文章基本信息

标题：Corrosion shape reconstruction of the mixed boundary in electrostatic imaging
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作者：Yuqing Hu ; Bingxian Wang ; Tongxing Li 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-19
DOI：10.1186/s13662-020-02864-x
出版社：Hindawi Publishing Corporation
摘要：We consider the corrosion detection problem in terms of the Laplace equation and study a simply connected bounded domain with Wentzell-type GIBC boundary condition. We derive the systems of integral equations and establish the equivalence to the inverse shape problem in a Sobolev space setting. For the direct problem, we use potential theory to simulate the Neumann data from Dirichlet data on Dirichlet boundary. Then we propose a Newton iterative approach based on the boundary integral equations derived from Green’s representation theorem. After describing the linearization and the iteration scheme for the inverse shape, we compute the Fréchet derivatives with respect to the unknowns. We conclude by presenting several numerical examples for shape reconstructions to show the validity of the proposed method.
关键词：Generalized impedance boundary condition (GIBC);Nonlinear integral equation;Iterative solution;Numerics;