Regularized Newton iteration method for a penetrable cavity with internal measurements in inverse scattering problem |
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Authors: | Lihan Liu Jingqiu Cai Yongzhi Steve Xu |
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Institution: | 1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, China;2. Department of Mathematics, University of Louisville, Louisville, Kentucky, USA |
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Abstract: | In this paper, we consider the inverse scattering problem of determining the shape of a cavity with a penetrable inhomogeneous medium of compact support from one source and a knowledge of measurements placed on a curve inside the cavity. First, the boundary value problem of the partial differential equations can be transformed into an equivalent system of nonlinear and ill-posed integral equations for the unknown boundary. Then, we apply the regularized Newton iterative method to reconstruct the boundary and prove the injectivity for the linearized system. Finally, we present some numerical examples to show the feasibility of our method. |
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Keywords: | cavity exterior transmission eigenvalue inverse scattering problem regularized Newton iteration method |
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