# HEATED_PLATE_WORKSHARE 2D Steady State Heat Equation Using OpenMP WORKSHARE

HEATED_PLATE_WORKSHARE is a FORTRAN90 program which illustrates the use of OpenMP's WORKSHARE directive for parallelizing FORTRAN array commands.

While the WORKSHARE directive has been part of the OpenMP standard for a considerable time, it does not seem to be well supported by vendors, perhaps in part because it is peculiar to FORTRAN, and not allowed in C. In any case, the example discussed here seems to show no improvement at all over the sequential code, when compiled using the Gnu gfortran compiler or the Intel ifort compiler!

The physical region, and the boundary conditions, are suggested by this diagram;

```                     W = 0
+------------------+
|                  |
W = 100  |                  | W = 100
|                  |
+------------------+
W = 100
```

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:

```                    I = 0
[0][0]-------------[0][N-1]
|                  |
J = 0  |                  |  J = N-1
|                  |
[M-1][0]-----------[M-1][N-1]
I = M-1
```

The steady state solution to the discrete heat equation satisfies the following condition at an interior grid point:

```        W[Central] = (1/4) * ( W[North] + W[South] + W[East] + W[West] )
```
where "Central" is the index of the grid point, "North" is the index of its immediate neighbor to the "north", and so on.

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:

```        W[Central]  <=  (1/4) * ( W[North] + W[South] + W[East] + W[West] )
```
If this process is repeated often enough, the difference between successive estimates of the solution will go to zero.

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.

### Languages:

HEATED_PLATE_WORKSHARE is available in a FORTRAN90 version.

### Related Data and Programs:

DIJKSTRA_OPENMP, a FORTRAN90 program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FFT_OPENMP, a FORTRAN90 program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.

HEATED_PLATE, 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.

HEATED_PLATE_OPENMP, a FORTRAN90 program which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.

HELLO_OPENMP, a FORTRAN90 program which prints out "Hello, world!" using the OpenMP parallel programming environment.

MD_OPENMP, a FORTRAN90 program which carries out a molecular dynamics simulation using OpenMP.

MPI, FORTRAN90 programs which implement parallel programming in a distributed memory environment, using message passing.

MXV_OPENMP, 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.

OPENMP, FORTRAN90 programs which illustrate the use of the OpenMP application program interface for carrying out parallel computations in a shared memory environment.

OPENMP_STUBS, a FORTRAN90 library which implements a "stub" version of OpenMP, so that an OpenMP program can be compiled, linked and executed on a system that does not have OpenMP installed.

PRIME_OPENMP, a FORTRAN90 program which counts the number of primes between 1 and N, using OpenMP for parallel execution.

PTHREADS, C programs which illustrate the use of the POSIX thread library to carry out parallel program execution.

QUAD_OPENMP, a FORTRAN90 program which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.

SATISFY_OPENMP, a FORTRAN90 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, using OpenMP for parallel execution.

SCHEDULE_OPENMP, a FORTRAN90 program which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.

SGEFA_OPENMP, a FORTRAN90 program which reimplements the SGEFA/SGESL linear algebra routines from LINPACK for use with OpenMP.

ZIGGURAT_OPENMP, a FORTRAN90 program which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.

### Reference:

1. Peter Arbenz, Wesley Petersen,
Introduction to Parallel Computing - A practical guide with examples in C,
Oxford University Press,
ISBN: 0-19-851576-6,
LC: QA76.58.P47.
2. Rohit Chandra, Leonardo Dagum, Dave Kohr, Dror Maydan, Jeff McDonald, Ramesh Menon,
Parallel Programming in OpenMP,
Morgan Kaufmann, 2001,
ISBN: 1-55860-671-8,
LC: QA76.642.P32.
3. Barbara Chapman, Gabriele Jost, Ruud vanderPas, David Kuck,
Using OpenMP: Portable Shared Memory Parallel Processing,
MIT Press, 2007,
ISBN13: 978-0262533027,
LC: QA76.642.C49.
4. Tim Mattson, Rudolf Eigenmann,
OpenMP: An API for Writing Portable SMP Application Software,
5. The GNU OpenMP Implementation.
6. The OpenMP web site
7. OpenMP Architecture Review Board,
OpenMP Application Program Interface,
Version 3.0,
May 2008.

### Examples and Tests:

HEATED_PLATE_LOCAL_GFORTRAN compiles, links, loads and runs the program using 1, 2 and 4 threads, the local interactive environment, and the GNU gfortran compiler.

HEATED_PLATE_LOCAL_IFORT compiles, links, loads and runs the program using 1, 2 and 4 threads, the local interactive environment, and the Intel ifort compiler.

HEATED_PLATE_ITHACA_GFORTRAN 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.

HEATED_PLATE_ITHACA_IFORT 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.

You can go up one level to the FORTRAN90 source codes.

Last revised on 15 July 2010.