Year: 2018
Author: Fang Hao, Hui Lv, Xiaoyan Liu
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 1 : pp. 41–61
Abstract
The method of fundamental solutions (MFS) and the Collocation Trefftz method have been known as two highly effective boundary-type methods for solving homogeneous equations. Despite many attractive features of these two methods, they also experience different aspects of difficulties. Recent advances in the selection of source location of the MFS and the techniques in reducing the condition number of the Trefftz method have made significant improvement in the performance of these two methods which have been proven to be theoretically equivalent. In this paper we will compare the numerical performance of these two methods under various smoothness of the boundary and boundary conditions.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2016-0184
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 1 : pp. 41–61
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Trefftz method the method of fundamental solution LOOCV multiple scale method non-harmonic boundary conditions.
Author Details
-
An overview of the method of fundamental solutions—Solvability, uniqueness, convergence, and stability
Cheng, Alexander H.D. | Hong, YongxingEngineering Analysis with Boundary Elements, Vol. 120 (2020), Iss. P.118
https://doi.org/10.1016/j.enganabound.2020.08.013 [Citations: 95] -
Meshless simulation of anti-plane crack problems by the method of fundamental solutions using the crack Green’s function
Ma, Ji | Chen, Wen | Zhang, Chuanzeng | Lin, JiComputers & Mathematics with Applications, Vol. 79 (2020), Iss. 5 P.1543
https://doi.org/10.1016/j.camwa.2019.09.016 [Citations: 7] -
The method of two-point angular basis function for solving Laplace equation
Kuo, Chung-Lun | Yeih, Weichung | Ku, Cheng-Yu | Fan, Chia-MingEngineering Analysis with Boundary Elements, Vol. 106 (2019), Iss. P.264
https://doi.org/10.1016/j.enganabound.2019.05.018 [Citations: 3]