The factorization method to reconstruct a combination of penetrable obstacle and arc

ABSTRACT

This paper considers the scattering of time-harmonic acoustic plane waves by a mixed scatterer. Such a scatterer is given as the union of a penetrable homogeneous medium with compact support and an open arc. Firstly, the well-posedness of the direct problem is established by the boundary integral method. Then, we study the factorization method for recovering the shape of the mixed scatterer. Furthermore, some numerical experiments are presented to demonstrate the feasibility and effectiveness of our approach.

Keywords:

• Factorization method
• inverse scattering problem
• mixed obstacle

2010 Mathematics Subject Classifications:

• 35Q65
• 35C15
• 78A45

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is supported by NSFC [Grant Numbers 11571132, 11171127].