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<html>
<head>
<title>
MASS - Mass Matrix Verification
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MASS <br> Mass Matrix Verification
</h1>
<hr>
<p>
<b>MASS</b>
is a FORTRAN90 program which
checks the mass matrix computation for a finite
element fluid flow computation.
</p>
<p>
The code was created by starting with routines extracted from the
POD_BASIS program. The new code computes, factors, and uses
the mass matrix.
</p>
<p>
This was a tricky process, because the original mass matrix
is computed in another executable program, not controlled by
me but by Professor Hyung-Chun Lee. Thus, an appalling number
of choices must match, including conventions about the ordering of nodes,
the quadrature rule, and so on. (We discovered our disagreements
one by one, and decided how to resolve them!)
</p>
<p>
After running this program many times, we finally
worked out the set of parameters to be used. We were satisfied
with the results in July 2003.
</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/case1_flow/case1_flow.html">
CASE1_FLOW</a>,
a dataset directory which
contains solutions to a flow problem.
</p>
<p>
<a href = "../../datasets/cavity_flow/cavity_flow.html">
CAVITY_FLOW</a>,
a dataset directory which
contains solutions to flow in a cavity.
</p>
<p>
<a href = "../../f_src/cvt_basis_flow/cvt_basis_flow.html">
CVT_BASIS_FLOW</a>,
a FORTRAN90 program which
can be used to analyze this data, and compute
a small set of "basis vectors" using CVT techniques.
</p>
<p>
<a href = "../../f77_src/hcell/hcell.html">
HCELL</a>,
a FORTRAN77 program which
solves the Navier Stokes equations in the H-Cell region.
</p>
<p>
<a href = "../../f77_src/inout/inout.html">
INOUT</a>,
a FORTRAN77 program which
solves the Navier Stokes equations in the "In-Out" region.
</p>
<p>
<a href = "../../datasets/inout_flow/inout_flow.html">
INOUT_FLOW</a>,
a dataset directory which
contains solutions to flow in the "inout" region.
</p>
<p>
<a href = "../../datasets/inout_flow2/inout_flow2.html">
INOUT_FLOW2</a>,
a dataset directory which
contains solutions to flow in the "inout" region.
</p>
<p>
<a href = "../../f_src/pod_basis_flow/pod_basis_flow.html">
POD_BASIS_FLOW</a>,
a FORTRAN90 program which
can be used to analyze flow data, and compute
a small set of "basis vectors" using POD techniques.
</p>
<p>
<a href = "../../datasets/tcell_flow/tcell_flow.html">
TCELL_FLOW</a>,
a dataset directory which
contains solutions to flow in
the T-cell region.
</p>
<p>
<a href = "../../f77_src/tcell_mass/tcell_mass.html">
TCELL_MASS</a>,
a FORTRAN77 program which
computes the mass matrix for the T-Cell problem.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Max Gunzburger,<br>
Finite Element Methods for Viscous Incompressible Flows,<br>
A Guide to Theory, Practice, and Algorithms,<br>
Academic Press, 1989,<br>
ISBN: 0-12-307350-2,<br>
LC: TA357.G86.
</li>
<li>
John Burkardt, Max Gunzburger, Hyung-Chun Lee,<br>
Centroidal Voronoi Tessellation-Based Reduced-Order
Modelling of Complex Systems,<br>
SIAM Journal on Scientific Computing,<br>
Volume 28, Number 2, 2006, pages 459-484.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "mass.f90">mass.f90</a>, the source code.
</li>
<li>
<a href = "mass.sh">mass.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>MASS_05</b> is a run of the program which uses the 500 solutions
associated with the INOUT_FLOW dataset.
<ul>
<li>
<a href = "mass_05_input.txt">mass_05_input.txt</a>,
the input file.
</li>
<li>
<a href = "mass_05_output.txt">mass_05_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for MASS.
</li>
<li>
<b>BANDWIDTH_DETERMINE</b> computes the lower bandwidth of a finite element matrix.
</li>
<li>
<b>BASIS_WRITE</b> writes a basis vector to a file.
</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_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>DATA_I4VEC_READ</b> reads an dataset of integer vectors stored in a file.
</li>
<li>
<b>DATA_R82_READ</b> reads a data set of pairs of R8 numbers stored in a file.
</li>
<li>
<b>DATA_R82_WRITE</b> writes a data set of pairs of real*8 numbers into a file.
</li>
<li>
<b>DATA_SIZE</b> counts the size of a data set stored in a file.
</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>FILE_EXIST</b> reports whether a file exists.
</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_INPUT</b> prints a prompt string and reads an integer from the user.
</li>
<li>
<b>I4_RANGE_INPUT</b> reads a pair of integers from the user, representing a range.
</li>
<li>
<b>MASS_MATRIX</b> computes the mass matrix.
</li>
<li>
<b>NODE_T6</b> returns the basis nodes for a 6 node triangle.
</li>
<li>
<b>R8BLT_CHECK</b> checks the dimensions of a banded lower triangular matrix.
</li>
<li>
<b>R8BLT_PRINT</b> prints a band lower triangular matrix.
</li>
<li>
<b>R8BLT_PRINT_SOME</b> prints some of a band lower triangular matrix.
</li>
<li>
<b>REFQBF</b> evaluates a reference element quadratic basis function.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>S_EQI</b> is a case insensitive comparison of two strings for equality.
</li>
<li>
<b>S_INPUT</b> prints a prompt string and reads a string from the user.
</li>
<li>
<b>S_OF_I4</b> converts an integer to a left-justified string.
</li>
<li>
<b>S_REP_CH</b> replaces all occurrences of one character by another.
</li>
<li>
<b>S_TO_I4</b> reads an integer value from a string.
</li>
<li>
<b>S_TO_R8</b> reads an R8 value from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>SINGULAR_VECTORS</b> computes the desired singular values.
</li>
<li>
<b>R8PBL_CHECK</b> checks the dimensions of a positive definite symmetric band matrix.
</li>
<li>
<b>R8PBL_WRITE</b> writes a symmetric banded matrix to a file.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TIMESTRING</b> writes the current YMDHMS date into a string.
</li>
<li>
<b>TRIANGLE_UNIT_SET</b> sets a quadrature rule in the unit triangle.
</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 May 2008.
</i>
<!-- John Burkardt -->
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