FEM2D_HEAT_SQUARE
A Problem in a Square Region for FEM2D_HEAT_

FEM2D_HEAT_SQUARE is a C++ library which defines the data associated with a time-dependent heat equation problem in a square region, to be linked and executed with the FEM2D_HEAT program.

This mesh uses 81 nodes and forms 32 quadratic triangular elements.

We assume that the equation to be solved is

dUdT - Laplacian U + K * U = F

K = 0,

F = (2*pi*pi-1)*sin(pi*x)*sin(pi*y)*exp(-t).

U = sin(pi*x) * sin(pi*y) * exp(-t).

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

FEM2D_HEAT_SQUARE is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Source Code:

• square.cpp, the user-supplied routines to evaluate the right hand side, linear coefficient, initial and boundary conditions;
• square.sh, commands to compile the user routines, link them with the partial program, and run the program;
• square_output.txt, output from a run of the program;
• square_nodes.png, a PNG image of the nodes;
• square_nodes.txt, a text file containing a list, for each node, of its X and Y coordinates;
• square_elements.png, a PNG image of the elements;
• square_elements.txt, a text file containing a list, for each element, of the six nodes that compose it;
• square_time.txt, a text file containing the solution times;
• u0000.txt, the solution U at time step 0;
• u0001.txt, the solution U at time step 1;
• u0002.txt, the solution U at time step 2;
• u0003.txt, the solution U at time step 3;
• u0004.txt, the solution U at time step 4;
• u0005.txt, the solution U at time step 5;
• u0006.txt, the solution U at time step 6;
• u0007.txt, the solution U at time step 7;
• u0008.txt, the solution U at time step 8;
• u0009.txt, the solution U at time step 9;
• u0010.txt, the solution U at time step 10;

The MATLAB program CONTOUR_SEQUENCE4 can make contour plots from the sequence of solutions:

• u0000.png, the solution U at time step 0;
• u0001.png, the solution U at time step 1;
• u0002.png, the solution U at time step 2;
• u0003.png, the solution U at time step 3;
• u0004.png, the solution U at time step 4;
• u0005.png, the solution U at time step 5;
• u0006.png, the solution U at time step 6;
• u0007.png, the solution U at time step 7;
• u0008.png, the solution U at time step 8;
• u0009.png, the solution U at time step 9;
• u0010.png, the solution U at time step 10;

You can go up one level to the C++ source codes.