| Abstract: | This paper proposes a semi-analytical and local meshless collocation method, the localized method of fundamental solutions (LMFS), to address three-dimensional (3D) acoustic inverse problems in complex domains. The proposed approach is a recently developed numerical scheme with potential of being mathematically simple, numerically accurate, and requiring less computational time and storage. In the LMFS, an overdetermined sparse linear system is constructed by using the known data at the nodes on the accessible boundary and by making the remaining nodes satisfy the governing equation. In the numerical procedure, the pseudoinverse of a matrix is solved via the truncated singular value decomposition, and thus the regularization techniques are not needed in solving the resulting linear system with well-conditioned matrix. Numerical experiments, involving the complicated geometry and the high noise level, confirm the effectiveness and performance of the LMFS for solving 3D acoustic inverse problems. |
