Open AccessLocalized MFS for three‐dimensional acoustic inverse problems on complicated domains
Author(s) -
Chen Zengtao,
Wang Fajie,
Cheng Suifu,
Wu Guozheng
Publication year - 2022
Publication title -
international journal of mechanical system dynamics
Language(s) - English
Resource type - Journals
eISSN - 2767-1402
pISSN - 2767-1399
DOI - 10.1002/msd2.12031
Subject(s) - overdetermined system , moore–penrose pseudoinverse , singular value decomposition , inverse problem , method of fundamental solutions , collocation (remote sensing) , mathematics , regularization (linguistics) , simple (philosophy) , numerical analysis , computer science , mathematical optimization , matrix (chemical analysis) , inverse , algorithm , singular boundary method , mathematical analysis , finite element method , boundary element method , geometry , artificial intelligence , philosophy , physics , epistemology , machine learning , thermodynamics , materials science , composite material
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 the potential of being mathematically simple, numerically 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 effectiveness and performance of the LMFS for solving 3D acoustic inverse problems.