Time domain scattering and inverse scattering problems in a locally perturbed half-plane

Abstract

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.

Keywords:

• Time domain scattering
• inverse scattering
• locally perturbed half-plane
• boundary integral equation
• linear sampling method

AMS Subject Classifications:

• 65L09
• 35R30

Acknowledgements

We would like to thank Prof. Peter Monk for his suggestions on this paper and we would also like to thank the anonymous referees for their valuable and insightful comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of Bo Chen and Fuming Ma was supported by the NSFC [grant number 11371172]. The work of Yukun Guo was supported by the NSFC [grant number 41474102].