Spectral Chebyshev-Fourier collocation for the Helmholtz and variable coefficient equations in a disk
Date
2008Source
Journal of Computational PhysicsVolume
227Issue
19Pages
8588-8603Google Scholar check
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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. © 2008 Elsevier Inc. All rights reserved.