Staggered-grid spectral element methods for elastic wave simulations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:285

Article

Chung, Eric T.¹  Yu, Tang Fei¹ 

[1] Chinese Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

关键词: Spectral element method;    Elastic wave;    Energy conservation;    Optimal convergence;    Dispersion error;    Staggered grid;   

DOI  :  10.1016/j.cam.2015.02.010

来源: Elsevier

【 摘 要 】

In this paper, we develop and analyze a new class of spectral element methods for the simulations of elastic wave propagation. The major components of the method are the spatial discretization and the choice of interpolation nodes. The spatial discretization is based on piecewise polynomial approximation defined on staggered grids. The resulting method combines the advantages of both staggered-grid based methods and classical non-staggered-grid based spectral element methods. Our new method is energy conserving and does not require the use of any numerical flux, because of the staggered local continuity of the basis functions. Our new method also uses Radau points as interpolation nodes, and the resulting mass matrix is diagonal, thus time marching is explicit and is very efficient. Moreover, we give a rigorous proof for the optimal convergence of the method. In terms of dispersion, we present a numerical study for the numerical dispersion and show that this error is of very high order. Finally, some numerical convergence tests and applications to unbounded domain problems with perfectly matched layer are shown. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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