A Multi-Scale Trefftz Method for Laplace Problems in a High-Aspect-Ratio Domain
We propose a multi-scale Trefftz method (MSTM) for dealing with the Laplace problems in a high-aspect-ratio domain. When the high-aspect-ratio domain is considered for a numerical simulation, it is well-known that there will appear some difficulties to jeopardize the simulation, especially for the boundary-type meshless methods. The MSTM is originated from the modified Trefftz method, one of the boundary-type meshless methods; hence, the MSTM is a mesh-free and integral-free numerical method. In order to overcome the difficulties appeared in the high-aspect-ratio domain, the numerical solutions of MSTM are expressed by the linear combinations of the T-complete functions, which are scaled by different characteristic lengths. Several numerical examples with slender domain are considered in this paper and the numerical results are provided to validate the efficacy of the proposed MSTM. From the numerical comparisons, the numerical accuracy can be greatly enhanced by scaling via different characteristic lengths. The proposed scheme not only keeps the advantages of the modified Trefftz method, but also has the ability to deal with the Laplace problem in a high-aspect-ratio domain.
Chia-Ming Fan Chein-Shan Liu J.J.Chang
Taiwan Ocean University National Taiwan University
国际会议
南京
英文
1
2009-10-18（万方平台首次上网日期，不代表论文的发表时间）