On the ill-conditioning of the MFS for irregular boundary data with sufficient regularity

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.