On the Determination of Locating the Source Points of the MFS Using Effective Condition Number
Mathematics and Natural Sciences
The method of fundamental solutions (MFS) is a highly accurate numerical method for solving homogeneous solutions subject to a properly selection of the sources location. In this work, we choose the effective condition number as a tool for the determination of a good source location of the MFS that leads to highly accurate results with low computational cost. Three approaches for the location of the fictitious source points are considered. An efficient algorithm for the evaluation of the effective condition number is proposed. We also compare the proposed method with the well-known LOOCV (leave-one-out cross validation) and show the advantages and shortcomings of each approach. Five numerical examples with different geometric shapes of the domain for both harmonic and non-harmonic boundary conditions in 2D and 3D are presented.
Journal of Computational and Applied Mathematics
(2023). On the Determination of Locating the Source Points of the MFS Using Effective Condition Number. Journal of Computational and Applied Mathematics, 423.
Available at: https://aquila.usm.edu/fac_pubs/21284