The adaptive algorithm for the selection of sources of the method of fundamental solutions

Abstract Despite all the efforts and success for finding the optimal location of the sources outside the domain for the method of fundamental solutions (MFS), this issue continues to attract the attention from researchers for seeking more efficient and reliable algorithms. In this paper, we propose to extend the adaptive greedy technique which applies the primal-dual formulation for the selection of source nodes in the MFS for Laplace equation with nonharmonic boundary conditions. Such approach is a data-dependent algorithm which adaptively selects the suitable source nodes based on the specific adaptive procedure. Both 2D and 3D examples are provided. Moreover, the proposed algorithm is easy to implement with high accuracy.

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