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A Pseudospectral Penalty Scheme for 2D Isotropic Elastic Wave Computations

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Abstract

In this paper, we present a pseudospectral scheme for solving 2D elastic wave equations. We start by analyzing boundary operators leading to the well-posedness of the problem. In addition, equivalent characteristic boundary conditions of common physical boundary conditions are discussed. These theoretical results are further employed to construct a Legendre pseudospectral penalty scheme based on a tensor product formulation for approximating waves on a general curvilinear quadrilateral domain. A stability analysis of the scheme is conducted for the case where a straight-sided quadrilateral element is used. The analysis shows that, by properly setting the penalty parameters, the scheme is stable at the semi-discrete level. Numerical experiments for testing the performance of the scheme are conducted, and the expected p- and h-convergence patterns are observed. Moreover, the numerical computations also show that the scheme is time stable, which makes the scheme suitable for long time simulations.

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Authors and Affiliations

  1. Department of Mathematics, National Cheng Kung University, No. 1 University Road, Tainan, 701, Taiwan

    Ko-An Feng, Chun-Hao Teng & Min-Hung Chen

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  1. Ko-An Feng
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  2. Chun-Hao Teng
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  3. Min-Hung Chen
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Correspondence to Chun-Hao Teng.

Additional information

This work is supported by National Science Council grant No. NSC 95-2120-M-001-003.

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Feng, KA., Teng, CH. & Chen, MH. A Pseudospectral Penalty Scheme for 2D Isotropic Elastic Wave Computations. J Sci Comput 33, 313–348 (2007). https://doi.org/10.1007/s10915-007-9154-8

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  • DOI: https://doi.org/10.1007/s10915-007-9154-8

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