HEATED_PLATE is a C program which solves the steady state heat equation in a 2D rectangular region, and is intended as a starting point for implementing an OpenMP parallel version.
The final estimate of the solution is written to a file in a format suitable for display by GRID_TO_BMP.
The sequential version of this program needs approximately 18/epsilon 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.
heated_plate epsilon output_file
FD1D_HEAT is a MATLAB program which uses the finite difference method to solve the 1D Time Dependent Heat Equations.
FD1D_PLOT is a MATLAB program which plots the output from the FD1D program;
FEM_50_HEAT is a MATLAB program which implements a finite element calculation specifically for the heat equation.
FEM1D_HEAT is a MATLAB program which uses the finite element method to solve the 1D Time Dependent Heat Equations.
FEM2D_HEAT is a C++ program which solves the 2D time dependent heat equation on the unit square.
FFH_SPARSE is a MATLAB program which solves the time dependent heat equation in an arbitrary triangulated 2D region, using MATLAB's sparse matrix storage format and solver.
FFT is a C program which demonstrates the computation of a Fast Fourier Transform, and is intended as a starting point for implementing an OpenMP parallel version.
GRID_TO_BMP is a C++ program which reads a text file of data on a rectangular grid and creates a BMP file containing a color image of the data.
HEAT_MPI is a C program which solves the 1D Time Dependent Heat Equation using MPI.
HEATED_PLATE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version.
HOT_PIPE is a MATLAB program which uses FEM_50_HEAT to solve the heat equation for a pipe model.
HOT_POINT is a MATLAB program which uses FEM_50_HEAT to solve the heat equation for a 2D region with a hot point.
MD is a C program which carries out a molecular dynamics simulation, and is intended as a starting point for implementing an OpenMP parallel version.
The program has a built in grid of M = 500, N = 500. It is only necessary to alter these definitions and recompile in order to run the problem on a different grid. Here are the output files and solution files from two runs.
You can go up one level to the C source codes.