On the Ill-Conditioning of the MFS For Irregular Boundary Data With Sufficient Regularity
Document Type
Article
Publication Date
4-1-2014
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
In this note, we revisit the issue of ill-conditioning of the method of fundamental solutions (MFS) which was reported by Chen et al. (Eng Anal Bound Elem 30:2006;405-10). Singular value decomposition (SVD) was original proposed by Ramachandran (Commun Numer Methods Eng 18:2002;789-801) to overcome the ill-conditioning of the MFS. The proposed SVD approach given by Ramachandran was somehow contradicted by the results obtained by Chen et al. which stated that Gaussian elimination is a better solver than SVD for non-noisy boundary conditions. For illustration, we provide counter examples to show that the truncated SVD is essential for irregular boundary data and non-smooth domains. © 2014 Elsevier Ltd.
Publication Title
Engineering Analysis with Boundary Elements
Volume
41
First Page
98
Last Page
102
Recommended Citation
Feng, G.,
Li, M.,
Chen, C.
(2014). On the Ill-Conditioning of the MFS For Irregular Boundary Data With Sufficient Regularity. Engineering Analysis with Boundary Elements, 41, 98-102.
Available at: https://aquila.usm.edu/fac_pubs/19941