Mathematical justification for RBF-MFS
In this note, the radial basis function-method of fundamental solution (RBF-MFS) which couples \textit{E. J. Kansa}'s technique [Comput. Math. Appl. 19, No.~8/9, 147-161 (1990; Zbl 0850.76048)] with the method of fundamental solution are revisited. The idea of RBF-MFS was originally proposed by \textit{M. A. Goldberg} [the numerical evaluation of particular solutions in the BEM -- a review. Boundary Elem. Commun., 99-106 (1995)] and used many engineers later. Here it is shown that the RBF-MFS is theoretically solvable for Hardy's multiquadratics and the cubic radial basis function for the Poisson operator. Numerical results indicate that the RBF-MFS is comparable to Kansa's method.
scientific article; zbMATH DE number 1762684
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