paraheat_pwc_sample

paraheat_pwc_sample, a MATLAB library which repeatedly calls paraheat_pwc() to set up and solve a parameterized steady heat equation in a 2D spatial domain, with a piecewise constant diffusivity, saving values of the finite element solution at selected points, and writing the saved data to a file.

Licensing:

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

Languages:

paraheat_pwc_sample is available in a MATLAB version.

Related Data and Programs:

paraheat_gaussian, a MATLAB program which sets up and solves a parameterized steady heat equation in a 2D spatial domain, with a gaussian diffusivity parameterized by (xc,yc), sc and vc.

paraheat_gaussian_plot, a MATLAB program which calls paraheat_gaussian() to set up and solve a parameterized steady heat equation in a 2D spatial domain, with a gaussian diffusivity and then uses radial basis functions (RBF) to reconstruct the finite element solution from a set of sample values.

paraheat_gaussian_sample, a MATLAB program which repeatedly calls paraheat_gaussian() to set up and solve a parameterized steady heat equation in a 2D spatial domain, with a gaussian diffusivity, saving values of the finite element solution at selected points, and writing the saved data to a file.

paraheat_pwc, a MATLAB program which sets up and solves a parameterized steady heat equation in a 2D spatial domain, with a parameterized piecewise constant diffusivity.

paraheat_pwc_1d, a MATLAB program which sets up and solves a parameterized steady heat equation in a 1D region, with a piecewise constant diffusivity.

paraheat_pwc_plot, a MATLAB program which calls paraheat_pwc() to set up and solve a parameterized steady heat equation in a 2D spatial domain, with a piecewise constant diffusivity and then uses radial basis functions (RBF) to reconstruct the finite element solution from a set of sample values.

Source Code:

• paraheat_pwc_sample.m, repeatedly calls paraheat_pwc() with different diffusivities, creating a datafile that stores the input and output.
• paraheat_pwc_sample_batch.m, calls paraheat_pwc_sample() in a batch run.
• paraheat_pwc_sample.sh, runs the paraheat_sample() batch test.
• paraheat_pwc_sample.txt, the output file.
• paraheat_pwc_sample_data.txt, the data file.

In some cases, plots are tagged with the random number seed associated with the problem.

• diffusivity_bars_123456789.png, a bar plot of the diffusivity function.
• diffusivity_patch_123456789.png, a patch plot of the diffusivity function.
• elements.png, a plot of the elements.
• fem_contour_123456789.png, a contour plot of the solution.
• fem_surface_123456789.png, a surface plot of the solution.
• grid.png, a plot of the grid.
• sensor_location_987654321.png, a plot of the sensor locations.