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An inverse problem of identifying inhomogeneity or crack in the workpiecemade of nonlinear magnetic material is investigated. To recover the shape fromthe local measurements, a piecewise constant level set algorithm is proposed.By means of the Lagrangian multiplier method, we derive the first variationw.r.t the level set function and obtain the descent direction by the adjointvariable method. Numerical results show the robustness and effectiveness of ouralgorithm applied to reconstruct some complex shapes.

Piecewise constant level set algorithm for an inverse elliptic problem in nonlinear electromagnetism