Hybrid Method for Inverse Elastic Obstacle Scattering Problems

Yuhan Yin () and Juan Liu
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Yuhan Yin: Department of Mathematics, Jinan University, Guangzhou 510632, China
Juan Liu: Department of Mathematics, Jinan University, Guangzhou 510632, China

Mathematics, 2023, vol. 11, issue 8, 1-21

Abstract: The problem of determining the shape of an object from knowledge of the far-field of a single incident wave in two-dimensional elasticity was considered. We applied an iterative hybrid method to tackle this problem. An advantage of this method is that it does not need a forward solver, and therefore, the exact boundary condition is not essential. By deriving the Fréchet derivatives of two boundary operators, we established reconstruction algorithms for objects with Dirichlet, Neumann, and Robin boundary conditions; by introducing a general boundary condition, we also established the reconstruction algorithm for objects with unknown physical properties. Numerical experiments showed the effectiveness of the proposed method.

Keywords: inverse scattering; elastic wave; far-field; obstacle reconstruction; iterative method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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