Piecewise Constant Level Set Algorithm for an Inverse Elliptic Problem in Nonlinear Electromagnetism (Advances in Applied Mathematics and Mechanics, 2018)
An inverse problem of identifying inhomogeneity or crack in the workpiecemade of nonlinear magnetic material is investigated. To recover the shape from thelocal measurements, a piecewise constant level set algorithm is proposed. By meansof the Lagrangian multiplier method, we derive the first variation w.r.t the piecewiseconstant level set function and obtain the descent direction by the adjoint variablemethod. Numerical results show the robustness and effectiveness of our algorithmapplied to reconstruct some complex shapes.