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fem2d_sample.html
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fem2d_sample.html
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<html>
<head>
<title>
FEM2D_SAMPLE - Evaluate a Finite Element Function of a 2D Argument
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FEM2D_SAMPLE <br> Evaluate a Finite Element Function of a 2D Argument
</h1>
<hr>
<p>
<b>FEM2D_SAMPLE</b>
is a FORTRAN90 program which
can evaluate a finite element function of a 2D argument.
</p>
<p>
The current version of the program can only handle finite element
meshes which are made of piecewise linear triangles of order 3 or 6.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>fem2d_sample</b> <i>fem_prefix</i> <i>sample_prefix</i>
</blockquote>
where <i>fem_prefix</i> is the common prefix for the FEM files:
<ul>
<li>
<i>fem_prefix</i><b>_nodes.txt</b>, the node coordinates.
</li>
<li>
<i>fem_prefix</i><b>_elements.txt</b>, the nodes that make up each element;
</li>
<li>
<i>fem_prefix</i><b>_values.txt</b>, the values defined at each node.
</li>
</ul>
and <i>sample_prefix</i> is the common prefix for the SAMPLE files,
for which the node file is input, and the values file is created by the program:
<ul>
<li>
<i>sample_prefix</i><b>_nodes.txt</b>, the node coordinates where samples are desired.
</li>
<li>
<i>sample_prefix</i><b>_values.txt</b>, the values computed at each sample node.
</li>
</ul>
</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">
Languages:
</h3>
<p>
<b>FEM2D_SAMPLE</b> is available in
<a href = "../../cpp_src/fem2d_sample/fem2d_sample.html">a C++ version</a> and
<a href = "../../f77_src/fem2d_sample/fem2d_sample.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fem2d_sample/fem2d_sample.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fem2d_sample/fem2d_sample.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/discrete_pdf_sample/discrete_pdf_sample.html">
DISCRETE_PDF_SAMPLE</a>,
a FORTRAN90 program which
demonstrates how to construct a Probability Density Function (PDF)
from a table of sample data, and then to use that PDF to create new samples.
</p>
<p>
<a href = "../../m_src/fem_basis_t3_display/fem_basis_t3_display.html">
FEM_BASIS_T3_DISPLAY</a>,
a MATLAB program which
displays a basis function associated with a linear triangle ("T3") mesh.
</p>
<p>
<a href = "../../m_src/fem_basis_t6_display/fem_basis_t6_display.html">
FEM_BASIS_T6_DISPLAY</a>,
a MATLAB program which
displays a basis function associated with a quadratic triangle ("T6") mesh.
</p>
<p>
<a href = "../../f_src/fem_io/fem_io.html">
FEM_IO</a>,
a FORTRAN90 library which
reads or writes node, element and data files defining a finite element model.
</p>
<p>
<a href = "../../m_src/fem_to_tec/fem_to_tec.html">
FEM_TO_TEC</a>,
a MATLAB program which
converts FEM models into TEC graphics files.
</p>
<p>
<a href = "../../f_src/fem1d_sample/fem1d_sample.html">
FEM1D_SAMPLE</a>,
a FORTRAN90 program which
samples a scalar or vector finite element function of one variable,
defined by <b>FEM</b> files,
returning interpolated values at the sample points.
</p>
<p>
<a href = "../../data/fem2d/fem2d.html">
FEM2D</a>,
a data directory which
contains examples of 2D FEM files,
text files that describe a 2D finite element geometry
and associated nodal values;
</p>
<p>
<a href = "../../f_src/fem2d_heat/fem2d_heat.html">
FEM2D_HEAT</a>,
a FORTRAN90 program which
solves the 2D time dependent heat equation on the unit square.
</p>
<p>
<a href = "../../f_src/fem2d_pack/fem2d_pack.html">
FEM2D_PACK</a>,
a FORTRAN90 library which
contains utilities for 2D finite element calculations.
</p>
<p>
<a href = "../../f_src/fem2d_poisson/fem2d_poisson.html">
FEM2D_POISSON</a>,
a FORTRAN90 program which
solves the 2D Poisson equation on a square, using the finite element method.
</p>
<p>
<a href = "../../f_src/fem2d_project/fem2d_project.html">
FEM2D_PROJECT</a>,
a FORTRAN90 program which
projects a function F(X,Y) into a given finite element space
of piecewise linear triangular elements.
</p>
<p>
<a href = "../../f_src/fem3d_sample/fem3d_sample.html">
FEM3D_SAMPLE</a>,
a FORTRAN90 program which
samples a finite element function of three variables,
returning interpolated values at the sample points.
</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 = "../../data/triangulation_order3/triangulation_order3.html">
TRIANGULATION_ORDER3</a>,
a data directory which
contains a description and
examples of how an order 3 (linear) triangulation is defined by a node
and element file.
</p>
<p>
<a href = "../../data/triangulation_order6/triangulation_order6.html">
TRIANGULATION_ORDER6</a>,
a data directory which
contains a description and
examples of how an order 6 (quadratic) triangulation is defined by a node
and element file.
</p>
<p>
<a href = "../../m_src/triangulation_order6_contour/triangulation_order6_contour.html">
TRIANGULATION_ORDER6_CONTOUR</a>,
a MATLAB program which
makes contours of a scalar quantity defined on the nodes of an order 6
triangulation.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Hans Rudolf Schwarz,<br>
Finite Element Methods,<br>
Academic Press, 1988,<br>
ISBN: 0126330107,<br>
LC: TA347.F5.S3313.
</li>
<li>
Gilbert Strang, George Fix,<br>
An Analysis of the Finite Element Method,<br>
Cambridge, 1973,<br>
ISBN: 096140888X,<br>
LC: TA335.S77.
</li>
<li>
Olgierd Zienkiewicz,<br>
The Finite Element Method,<br>
Sixth Edition,<br>
Butterworth-Heinemann, 2005,<br>
ISBN: 0750663200,<br>
LC: TA640.2.Z54.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "fem2d_sample.f90">fem2d_sample.f90</a>, the source code.
</li>
<li>
<a href = "fem2d_sample.sh">fem2d_sample.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>SQ</b> is FEM data for the function f(x,y)=x^2+y^2, on a 5x5 grid
of nodes, organized into linear triangles. The sample data seeks the values
of this function on a 4x4 evenly spaced grid.
<ul>
<li>
<a href = "fem_sq_nodes.txt">fem_sq_nodes.txt</a>,
defines the FEM nodes.
</li>
<li>
<a href = "fem_sq_elements.txt">fem_sq_elements.txt</a>,
defines the FEM elements.
</li>
<li>
<a href = "fem_sq_values.txt">fem_sq_values.txt</a>,
defines the FEM nodal values.
</li>
<li>
<a href = "sample_sq_nodes.txt">sample_sq_nodes.txt</a>,
defines the sample nodes.
</li>
<li>
<a href = "sample_sq_values.txt">sample_sq_values.txt</a>,
defines the sample nodal values.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for FEM2D_SAMPLE.
</li>
<li>
<b>BASIS_MN_T3:</b> all bases at N points for a T3 element.
</li>
<li>
<b>BASIS_MN_T6:</b> all bases at N points for a T6 element.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is a case insensitive comparison of two characters for equality.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer ( kind = 4 ) value of a base 10 digit.
</li>
<li>
<b>FEM2D_EVALUATE</b> samples an FEM function on a T3 or T6 triangulation.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>GET_SEED</b> returns a seed for the random number generator.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4_UNIFORM</b> returns a scaled pseudorandom I4.
</li>
<li>
<b>I4COL_COMPARE</b> compares columns I and J of an I4COL.
</li>
<li>
<b>I4COL_SORT_A</b> ascending sorts an I4COL.
</li>
<li>
<b>I4COL_SWAP</b> swaps columns I and J of an I4COL.
</li>
<li>
<b>I4MAT_DATA_READ</b> reads data from an I4MAT file.
</li>
<li>
<b>I4MAT_HEADER_READ</b> reads the header from an I4MAT.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads data from an R8MAT file.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>S_TO_I4</b> reads an integer ( kind = 4 ) value from a string.
</li>
<li>
<b>S_TO_I4VEC</b> reads an integer ( kind = 4 ) vector from a string.
</li>
<li>
<b>S_TO_R8</b> reads an R8 from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads an R8VEC from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>SORT_HEAP_EXTERNAL</b> externally sorts a list of items into ascending order.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRIANGULATION_ORDER3_NEIGHBOR_TRIANGLES</b> determines triangle neighbors.
</li>
<li>
<b>TRIANGULATION_ORDER6_NEIGHBOR_TRIANGLES</b> determines triangle neighbors.
</li>
<li>
<b>TRIANGULATION_SEARCH_DELAUNAY</b> searches a Delaunay triangulation for a point.
</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 17 January 2010.
</i>
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