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.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Numerical Analysis
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics