  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 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.
