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<html>
<head>
<title>
FEM1D_SAMPLE - Evaluate a Finite Element Function of a 1D Argument
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FEM1D_SAMPLE <br> Evaluate a Finite Element Function of a 1D Argument
</h1>
<hr>
<p>
<b>FEM1D_SAMPLE</b>
is a FORTRAN90 program which
can evaluate a finite element function of a 1D argument.
</p>
<p>
The current version of the program can only handle finite element
meshes which are made of piecewise constant or piecewise linear basis functions.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>fem1d_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>FEM1D_SAMPLE</b> is available in
<a href = "../../cpp_src/fem1d_sample/fem1d_sample.html">a C++ version</a> and
<a href = "../../f77_src/fem1d_sample/fem1d_sample.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fem1d_sample/fem1d_sample.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fem1d_sample/fem1d_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 = "../../data/fem1d/fem1d.html">
FEM1D</a>,
a data directory which
contains examples of 1D FEM files,
three text files that describe a 1D finite element model;
</p>
<p>
<a href = "../../f_src/fem1d/fem1d.html">
FEM1D</a>,
a FORTRAN90 program which
applies the finite element method to a 1D linear two point boundary value problem.
</p>
<p>
<a href = "../../f_src/fem1d_adaptive/fem1d_adaptive.html">
FEM1D_ADAPTIVE</a>,
a FORTRAN90 program which
applies the finite element method to a 1D linear two point boundary value problem
using adaptive refinement to improve the solution.
</p>
<p>
<a href = "../../f_src/fem1d_bvp_linear/fem1d_bvp_linear.html">
FEM1D_BVP_LINEAR</a>,
a FORTRAN90 program which
applies the finite element method, with piecewise linear elements,
to a two point boundary value problem in one spatial dimension.
</p>
<p>
<a href = "../../f_src/fem1d_heat_steady/fem1d_heat_steady.html">
FEM1D_HEAT_STEADY</a>,
a FORTRAN90 program which
uses the finite element method to solve the steady (time independent)
heat equation in 1D.
</p>
<p>
<a href = "../../f_src/fem1d_nonlinear/fem1d_nonlinear.html">
FEM1D_NONLINEAR</a>,
a FORTRAN90 program which
applies the finite element method to a 1D nonlinear two point boundary value problem.
</p>
<p>
<a href = "../../f_src/fem1d_pack/fem1d_pack.html">
FEM1D_PACK</a>,
a FORTRAN90 library which
contains utilities for 1D finite element calculations.
</p>
<p>
<a href = "../../f_src/fem1d_pmethod/fem1d_pmethod.html">
FEM1D_PMETHOD</a>,
a FORTRAN90 program which
applies the p-method version of the finite element method to a 1D linear
two point boundary value problem.
</p>
<p>
<a href = "../../f_src/fem1d_project/fem1d_project.html">
FEM1D_PROJECT</a>,
a FORTRAN90 program which
projects data into a finite element space, including the least squares
approximation of data, or the projection of a finite element solution
from one mesh to another.
</p>
<p>
<a href = "../../f_src/fem2d_sample/fem2d_sample.html">
FEM2D_SAMPLE</a>,
a FORTRAN90 program which
evaluates a finite element function defined on an order 3 or order 6 triangulation.
</p>
<p>
<a href = "../../f_src/fem3d_sample/fem3d_sample.html">
FEM3D_SAMPLE</a>,
a FORTRAN90 program which
evaluates a finite element function defined on 3D tetrahedral mesh.
</p>
<p>
<a href = "../../f_src/piecewise_linear_product_integral/piecewise_linear_product_integral.html">
PIECEWISE_LINEAR_PRODUCT_INTEGRAL</a>,
a FORTRAN90 library which
calculates the exact value of the integral of the product of two
piecewise linear functions F(X) and G(X).
</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 = "fem1d_sample.f90">fem1d_sample.f90</a>, the source code.
</li>
<li>
<a href = "fem1d_sample.sh">fem1d_sample.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>P1</b> is FEM data for the vector function f(x)=[ 1, x, x^2], on a grid of 11
evenly spaced nodes from -5 to 5, using piecewise constant basis functions.
<ul>
<li>
<a href = "p1_fem_nodes.txt">p1_fem_nodes.txt</a>,
the FEM nodes.
</li>
<li>
<a href = "p1_fem_elements.txt">p1_fem_elements.txt</a>,
the FEM elements.
</li>
<li>
<a href = "p1_fem_values.txt">p1_fem_values.txt</a>,
the FEM nodal values.
</li>
<li>
<a href = "p1_sample_nodes.txt">p1_sample_nodes.txt</a>,
the sample nodes.
</li>
<li>
<a href = "p1_sample_values.txt">p1_sample_values.txt</a>,
the sample nodal values.
</li>
</ul>
</p>
<p>
<b>P2</b> is FEM data for the vector function f(x)=[ 1, x, x^2], on a grid of 11
evenly spaced nodes from -5 to 5, using piecewise linear basis functions.
<ul>
<li>
<a href = "p2_fem_nodes.txt">p2_fem_nodes.txt</a>,
the FEM nodes.
</li>
<li>
<a href = "p2_fem_elements.txt">p2_fem_elements.txt</a>,
the FEM elements.
</li>
<li>
<a href = "p2_fem_values.txt">p2_fem_values.txt</a>,
the FEM nodal values.
</li>
<li>
<a href = "p2_sample_nodes.txt">p2_sample_nodes.txt</a>,
the sample nodes.
</li>
<li>
<a href = "p2_sample_values.txt">p2_sample_values.txt</a>,
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 FEM1D_SAMPLE.
</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 value of a base 10 digit.
</li>
<li>
<b>DTABLE_DATA_READ</b> reads data from a DTABLE file.
</li>
<li>
<b>DTABLE_HEADER_READ</b> reads the header from a DTABLE file.
</li>
<li>
<b>DTABLE_WRITE0</b> writes a DTABLE file with no headers.
</li>
<li>
<b>FEM1D_EVALUATE</b> evaluates a 1D FEM function at sample points.
</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_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>ITABLE_DATA_READ</b> reads data from an ITABLE file.
</li>
<li>
<b>ITABLE_HEADER_READ</b> reads the header from an integer table file.
</li>
<li>
<b>R8VEC_BRACKET4</b> finds the nearest interval to each of a vector of values.
</li>
<li>
<b>S_TO_I4</b> reads an I4 from a string.
</li>
<li>
<b>S_TO_I4VEC</b> reads an I4VEC 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>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 01 June 2009.
</i>
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