Efficient methodology for solving an inverse magnetostatic problem by utilizing material sensitivity

This paper presents an original approach for determining the unknown remanent magnetization of a ferromagnetic thin shell by utilizing material sensitivity information. To achieve this, first, the forward problem is formulated in term of the equivalent magnetic charge method for minimizing system unknowns. Then, a material sensitivity formula, which gives the first-order gradient information of an objective function with respect to the magnetic charge, is analytically derived by exploiting the governing integral system equation, augmented objective function, and adjoint variable method. The formula facilitates applying the deterministic approach to searching for an optimal charge distribution and saving computing time for solving an inverse problem in three dimensions as well. The proposed method has been successfully applied to a scale model ship and the results have been validated on a mock-up with real measurements.