Communications in Mathematical Sciences
Volume 16 (2018)
The direct and inverse elastic scattering problems for two scatterers in contact
Pages: 857 – 877
This paper is concerned with the elastic scattering problem of a combined scatterer, which consists of a penetrable obstacle and a hard crack touching with each other. By using the boundary integral equation method, the direct scattering problem is formulated as a boundary integral system, then we obtain the existence and uniqueness of a weak solution according to Fredholm theory. The inverse scattering problem we are dealing with is the shape reconstruction of the combined scatterer from the knowledge of far field patterns due to the incident plane compressional and shear waves. Based on an analysis of a particular transmission eigenvalue problem, the linear sampling method is established to reconstruct the combined scatterer. The numerical experiments show the feasibility and validity of the proposed method.
elastic scattering, combined scatterer, linear sampling method
2010 Mathematics Subject Classification
This research is supported by National Natural Science Foundation of People’s Republic of China, No. 11571132, and the Fundamental Research Funds for South-Central University for Nationalities, No. CZT18010.
Received 24 September 2017
Received revised 26 February 2018
Accepted 26 February 2018
Published 30 August 2018