Equivalent source methods for 3-D force calculation with nodal and mixed FEM in magnetostatic problems

In this paper, the application of equivalent source methods for the numerical computation of total and local forces in three-dimensional magnetostatics is proposed. A nodal two-scalar potential formulation and a mixed face-edge formulation are used to solve the field problem and to derive force values, which are then compared to analytical results. The numerical accuracy of the proposed methods, in connection both to the used formulation and to the level of refinement of the mesh, is analyzed and discussed. It is shown that results coming from the mixed solution are more accurate than those obtained with the nodal one.