Mathematical and numerical studies on meshless methods for exterior unbounded domain problems
Resource
Journal of Computational Physics, 230(17), 6900-6915
Journal
Journal of Computational Physics
Pages
6900-6915
Date Issued
2011
Date
2011
Author(s)
Shigeta, Takemi
Young, D.L.
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. © 2011 Elsevier Inc.
Type
journal article
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