Mathematical and numerical studies on meshless methods for exterior unbounded domain problems |
| |
Authors: | Takemi Shigeta DL Young |
| |
Institution: | Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan |
| |
Abstract: | The method of fundamental solutions (MFS) is an efficient meshless method for solving boundary value problems in an exterior unbounded domain. The numerical solution obtained by the MFS is accurate, while the corresponding matrix equation is ill-conditioned. A modified MFS (MMFS) with the proper basis functions is proposed by the introduction of the modified Trefftz method (MTM). The concrete expressions of the corresponding condition numbers are given in mathematical forms and the solvability by these methods is mathematically proven. Thereby, the optimal parameter minimizing the condition number is also mathematically given. Numerical experiments show that the condition numbers of the matrices corresponding to the MTM and the MMFS are reduced and that the numerical solution by the MMFS is more accurate than the one by the conventional method. |
| |
Keywords: | Condition number Exterior unbounded domain Laplace equation Method of fundamental solutions Modified Trefftz method |
本文献已被 ScienceDirect 等数据库收录! |
|