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Volume 7, Issue 3
Piecewise Constant Level Set Algorithm for an Inverse Elliptic Problem in Nonlinear Electromagnetism

Xiangyin Kong, Zhengfang Zhang & Zhengda Huang

DOI: 10.4208/aamm.2012.m42

Adv. Appl. Math. Mech., 7 (2015), pp. 387-406.

Published online: 2018-05

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  • 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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@Article{AAMM-7-387, author = {Kong , XiangyinZhang , Zhengfang and Huang , Zhengda}, title = {Piecewise Constant Level Set Algorithm for an Inverse Elliptic Problem in Nonlinear Electromagnetism}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {3}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2012.m42}, url = {http://global-sci.org/intro/article_detail/aamm/12054.html} }
TY - JOUR T1 - Piecewise Constant Level Set Algorithm for an Inverse Elliptic Problem in Nonlinear Electromagnetism AU - Kong , Xiangyin AU - Zhang , Zhengfang AU - Huang , Zhengda JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 387 EP - 406 PY - 2018 DA - 2018/05 SN - 7 DO - http://doi.org/10.4208/aamm.2012.m42 UR - https://global-sci.org/intro/article_detail/aamm/12054.html KW - AB -

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.

Kong , XiangyinZhang , Zhengfang and Huang , Zhengda. (2018). Piecewise Constant Level Set Algorithm for an Inverse Elliptic Problem in Nonlinear Electromagnetism. Advances in Applied Mathematics and Mechanics. 7 (3). 387-406. doi:10.4208/aamm.2012.m42
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