The inverse scattering problem for partially penetrable obstacles

Abstract

We consider the direct and inverse problems for the scattering of a partially penetrable obstacle. Here ‘partially penetrable obstacle’ means that the waves transmit into the obstacle just from partial boundary of the obstacle with the rest of the boundary touching a known perfect and thin scatterer. The solvability of the direct scattering problem is presented using the classical boundary integral equation method. An interesting interior transmission problem is investigated for the purpose of solving the inverse obstacle scattering problem. Then the linear sampling method is proposed to reconstruct the shape and location of the obstacle from near field measurements. We note that the inversion algorithm can be implemented by avoiding the use of background Green function as a test function due to a mixed reciprocal principle.

Keywords:

• Direct and inverse scattering
• partially penetrable obstacle
• interior transmission problem
• linear sampling method

AMS Subject Classifications:

• 35Q60
• 35C15
• 78A45

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is supported by the fundamental research funds for South-Central University for Nationalities [grant number ZCY16008]. The second author is supported by National Natural Science Foundation of People’s Republic of China [grant number 11571132], [grant number 11171127].