laplacian

laplacian, a MATLAB code which evaluates a discretized approximation to the Laplacian operator on data on an evenly spaced grid, within a circle, an interval, or a torus. For the case of the interval, the data may be supplied on an unevenly spaced grid.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

laplacian is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

laplacian_test

laplacian_matrix, a MATLAB code which carries out computations related to the discrete laplacian operator, including full or sparse evaluation, evaluation for unequally spaced data sampling points, application to data samples, solution of associated linear systems, eigenvalues and eigenvectors, and extension to 2D and 3D geometry.

test_matrix, a MATLAB code which defines test matrices for which some of the determinant, eigenvalues, inverse, null vectors, P*L*U factorization or linear system solution are already known.

Source Code:

• laplacian3_circle.m, 3 point Laplacian on a circle.
• laplacian3_interval.m, 3 point Laplacian on an interval.
• laplacian3_interval_uneven.m, 3 point Laplacian on an interval using uneven spacing.
• laplacian5_plane.m, 5 point Laplacian on a plane.
• laplacian5_torus.m, 5 point Laplacian on a torus.
• laplacian5_torus_vector.m, 5 point Laplacian on a torus, vectorized version.
• laplacian9_torus.m, 9 point Laplacian on a torus.