Braxton Osting

This Matlab code is an implementation of a finite-volume discretization for the planar Maxwell equations. The accompanying paper can be downloaded here. A more complete description of the code is available at the website of my collaborator, Harish Bhat.

This Mathematica code uses a recursive algorithm to evaluate the lattice Green's function for the Helmholtz operator on a square lattice. The lattice Green's function is then used to solve a thin-slit diffraction problem for two-dimensional lattice waves. The accompanying paper can be downloaded here.

The fundamental modes of vibration for an idealized drum of given shape satisfy the Laplace–Dirichlet eigenproblem. This Mathematica code computes the first few eigenpairs of the Laplacian on an ellipse with Dirichlet boundary conditions. In elliptical coordinates, the Laplace–Dirichlet equations on an ellipse are separable. In the "angular" coordinate (parameterizing confocal ellipses), the solution satisfies the Mathieu equation, and in the "radial" coordinate (parameterizing confocal hyperbolas), the solution satisfies the modified Mathieu equation. The eigenfunctions are such that the solutions to the Mathieu equation are periodic, and the solutions to the modified Mathieu equation vanish on the boundary of the ellipse.