A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory

JOURNAL OF COMPUTATIONAL PHYSICS

卷:314

Article

Stolk, Christiaan C.¹ 

[1] Korteweg de Vries Inst Math, Sci Pk 105-107, NL-1090 XG Amsterdam, Netherlands

关键词: Helmholtz equation;    Finite difference method;    Numerical dispersion;    Multigrid;    Domain decomposition;   

DOI  :  10.1016/j.jcp.2016.03.023

来源: Elsevier

【 摘 要 】

We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed. Their coefficients are piecewise polynomial functions of hk, chosen such that phase and amplitude errors are minimal. The phase errors of the scheme are very small, approximately as small as those of the 2-D quasi-stabilized FEM method and substantially smaller than those of alternatives in 3-D, assuming the same number of gridpoints per wavelength is used. In numerical experiments, accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths. When used as a coarse level discretization in a multigrid method the scheme can even be used with down to three points per wavelength. Tests on 3-D examples with up to 10(8) degrees of freedom show that with a recently developed hybrid solver, the use of coarser meshes can lead to corresponding savings in computation time, resulting in good simulation times compared to the literature. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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