HEATED_PLATE_OPENMP is a FORTRAN77 program which illustrates the use of the OpenMP application program interface by employing an iteration that solves the 2D steady state heat equation.
The sequential version of this program needs approximately 18/eps iterations to complete.
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.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
HEATED_PLATE_OPENMP is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version.
DIJKSTRA_OPENMP, a FORTRAN77 program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.
FFT_OPENMP, a FORTRAN77 program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.
HEATED_PLATE, a FORTRAN77 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.
HELLO_OPENMP, a FORTRAN77 program which prints out "Hello, world!" using the OpenMP parallel programming environment.
MANDELBROT_OPENMP, a FORTRAN77 program which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution.
MD_OPENMP, a FORTRAN77 program which carries out a molecular dynamics simulation using OpenMP.
MULTITASK_OPENMP, a FORTRAN77 program which demonstrates how to "multitask", that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.
MXM_OPENMP, a FORTRAN77 program which computes a dense matrix product C=A*B, using OpenMP for parallel execution.
MXV_OPENMP, a FORTRAN77 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, FORTRAN77 programs which illustrate the use of the OpenMP application program interface for carrying out parallel computations in a shared memory environment.
POISSON_OPENMP, a FORTRAN77 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.
PRIME_OPENMP, a FORTRAN77 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 FORTRAN77 program which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.
RANDOM_OPENMP, a FORTRAN77 program which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.
SATISFY_OPENMP, a FORTRAN77 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 FORTRAN77 program which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.
SGEFA_OPENMP, a FORTRAN77 program which reimplements the SGEFA/SGESL linear algebra routines from LINPACK for use with OpenMP.
ZIGGURAT_OPENMP, a FORTRAN77 program which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.
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.