Source point selection in the MFS using orthogonal matching pursuit: Two-dimensional elastic wave scattering by a rectangular cavity

In this paper, we apply orthogonal matching pursuit (OMP) to the source point selection in the method of fundamental solutions (MFS) and discuss its effectiveness. The proposed method initially places an excess number of source points relative to the collocation points within the complementary domain of the analysis region and then selects the source points that efficiently reduce the residual of the system of equations. We apply the proposed method to two-dimensional elastic wave scattering by a rectangular cavity, a well-known challenging problem in MFS analysis. Numerical examples demonstrate the effectiveness of the proposed method by comparing its performance with the conventional MFS using truncated singular value decomposition (TSVD). The proposed method provides solutions that more accurately satisfy the traction-free boundary conditions compared to the conventional method, indicating its potential advantages.