Some comments on the ill-conditioning of the method of fundamental solutions

• Published in: Engineering analysis with boundary elements Vol. 30; no. 5; pp. 405 - 410
• Main Authors: Chen, C.S., Cho, Hokwon A., Golberg, M.A.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.05.2006; Elsevier
• Subjects: Accuracy; Boundary conditions; Boundary element method; Boundary-integral methods; Computational techniques; Decomposition; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Gaussian elimination; Ill-conditioning; Mathematical analysis; Mathematical methods in physics; Method of fundamental solutions; Physics; Singular value decomposition; Stability; Ill-conditioning; Method of fundamental solutions; Singular value decomposition; Modelling; Truncation
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/j.enganabound.2006.01.001

In this paper, we consider the accuracy and stability of implementing the method of fundamental solutions. In contrast to the results shown in [5], we find that Gaussian elimination can be used reliably to solve the MFS equations and the use of the singular value decomposition shows no improvement over Gaussian elimination provided that the boundary condition is non-noisy. However, for noisy boundary conditions, there is evidence that the singular value decomposition with truncation is more accurate than Gaussian elimination.