Design sensitivity analysis for nonlinear magnetostatic problems using finite element method

The authors present a sensitivity analysis for the shape design problems of a two-dimensional nonlinear magnetostatic system. In order to derive the design sensitivity, the algebraic equation resulting from the finite element method is exploited and the adjoint variable method is used. This algorithm is applied to the shape design problem of a quadrupole magnet which operates in the magnetic saturation region. Numerical results validate the algorithm. The optimal pole shape with a tolerable deviation is obtained after several iterations