Time domain scattering and inverse scattering problems in a locally perturbed half-plane. (English) Zbl 1431.65151
Summary: This paper is concerned with efficient numerical methods for solving the time-dependent scattering and inverse scattering problems of acoustic waves in a locally perturbed half-plane. By symmetric continuation, the scattering problem is reformulated as an equivalent symmetric problem defined in the whole plane. The retarded potential boundary integral equation method is modified to solve the forward problem. Then we consider the inverse scattering problem of determinating the local perturbation from the measured scattered data. The time domain linear sampling method is employed to deal with the inverse problem. The computation schemes proposed in this paper are relatively simple and easy to implement. Several numerical examples are presented to show the effectiveness of the proposed methods.
MSC:
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 65L09 | Numerical solution of inverse problems involving ordinary differential equations |
| 35R30 | Inverse problems for PDEs |
| 65M38 | Boundary element methods for initial value and initial-boundary value problems involving PDEs |
| 76Q05 | Hydro- and aero-acoustics |
| 65D25 | Numerical differentiation |
| 62D05 | Sampling theory, sample surveys |
| 35B20 | Perturbations in context of PDEs |
Keywords:
time domain scattering; inverse scattering; locally perturbed half-plane; boundary integral equation; linear sampling methodReferences:
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