Simultaneous reconstruction of the shape and surface impedance from Cauchy data for the Helmholtz equation

Abstract

In this paper, we are concerned with the coefficients identification for the Helmholtz equation. This problem consists of determining the shape and surface impedance from boundary Cauchy data. We propose two reconstruction algorithms to simultaneously recover the shape and the surface impedance of the obstacle within a body. This problem is ill-posed, thus we apply regularization techniques in order to improve the corresponding approximation. The numerical results show that the proposed algorithms are stable and effective.

Keywords:

• Helmholtz equation
• trust-region-reflective optimization algorithm
• Levenberg–Marquardt algorithm
• ill-posed problem

AMS Mathematics Subject Classification 2010:

• 65N20
• 65N21

Disclosure statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Funding

The research of J.C. Liu was supported by the Fundamental Research Funds for the Central Universities (No.2014QNA57) and the NSF of China (No. 11326236, No. 11601512, No. 11501562).