Paper Info
Title
Mathematical and numerical studies on meshless methods for exterior unbounded domain problems
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.
Year
DOI
Venue
2011
10.1016/j.jcp.2011.05.017
J. Comput. Physics
Keywords
Field
DocType
numerical study,conventional method,corresponding condition number,exterior unbounded domain,laplace equation,modified mfs,corresponding matrix equation,method of fundamental solution,exterior unbounded domain problem,numerical experiment,modified trefftz method,efficient meshless method,condition number,method of fundamental solutions,fundamental solution,numerical solution,boundary value problem,matrix equation
Boundary value problem,Condition number,Mathematical optimization,Meshfree methods,Mathematical analysis,Matrix (mathematics),Method of fundamental solutions,Singular boundary method,Trefftz method,Mathematics,Regularized meshless method
Journal
Volume
Issue
ISSN
230
17
Journal of Computational Physics
Citations 
PageRank 
References 
2
0.61
1
Authors
2
Name
Order
Citations
PageRank
Takemi Shigeta1111.97
D. L. Young2164.59