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Description
This study proposes combining the method of fundamental solutions (MFS) and particle swarm optimization (PSO) to accurately and stably analyze boundary detection problems. The boundary detection problems, considered in this study, are governed by the two-dimensional Laplace equation. In the boundary detection problems, the spatial position for part of the boundary portion is unknown, so it is challenging to analyze the boundary detection problems by any numerical scheme. We utilized the MFS, one the most promising boundary-type meshless methods, for spatial discretization of the considered boundary detection problems. The numerical solutions of the MFS are extremely accurate if the optimal location of sources, which should be located out of the computational domain, can be determined. Hence, in this study, we used the PSO, one of the meta-heuristic algorithms, to simultaneously determine the optimal location of the source in the MFS and the unknown spatial location of the boundary portion. Several numerical examples will be adopted to verify the effectiveness of the proposed numerical scheme for solving the boundary detection problems. Besides, some factors in the numerical scheme will be examined and these comparisons will be provided to demonstrate the merits of the proposed numerical scheme.
