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<html>
<head>
<title>
HEATED_PLATE_OPENMP - 2D Steady State Heat Equation Using OpenMP
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
HEATED_PLATE_OPENMP <br> 2D Steady State Heat Equation Using OpenMP
</h1>
<hr>
<p>
<b>HEATED_PLATE_OPENMP</b>
is a FORTRAN90 program which
illustrates the use of the OpenMP application program interface
by employing an iteration that solves the 2D steady state
heat equation.
</p>
<p>
The sequential version of this program needs approximately
18/eps iterations to complete.
</p>
<p>
The physical region, and the boundary conditions, are suggested
by this diagram;
<pre>
W = 0
+------------------+
| |
W = 100 | | W = 100
| |
+------------------+
W = 100
</pre>
</p>
<p>
The region is covered with a grid of M by N nodes, and an N by N
array W is used to record the temperature. The correspondence between
array indices and locations in the region is suggested by giving the
indices of the four corners:
<pre>
I = 0
[0][0]-------------[0][N-1]
| |
J = 0 | | J = N-1
| |
[M-1][0]-----------[M-1][N-1]
I = M-1
</pre>
</p>
<p>
The steady state solution to the discrete heat equation satisfies the
following condition at an interior grid point:
<pre>
W[Central] = (1/4) * ( W[North] + W[South] + W[East] + W[West] )
</pre>
where "Central" is the index of the grid point, "North" is the index
of its immediate neighbor to the "north", and so on.
</p>
<p>
Given an approximate solution of the steady state heat equation, a
"better" solution is given by replacing each interior point by the
average of its 4 neighbors - in other words, by using the condition
as an ASSIGNMENT statement:
<pre>
W[Central] <= (1/4) * ( W[North] + W[South] + W[East] + W[West] )
</pre>
If this process is repeated often enough, the difference between successive
estimates of the solution will go to zero.
</p>
<p>
This program carries out such an iteration, using a tolerance specified by
the user, and writes the final estimate of the solution to a file that can
be used for graphic processing.
</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>HEATED_PLATE_OPENMP</b> is available in
<a href = "../../c_src/hello/hello.html">a C version</a> and
<a href = "../../cpp_src/hello/hello.html">a C++ version</a> and
<a href = "../../f77_src/hello/hello.html">a FORTRAN77 version</a> and
<a href = "../../f_src/hello/hello.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/dijkstra_openmp/dijkstra_openmp.html">
DIJKSTRA_OPENMP</a>,
a FORTRAN90 program which
uses OpenMP to parallelize a simple example of Dijkstra's
minimum distance algorithm for graphs.
</p>
<p>
<a href = "../../f_src/fft_openmp/fft_openmp.html">
FFT_OPENMP</a>,
a FORTRAN90 program which
demonstrates the computation of a Fast Fourier Transform
in parallel, using OpenMP.
</p>
<p>
<a href = "../../f_src/heated_plate/heated_plate.html">
HEATED_PLATE</a>,
a FORTRAN90 program which
solves the steady (time independent) heat equation in a 2D
rectangular region, and is intended as
a starting point for implementing an OpenMP parallel version.
</p>
<p>
<a href = "../../f_src/heated_plate_workshare/heated_plate_workshare.html">
HEATED_PLATE_WORKSHARE</a>,
a FORTRAN90 program which
solves the steady (time independent) heat equation in a 2D
rectangular region, using OpenMP's WORKSHARE directive to run in parallel
(however, the results suggest that WORKSHARE is not supported by the
GFORTRAN and IFORT compilers!)
</p>
<p>
<a href = "../../f_src/hello_openmp/hello_openmp.html">
HELLO_OPENMP</a>,
a FORTRAN90 program which
prints out "Hello, world!" using the OpenMP parallel programming environment.
</p>
<p>
<a href = "../../f_src/mandelbrot_openmp/mandelbrot_openmp.html">
MANDELBROT_OPENMP</a>,
a FORTRAN90 program which
generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set,
using OpenMP for parallel execution.
</p>
<p>
<a href = "../../f_src/md_openmp/md_openmp.html">
MD_OPENMP</a>,
a FORTRAN90 program which
carries out a molecular dynamics simulation using OpenMP.
<p>
<p>
<a href = "../../f_src/multitask_openmp/multitask_openmp.html">
MULTITASK_OPENMP</a>,
a FORTRAN90 program which
demonstrates how to "multitask", that is, to execute several unrelated
and distinct tasks simultaneously, using OpenMP for parallel execution.
</p>
<p>
<a href = "../../f_src/mxv_openmp/mxv_openmp.html">
MXM_OPENMP</a>,
a FORTRAN90 program which
computes a dense matrix product C=A*B,
using OpenMP for parallel execution.
<p>
<p>
<a href = "../../f_src/mxv_openmp/mxv_openmp.html">
MXV_OPENMP</a>,
a FORTRAN90 program which
compares the performance of plain vanilla Fortran and the FORTRAN90
intrinsic routine MATMUL, for the matrix multiplication problem
y=A*x, with and without parallelization by OpenMP.
<p>
<p>
<a href = "../../f_src/openmp/openmp.html">
OPENMP</a>,
FORTRAN90 programs which
illustrate the use of the OpenMP application program interface
for carrying out parallel computations in a shared memory environment.
</p>
<p>
<a href = "../../f_src/poisson_openmp/poisson_openmp.html">
POISSON_OPENMP</a>,
a FORTRAN90 program which
computes an approximate solution to the Poisson equation in a rectangle,
using the Jacobi iteration to solve the linear system, and OpenMP to
carry out the Jacobi iteration in parallel.
</p>
<p>
<a href = "../../f_src/prime_openmp/prime_openmp.html">
PRIME_OPENMP</a>,
a FORTRAN90 program which
counts the number of primes between 1 and N, using OpenMP for parallel execution.
</p>
<p>
<a href = "../../f_src/quad_openmp/quad_openmp.html">
QUAD_OPENMP</a>,
a FORTRAN90 program which
approximates an integral using a quadrature rule, and carries out the
computation in parallel using OpenMP.
</p>
<p>
<a href = "../../f_src/random_openmp/random_openmp.html">
RANDOM_OPENMP</a>,
a FORTRAN90 program which
illustrates how a parallel program using OpenMP can generate multiple
distinct streams of random numbers.
</p>
<p>
<a href = "../../f_src/satisfy_openmp/satisfy_openmp.html">
SATISFY_OPENMP</a>,
a FORTRAN90 program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem,
using OpenMP for parallel execution.
<p>
<p>
<a href = "../../f_src/schedule_openmp/schedule_openmp.html">
SCHEDULE_OPENMP</a>,
a FORTRAN90 program which
demonstrates the default, static, and dynamic methods of "scheduling"
loop iterations in OpenMP to avoid work imbalance.
<p>
<p>
<a href = "../../f_src/sgefa_openmp/sgefa_openmp.html">
SGEFA_OPENMP</a>,
a FORTRAN90 program which
reimplements the SGEFA/SGESL linear algebra routines from
LINPACK for use with OpenMP.
</p>
<p>
<a href = "../../f_src/ziggurat_openmp/ziggurat_openmp.html">
ZIGGURAT_OPENMP</a>,
a FORTRAN90 program which
demonstrates how the ZIGGURAT library can be used to generate random numbers
in an OpenMP parallel program.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Peter Arbenz, Wesley Petersen,<br>
Introduction to Parallel Computing - A practical guide with examples in C,<br>
Oxford University Press,<br>
ISBN: 0-19-851576-6,<br>
LC: QA76.58.P47.
</li>
<li>
Rohit Chandra, Leonardo Dagum, Dave Kohr, Dror Maydan,
Jeff McDonald, Ramesh Menon,<br>
Parallel Programming in OpenMP,<br>
Morgan Kaufmann, 2001,<br>
ISBN: 1-55860-671-8,<br>
LC: QA76.642.P32.
</li>
<li>
Barbara Chapman, Gabriele Jost, Ruud vanderPas, David Kuck,<br>
Using OpenMP: Portable Shared Memory Parallel Processing,<br>
MIT Press, 2007,<br>
ISBN13: 978-0262533027,<br>
LC: QA76.642.C49.
</li>
<li>
<a href = "http://www.openmp.org/">The OpenMP web site</a>
</li>
<li>
OpenMP Architecture Review Board,<br>
OpenMP Application Program Interface,<br>
Version 3.0,<br>
May 2008.
</li>
</ol>
</p>
<h3 align = "center">
Source code:
</h3>
<p>
<ul>
<li>
<a href = "heated_plate_openmp.f90">heated_plate_openmp.f90</a>,
the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>HEATED_PLATE_LOCAL_GFORTRAN</b> compiles, links, loads and runs the program
using 1, 2 and 4 threads, the local interactive environment,
and the GNU gfortran compiler.
<ul>
<li>
<a href = "heated_plate_local_gfortran.sh">heated_plate_local_gfortran.sh</a>,
BASH commands.
</li>
<li>
<a href = "heated_plate_local_gfortran_output.txt">heated_plate_local_gfortran_output.txt</a>,
the output file;
</li>
</ul>
</p>
<p>
<b>HEATED_PLATE_LOCAL_IFORT</b> compiles, links, loads and runs the program
using 1, 2 and 4 threads, the local interactive environment,
and the Intel ifort compiler.
<ul>
<li>
<a href = "heated_plate_local_ifort.sh">heated_plate_local_ifort.sh</a>,
BASH commands.
</li>
<li>
<a href = "heated_plate_local_ifort_output.txt">heated_plate_local_ifort_output.txt</a>,
the output file;
</li>
</ul>
</p>
<p>
<b>HEATED_PLATE_ITHACA_GFORTRAN</b> compiles, links, loads and runs the program
using 1, 2 and 4 threads, using the PBS queueing system on Virginia
Tech's Ithaca cluster, and the GNU gfortran compiler.
<ul>
<li>
<a href = "heated_plate_ithaca_gfortran.sh">heated_plate_ithaca_gfortran.sh</a>,
BASH commands.
</li>
<li>
<a href = "heated_plate_ithaca_gfortran_output.txt">heated_plate_ithaca_gfortran_output.txt</a>,
the output file;
</li>
</ul>
</p>
<p>
<b>HEATED_PLATE_ITHACA_IFORT</b> compiles, links, loads and runs the program
using 1, 2 and 4 threads, using the PBS queueing system on Virginia
Tech's Ithaca cluster,
and the Intel ifort compiler.
<ul>
<li>
<a href = "heated_plate_ithaca_ifort.sh">heated_plate_ithaca_ifort.sh</a>,
BASH commands.
</li>
<li>
<a href = "heated_plate_ithaca_ifort_output.txt">heated_plate_ithaca_ifort_output.txt</a>,
the output file;
</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 10 July 2010.
</i>
<!-- John Burkardt -->
</body>
</html>