Numerical solution of the Helmholtz equation with high wavenumbers
نویسندگان
چکیده
This paper investigates the pollution effect, and explores the feasibility of a local spectral method, the discrete singular convolution (DSC) algorithm for solving the Helmholtz equation with high wavenumbers. Fourier analysis is employed to study the dispersive error of the DSC algorithm. Our analysis of dispersive errors indicates that the DSC algorithm yields a dispersion vanishing scheme. The dispersion analysis is further confirmed by the numerical results. For oneand higher-dimensional Helmholtz equations, the DSC algorithm is shown to be an essentially pollution-free scheme. Furthermore, for large-scale computation, the grid density of the DSC algorithm can be close to the optimal two grid points per wavelength. The present study reveals that the DSC algorithm is accurate and efficient for solving the Helmholtz equation with high wavenumbers. Copyright 2003 John Wiley & Sons, Ltd.
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