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

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.