Piecewise Constant Level Set Algorithm for an Inverse Elliptic Problem in Nonlinear Electromagnetism
Year: 2015
Author: Xiangyin Kong, Zhengfang Zhang, Zhengda Huang
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 3 : pp. 387–406
Abstract
An inverse problem of identifying inhomogeneity or crack in the workpiece made of nonlinear magnetic material is investigated. To recover the shape from the local measurements, a piecewise constant level set algorithm is proposed. By means of the Lagrangian multiplier method, we derive the first variation w.r.t the piecewise constant level set function and obtain the descent direction by the adjoint variable method. Numerical results show the robustness and effectiveness of our algorithm applied to reconstruct some complex shapes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2012.m42
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 3 : pp. 387–406
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20