A Pseudospectral Penalty Scheme for 2D Isotropic Elastic Wave Computations |
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Authors: | Ko-An Feng Chun-Hao Teng Min-Hung Chen |
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Affiliation: | (1) Department of Mathematics, National Cheng Kung University, No. 1 University Road, Tainan, 701, Taiwan |
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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.
This work is supported by National Science Council grant No. NSC 95-2120-M-001-003. |
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Keywords: | Pseudospectral penalty methods Multidomain schemes Elastic waves Velocity-stress formulation |
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