A new investigation into regularization techniques for the method of fundamental solutions

This study examines different regularization approaches to investigate the solution stability of the method of fundamental solutions (MFS). We compare three regularization methods in conjunction with two different regularization parameters to find the optimal stable MFS scheme. Meanwhile, we have investigated the relationship among the condition number, the effective condition number, and the MFS solution accuracy. Numerical results show that the damped singular value decomposition under the parameter choice of the generalized cross-validation performs the best in terms of the MFS stability analysis. We also find that the condition number is a superior criterion to the effective condition number.