This paper proposes a semi‐analytical and local meshless collocation method,the loca-lized method of fundamental solutions(LMFS),to address three‐dimensional(3D)acoustic inverse problems in complex domains.The propo...This paper proposes a semi‐analytical and local meshless collocation method,the loca-lized 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 the potential of being mathematically simple,nu-merically accurate,and requiring less computational time and storage.In 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 a well‐conditioned matrix.Numerical experiments,involving complicated geometry and the high noise level,confirm the ef-fectiveness and performance of the LMFS for solving 3D acoustic inverse problems.展开更多
基金National Natural Science Foundation of China,Grant/Award Number:11802151Natural Science Foundation of Shandong Province of China,Grant/Award Number:ZR2019BA008+1 种基金supported by the National Natural Science Foundation of China(No.11802151)the Natural Science Foundation of Shandong Province of China(No.ZR2019BA008).
文摘This paper proposes a semi‐analytical and local meshless collocation method,the loca-lized 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 the potential of being mathematically simple,nu-merically accurate,and requiring less computational time and storage.In 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 a well‐conditioned matrix.Numerical experiments,involving complicated geometry and the high noise level,confirm the ef-fectiveness and performance of the LMFS for solving 3D acoustic inverse problems.
