A Problem in a Square Region for FEM2D_HEAT_SPARSE

**FEM2D_HEAT_SPARSE_SQUARE** is a MATLAB library which
defines the geometry and other data of the square problem,
so that a solution can be computed by **fem2d_heat_sparse**.

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

We assume that the equation to be solved is

withdUdT - Laplacian U + K * U = F

andK = 0,

The exact solution is:F = (2*pi*pi-1)*sin(pi*x)*sin(pi*y)*exp(-t).

which is the formula we use to define our functionsU = sin(pi*x) * sin(pi*y) * exp(-t).

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

**FEM2D_HEAT_SPARSE_SQUARE** is available in
a MATLAB version.

CONTOUR_SEQUENCE4, a MATLAB program which makes a sequence of contour plots based on a single XY coordinate file, and a sequence of Z(X,Y) data files.

FEM2D_HEAT_SPARSE, 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.

- dirichlet_condition.m, the user-supplied routine to evaluate the boundary conditions;
- initial_condition.m, the user-supplied routines to evaluate the initial conditions;
- k_coef.m, the user-supplied routines to evaluate the linear coefficient.
- rhs.m, the user-supplied routines to evaluate the right hand side;
- square_output.txt, output from a run of the program;
- square_nodes.png, a PNG image of the 49 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 32 elements;
- square_elements.txt, a text file containing a list, for each element, of the six nodes that compose it;

The following solution data was computed over 10 time steps:

- 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 MATLAB source code page.