Paper Info
Title
Stability analysis of method of fundamental solutions for mixed boundary value problems of Laplace’s equation
Abstract
Since the stability of the method of fundamental solutions (MFS) is a severe issue, the estimation on the bounds of condition number Cond is important to real application. In this paper, we propose the new approaches for deriving the asymptotes of Cond, and apply them for the Dirichlet problem of Laplace’s equation, to provide the sharp bound of Cond for disk domains. Then the new bound of Cond is derived for bounded simply connected domains with mixed types of boundary conditions. Numerical results are reported for Motz’s problem by adding singular functions. The values of Cond grow exponentially with respect to the number of fundamental solutions used. Note that there seems to exist no stability analysis for the MFS on non-disk (or non-elliptic) domains. Moreover, the expansion coefficients obtained by the MFS are oscillatingly large, to cause the other kind of instability: subtraction cancelation errors in the final harmonic solutions.
Year
DOI
Venue
2010
10.1007/s00607-010-0081-4
Computing
Keywords
DocType
Volume
Dirichlet problem,condition number Cond,disk domain,stability analysis,boundary condition,mixed type,mixed boundary value problem,numerical result,new approach,fundamental solution,final harmonic solution
Journal
88
Issue
ISSN
Citations 
1-2
1436-5057
8
PageRank 
References 
Authors
1.16
2
3
Name
Order
Citations
PageRank
Zi-Cai Li112518.79
Jin Huang2384.88
Hung-Tsai Huang3184.99