Name
Title | ||
|---|---|---|
Spectral Chebyshev-Fourier collocation for the Helmholtz and variable coefficient equations in a disk |
Abstract | ||
|---|---|---|
The paper is concerned with the spectral collocation solution of the Helmholtz equation in a disk in the polar coordinates r and @q. We use spectral Chebyshev collocation in r, spectral Fourier collocation in @q, 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. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.jcp.2008.06.009 | J. Comput. Physics |
Keywords | Field | DocType |
spectral convergence,chebyshev polynomials,quasi optimal cost,matrix decomposition algorithm,spectral chebyshev collocation,approximate solution,spectral collocation,spectral collocation solution,fast fourier,neumann boundary condition,helmholtz equation,numerical result,spectral chebyshev-fourier collocation,variable coefficient equation,chebyshev polynomial,polar coordinate,matrix decomposition,fast fourier transform | Chebyshev polynomials,Mathematical optimization,Orthogonal collocation,Mathematical analysis,Fourier transform,Helmholtz equation,Spectral method,Neumann boundary condition,Collocation method,Mathematics,Collocation | Journal |
Volume | Issue | ISSN |
227 | 19 | Journal of Computational Physics |
Citations | PageRank | References |
5 | 0.70 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernard Bialecki | 1 | 114 | 18.61 |
| Andreas Karageorghis | 2 | 204 | 47.54 |