Article ID Journal Published Year Pages File Type
520424 Journal of Computational Physics 2008 16 Pages PDF
Abstract

The paper is concerned with the spectral collocation solution of the Helmholtz equation in a disk in the polar coordinates r and θ. We use spectral Chebyshev collocation in r, spectral Fourier collocation in θ, and a simple integral condition to specify the value of the approximate solution at the center of the disk. The scheme is solved at a quasi optimal cost using the idea of superposition, a matrix decomposition algorithm, and fast Fourier transforms. Both the Dirichlet and Neumann boundary conditions are considered and extensions to equations with variable coefficients are discussed. Numerical results confirm the spectral convergence of the method.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
Authors
, ,