
</li>
<li>
<a href = "mesh08_nodes.png">mesh08_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nodes in mesh #8.
</li>
<li>
<a href = "mesh08_elements.png">mesh08_elements.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the elements in mesh #8.
</li>
<li>
<a href = "mesh09_nodes.png">mesh09_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nodes in mesh #9.
</li>
<li>
<a href = "mesh09_elements.png">mesh09_elements.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the elements in mesh #9.
</li>
</ul>
</p>
<p>
<b>TEST_MESH</b> includes a routine, <b>MESH00_POLY</b>, which
can create a
<a href = "../../data/poly/poly.html">
POLY file</a> containing the mesh information, suitable for
display by
<a href = "../../g_src/showme/showme.html">
SHOWME</a>, or for processing by
<a href = "../../cpp_src/triangle/triangle.html">
TRIANGLE</a>. POLY files you may copy include:
<ul>
<li>
<a href = "mesh01.poly">mesh01.poly</a>,
a POLY file of mesh #1.
</li>
<li>
<a href = "mesh02.poly">mesh02.poly</a>,
a POLY file of mesh #2.
</li>
<li>
<a href = "mesh03.poly">mesh03.poly</a>,
a POLY file of mesh #3.
</li>
<li>
<a href = "mesh04.poly">mesh04.poly</a>,
a POLY file of mesh #4.
</li>
<li>
<a href = "mesh05.poly">mesh05.poly</a>,
a POLY file of mesh #5.
</li>
<li>
<a href = "mesh06.poly">mesh06.poly</a>,
a POLY file of mesh #6.
</li>
<li>
<a href = "mesh07.poly">mesh07.poly</a>,
a POLY file of mesh #7.
</li>
<li>
<a href = "mesh08.poly">mesh08.poly</a>,
a POLY file of mesh #8.
</li>
<li>
<a href = "mesh09.poly">mesh09.poly</a>,
a POLY file of mesh #9.
</li>
</ul>
</p>
<p>
Versions of these meshes have also been stored in the
<a href = "../../datasets/hbsmc/hbsmc.html">
Harwell Boeing Sparse Matrix Collection</a>:
<ul>
<li>
<a href = "../../datasets/hbsmc/jagmesh1_psa.txt">
jagmesh1_psa.txt</a>,
an HBSMC file for mesh #1.
</li>
<li>
<a href = "../../datasets/hbsmc/jagmesh2_psa.txt">
jagmesh2_psa.txt</a>,
an HBSMC file for mesh #2.
</li>
<li>
<a href = "../../datasets/hbsmc/jagmesh3_psa.txt">
jagmesh3_psa.txt</a>,
an HBSMC file for mesh #3.
</li>
<li>
<a href = "../../datasets/hbsmc/jagmesh4_psa.txt">
jagmesh4_psa.txt</a>,
an HBSMC file for mesh #4.
</li>
<li>
<a href = "../../datasets/hbsmc/jagmesh5_psa.txt">
jagmesh5_psa.txt</a>,
an HBSMC file for mesh #5.
</li>
<li>
<a href = "../../datasets/hbsmc/jagmesh6_psa.txt">
jagmesh6_psa.txt</a>,
an HBSMC file for mesh #6.
</li>
<li>
<a href = "../../datasets/hbsmc/jagmesh7_psa.txt">
jagmesh7_psa.txt</a>,
an HBSMC file for mesh #7.
</li>
<li>
<a href = "../../datasets/hbsmc/jagmesh8_psa.txt">
jagmesh8_psa.txt</a>,
an HBSMC file for mesh #8.
</li>
<li>
<a href = "../../datasets/hbsmc/jagmesh9_psa.txt">
jagmesh9_psa.txt</a>,
an HBSMC file for mesh #9.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CH_IS_DIGIT</b> returns .TRUE. if a character is a decimal digit.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>DIGIT_INC</b> increments a decimal digit.
</li>
<li>
<b>DIGIT_TO_CH</b> returns the character representation of a decimal digit.
</li>
<li>
<b>EDGE_LIST</b> creates a list of the unique edges in a graph.
</li>
<li>
<b>ELEMENT3_EPS</b> creates an EPS file containing an image of the mesh.
</li>
<li>
<b>FILE_NAME_INC</b> generates the next filename in a series.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of integer division.
</li>
<li>
<b>I4_SWAP</b> swaps two I4's.
</li>
<li>
<b>I4_WRAP</b> forces an integer to lie between given limits by wrapping.
</li>
<li>
<b>MESH_NODE_MATRIX</b> returns the node adjacency matrix of a mesh.
</li>
<li>
<b>MESH_POLY</b> creates a POLY file of a mesh, for input to TRIANGLE.
</li>
<li>
<b>MESH00_ELEMENT_NODES</b> returns the element->node data of a mesh given its number.
</li>
<li>
<b>MESH00_ELEMENT3_EPS</b> creates an image of a mesh, given its number.
</li>
<li>
<b>MESH00_ELEMENT_NUM</b> returns the number of elements of a mesh given its number.
</li>
<li>
<b>MESH00_HOLE_NUM</b> returns the number of holes in a mesh given its number.
</li>
<li>
<b>MESH00_HOLE_XY</b> returns hole coordinates of a mesh given its number.
</li>
<li>
<b>MESH00_NAME</b> returns the name of a mesh given its number.
</li>
<li>
<b>MESH00_NODE_EPS</b> creates an image of the nodes of a mesh, given its number.
</li>
<li>
<b>MESH00_NODE_NUM</b> returns the number of nodes of a mesh given its number.
</li>
<li>
<b>MESH00_NODE_XY</b> returns the node coordinates of a mesh given its number.
</li>
<li>
<b>MESH00_NUM</b> returns the number of meshes.
</li>
<li>
<b>MESH00_POLY</b> creates a POLY file of a mesh, given its number.
</li>
<li>
<b>MESH01_ELEMENT_NODES</b> returns the element->node data of mesh #01.
</li>
<li>
<b>MESH01_ELEMENT_NUM</b> returns the number of elements of mesh #01.
</li>
<li>
<b>MESH01_HOLE_NUM</b> returns the number of holes in mesh #01.
</li>
<li>
<b>MESH01_HOLE_XY</b> returns hole coordinates of mesh #01.
</li>
<li>
<b>MESH01_NAME</b> returns the name of mesh #01.
</li>
<li>
<b>MESH01_NODE_ELEMENT_NUM</b> returns the number of nodes-element items of mesh #01.
</li>
<li>
<b>MESH01_NODE_NUM</b> returns the number of nodes of mesh #01.
</li>
<li>
<b>MESH01_NODE_ELEMENT</b> returns the node-element data of mesh #01.
</li>
<li>
<b>MESH01_NODE_XY</b> returns the nodes of mesh #01.
</li>
<li>
<b>MESH02_ELEMENT_NODES</b> returns the element->node data of mesh #02.
</li>
<li>
<b>MESH02_ELEMENT_NUM</b> returns the number of elements of mesh #02.
</li>
<li>
<b>MESH02_HOLE_NUM</b> returns the number of holes in mesh #02.
</li>
<li>
<b>MESH02_HOLE_XY</b> returns hole coordinates of mesh #02.
</li>
<li>
<b>MESH02_NAME</b> returns the name of mesh #02.
</li>
<li>
<b>MESH02_NODE_ELEMENT_NUM</b> returns the number of nodes-element items of mesh #02.
</li>
<li>
<b>MESH02_NODE_ELEMENT</b> returns the node-element data of mesh #02.
</li>
<li>
<b>MESH02_NODE_NUM</b> returns the number of nodes of mesh #02.
</li>
<li>
<b>MESH02_NODE_XY</b> returns the nodes of mesh #02.
</li>
<li>
<b>MESH03_ELEMENT_NODES</b> returns the element->node data of mesh #03.
</li>
<li>
<b>MESH03_ELEMENT_NUM</b> returns the number of elements of mesh #03.
</li>
<li>
<b>MESH03_HOLE_NUM</b> returns the number of holes in mesh #03.
</li>
<li>
<b>MESH03_HOLE_XY</b> returns hole coordinates of mesh #03.
</li>
<li>
<b>MESH03_NAME</b> returns the name of mesh #03.
</li>
<li>
<b>MESH03_NODE_NUM</b> returns the number of nodes of mesh #03.
</li>
<li>
<b>MESH03_NODE_XY</b> returns the nodes of mesh #03.
</li>
<li>
<b>MESH04_ELEMENT_NODES</b> returns the element->node data of mesh #04.
</li>
<li>
<b>MESH04_ELEMENT_NUM</b> returns the number of elements of mesh #04.
</li>
<li>
<b>MESH04_HOLE_NUM</b> returns the number of holes in mesh #04.
</li>
<li>
<b>MESH04_HOLE_XY</b> returns hole coordinates of mesh #04.
</li>
<li>
<b>MESH04_NAME</b> returns the name of mesh #04.
</li>
<li>
<b>MESH04_NODE_NUM</b> returns the number of nodes of mesh #04.
</li>
<li>
<b>MESH04_NODE_XY</b> returns the nodes of mesh #04.
</li>
<li>
<b>MESH05_ELEMENT_NODES</b> returns the element->node data of mesh #05.
</li>
<li>
<b>MESH05_ELEMENT_NUM</b> returns the number of elements of mesh #05.
</li>
<li>
<b>MESH05_HOLE_NUM</b> returns the number of holes in mesh #05.
</li>
<li>
<b>MESH05_HOLE_XY</b> returns hole coordinates of mesh #05.
</li>
<li>
<b>MESH05_NAME</b> returns the name of mesh #05.
</li>
<li>
<b>MESH05_NODE_NUM</b> returns the number of nodes of mesh #05.
</li>
<li>
<b>MESH05_NODE_XY</b> returns the nodes of mesh #05.
</li>
<li>
<b>MESH06_ELEMENT_NODES</b> returns the element->node data of mesh #06.
</li>
<li>
<b>MESH06_ELEMENT_NUM</b> returns the number of elements of mesh #06.
</li>
<li>
<b>MESH06_HOLE_NUM</b> returns the number of holes in mesh #06.
</li>
<li>
<b>MESH06_HOLE_XY</b> returns hole coordinates of mesh #06.
</li>
<li>
<b>MESH06_NAME</b> returns the name of mesh #06.
</li>
<li>
<b>MESH06_NODE_NUM</b> returns the number of nodes of mesh #06.
</li>
<li>
<b>MESH06_NODE_XY</b> returns the nodes of mesh #06.
</li>
<li>
<b>MESH07_ELEMENT_NODES</b> returns the element->node data of mesh #07.
</li>
<li>
<b>MESH07_ELEMENT_NUM</b> returns the number of elements of mesh #07.
</li>
<li>
<b>MESH07_HOLE_NUM</b> returns the number of holes in mesh #07.
</li>
<li>
<b>MESH07_HOLE_XY</b> returns hole coordinates of mesh #07.
</li>
<li>
<b>MESH07_NAME</b> returns the name of mesh #07.
</li>
<li>
<b>MESH07_NODE_NUM</b> returns the number of nodes of mesh #07.
</li>
<li>
<b>MESH07_NODE_XY</b> returns the nodes of mesh #07.
</li>
<li>
<b>MESH08_ELEMENT_NODES</b> returns the element->node data of mesh #08.
</li>
<li>
<b>MESH08_ELEMENT_NUM</b> returns the number of elements of mesh #08.
</li>
<li>
<b>MESH08_HOLE_NUM</b> returns the number of holes in mesh #08.
</li>
<li>
<b>MESH08_HOLE_XY</b> returns hole coordinates of mesh #08.
</li>
<li>
<b>MESH08_NAME</b> returns the name of mesh #08.
</li>
<li>
<b>MESH08_NODE_NUM</b> returns the number of nodes of mesh #08.
</li>
<li>
<b>MESH08_NODE_XY</b> returns the nodes of mesh #08.
</li>
<li>
<b>MESH09_ELEMENT_NODES</b> returns the element->node data of mesh #09.
</li>
<li>
<b>MESH09_ELEMENT_NUM</b> returns the number of elements of mesh #09.
</li>
<li>
<b>MESH09_HOLE_NUM</b> returns the number of holes in mesh #09.
</li>
<li>
<b>MESH09_HOLE_XY</b> returns hole coordinates of mesh #09.
</li>
<li>
<b>MESH09_NAME</b> returns the name of mesh #09.
</li>
<li>
<b>MESH09_NODE_NUM</b> returns the number of nodes of mesh #09.
</li>
<li>
<b>MESH09_NODE_XY</b> returns the nodes of mesh #09.
</li>
<li>
<b>NODE_EPS</b> creates an EPS file containing an image of the nodes.
</li>
<li>
<b>SORT_HEAP_EXTERNAL</b> externally sorts a list of items into linear order.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 20 May 2006.
</i>
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