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Regularized Newton iteration method for a penetrable cavity with internal measurements in inverse scattering problem
Author(s) -
Liu Lihan,
Cai Jingqiu,
Steve Xu Yongzhi
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6074
Subject(s) - mathematics , inverse scattering problem , mathematical analysis , inverse problem , boundary value problem , partial differential equation , iterative method , newton's method , integral equation , boundary (topology) , nonlinear system , mathematical optimization , physics , quantum mechanics
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.