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Piecewise Constant Level Set Algorithm for an Inverse Elliptic Problem in Nonlinear Electromagnetism

Published online by Cambridge University Press:  28 May 2015

Xiangyin Kong,
Zhengfang Zhang and
Zhengda Huang
Xiangyin Kong
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
Zhengfang Zhang
Affiliation:
Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China
Zhengda Huang*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
*
*Corresponding author. Email: xiangyinkong@163.com (X. Kong), zhengfangzhang@hdu.edu.cn (Z. Zhang), zhengfangzhang@hdu.edu.cn (Z. Huang)

Abstract

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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.

Keywords

65K1035Q6074M10Nonlinear electromagnetismadjoint variable methodshape reconstructionpiecewise constant level set algorithm

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 3 , June 2015, pp. 387 - 406
Copyright
Copyright © Global-Science Press 2015 

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