Weighted Radial Basis Collocation Method for the Nonlinear Inverse Helmholtz Problems

Minghao Hu, Lihua Wang (), Fan Yang and Yueting Zhou
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Minghao Hu: School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
Lihua Wang: School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
Fan Yang: School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
Yueting Zhou: School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China

Mathematics, 2023, vol. 11, issue 3, 1-29

Abstract: In this paper, a meshfree weighted radial basis collocation method associated with the Newton’s iteration method is introduced to solve the nonlinear inverse Helmholtz problems for identifying the parameter. All the measurement data can be included in the least-squares solution, which can avoid the iteration calculations for comparing the solutions with part of the measurement data in the Galerkin-based methods. Appropriate weights are imposed on the boundary conditions and measurement conditions to balance the errors, which leads to the high accuracy and optimal convergence for solving the inverse problems. Moreover, it is quite easy to extend the solution process of the one-dimensional inverse problem to high-dimensional inverse problem. Nonlinear numerical examples include one-, two- and three-dimensional inverse Helmholtz problems of constant and varying parameter identification in regular and irregular domains and show the high accuracy and exponential convergence of the presented method.

Keywords: weighted radial basis collocation method; Newton’s iteration method; nonlinear; inverse Helmholtz problems; parameter identification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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