Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6929736 | Journal of Computational Physics | 2016 | 16 Pages |
Abstract
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: rkcoshâ¡(kθ) and rksinhâ¡(kθ), 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.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Chein-Shan Liu, Chung-Lun Kuo,