Communications in Mathematical Sciences
Volume 17 (2019)
The factorization method for partially penetrable obstacle in elastic scattering
Pages: 1757 – 1777
This paper considers the elastic scattering problem of a partially penetrable obstacle. By partially penetrable obstacle, we mean that the elastic incident waves can only transmit from partial boundary into the interior of the obstacle. Firstly, using the boundary integral equation method, the direct scattering problem is discussed in a brief way. Then the inverse scattering problem of reconstructing the shape and location of the obstacle from the knowledge of far field patterns due to the incident plane compressional and shear waves is considered. To this end, we use the well known factorization method to deal with it and establish the theory foundation of this method. Finally, some numerical examples are presented to illustrate the validity and feasibility of the proposed method.
partially penetrable obstacle, factorization method, inverse elastic scattering
2010 Mathematics Subject Classification
This paper is supported by the Fundamental Research Funds for South-Central University for Nationalities, No.CZT18010 and the National Natural Science Foundation of People’s Republic of China No.11801575.
Received 2 November 2018
Accepted 10 March 2019
Published 6 January 2020