A multiple-direction Trefftz method for solving the multi-dimensional wave equation in an arbitrary spatial domain

作者：Liu, Chein-Shan; Kuo, Chung-Lun^*

来源：Journal of Computational Physics, 2016, 321: 39-54.

DOI：10.1016/j.jcp.2016.05.030

• Multi-dimensional wave equation
• Trefftz method
• Wave polynomials
• Multiple-scale Trefftz method
• Multiple-direction Trefftz method
• Minkowski space

In this paper we first express the wave equation in terms of the Minkowskian polar coordinates and generate a set of complete hyperbolic type Trefftz bases: r(k) cosh(k theta) and r(k) sinh(k theta), which are further transformed to wave polynomials as the trial solution bases for the one-dimensional wave equation. In order to stably solve the wave propagation problems long-term we develop a multiple-scale Trefftz method (MSTM), of which the scales are determined a priori by the collocation points. Then we derive a very simple method of multi-dimensional wave polynomials, equipped with different spatial directions which being the normalized wavenumber vectors, as the polynomial Trefftz bases for solving the multi-dimensional wave equations, which is named a multiple-direction Trefftz method (MDTM). Several numerical examples of two-and three-dimensional wave equations demonstrate that the present method is efficient and stable.

• 出版日期2016-9-15
• 单位河海大学