A Pseudospectral Penalty Scheme for 2D Isotropic Elastic Wave Computations

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 theor...

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Bibliographic Details
Published in:Journal of scientific computing 2007-12, Vol.33 (3), p.313-348
Main Authors: Feng, Ko-An, Teng, Chun-Hao, Chen, Min-Hung
Format: Article
Language:English
Subjects:
Boundary conditions
Elastic waves
Quadrilaterals
Stability analysis
Tensors
Wave equations
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Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-007-9154-8