FEM2D_HEAT_SQUARE\
A Problem in a Square Region for FEM2D_HEAT_ {#fem2d_heat_square-a-problem-in-a-square-region-for-fem2d_heat_ align=”center”}
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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
with
K = 0,
and
F = (2*pi*pi-1)*sin(pi*x)*sin(pi*y)*exp(-t).
The exact solution is:
U = sin(pi*x) * sin(pi*y) * exp(-t).
which is the formula we use to define our functions G (for the
boundary conditions) and H (for the initial conditions).
Licensing: {#licensing align=”center”}
The computer code and data files described and made available on this
web page are distributed under the GNU LGPL
license.
Languages: {#languages align=”center”}
FEM2D_HEAT_SQUARE is available in a C++
version and a
FORTRAN90 version
and a MATLAB
version.
Source Code: {#source-code align=”center”}
- square.cpp, the user-supplied routines to evaluate the
right hand side, linear coefficient, initial and boundary
conditions;
- 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.
Last revised on 30 August 2006.
