A Pseudospectral Scheme for Isotropic Elastic Wave Equations in2-Dimensional Space

• Main Authors: Ko-an Feng, 馮可安
• Other Authors: Chun-hao Teng
• Format: Others
• Language: en_US
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/35334079151437891117

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 95 === 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 evidences also show that the scheme is time stable, which makes the scheme suitable for long time simulations.