Communications in Mathematical Sciences

Volume 17 (2019)

Number 7

The factorization method for partially penetrable obstacle in elastic scattering

Pages: 1757 – 1777

DOI: https://dx.doi.org/10.4310/CMS.2019.v17.n7.a1

Authors

Jun Guo (School of Mathematics and Statistics, South-Central University For Nationalities, Wuhan, China)

En-Guo Gu (School of Mathematics and Statistics, South-Central University For Nationalities, Wuhan, China)

Jian He (Department of Basic Courses, Air Force Early Warning Academy, Wuhan, China)

Lei Xiao (School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, China)

Abstract

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.

Keywords

partially penetrable obstacle, factorization method, inverse elastic scattering

2010 Mathematics Subject Classification

35Q30, 35R30

Full Text (PDF format)

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