paraheat_gaussian_plot

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 parameterized by (xc,yc), sc and vc, and then uses radial basis functions (RBF) to reconstruct the finite element solution from a set of sample values.

Licensing:

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

Languages:

paraheat_gaussian_plot is available in a MATLAB version.

Related Data and Programs:

paraheat_gaussian, a MATLAB library which can set up and solve a parameterized steady heat equation in a 2D spatial domain, using diffusivity parameterized by vc, and reporting selected solution values vs.

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 library which can set up and solve a parameterized steady heat equation in a 2D spatial domain, using diffusivity parameterized by vc, and reporting selected solution values vs.

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.

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.

Source Code:

• paraheat_gaussian_plot.m, calls paraheat_gaussian() to generate sensor data of a finite element solution for a given diffusivity, and then reconstructs the finite element solution from the sensor data, using radial basis functions.
• paraheat_gaussian_plot_batch.m, a MATLAB script needed to run paraheat_gaussian_plot in batch.
• paraheat_gaussian_plot.sh, runs the program.
• paraheat_gaussian_plot.txt, the output file.

• diffusivity_gaussian_contour_987654321.png, a contour plot of the diffusivity function.
• diffusivity_gaussian_surface_987654321.png, a surface plot of the diffusivity function.
• fem_contour_987654321.png, a contour plot of the solution.
• fem_contour_rbf_987654321.png, a contour plot of the reconstructed solution.
• fem_surface_987654321.png, a surface plot of the solution.
• fem_surface_rbf_987654321.png, a surface plot of the reconstructed solution.