Level set method for the inverse elliptic problem in nonlinear electromagnetism. (English) Zbl 1207.78045

The paper deals with the inverse problem for a quasilinear PDE in a 2-dimensional domain, where a spatial inhomogeneity is to be identified from certain boundary values of the solution of the PDE. A typical example related to this problem is the identification of a crack inside a magnetic material (hard magnetic steel), where measurements of the magnetic induction are given on the outer boundary of the workpiece. The reconstruction is realized by the minimization of a cost function using the steepest descent method, where the gradient directions are evaluated using the sensitivity equation and the adjoint variable method. The efficiency of the proposed method is illustrated by numerical simulations in the cases of a single as well as multiple inhomogeneities.


78M50 Optimization problems in optics and electromagnetic theory
35R30 Inverse problems for PDEs
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
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