Analogies between finite difference and finite element methods for scalar and vector potential formulations in magnetic field calculations

摘要

Numerical 3D formulations using scalar ? and vector A potentials are examined for magnetic fields, with emphasis on the finite difference (FDM) and finite element (FEM) methods using nodal and facet elements. It is shown that for hexahedral elements the FDM equations may be presented in a form similar to the FEM equations; to accomplish this the coefficients defining volume integrals in FEM need to be expressed in an approximate manner, while the nodes in FDM require supplementary association with middle points of edges, facets and volumes. The analogy between a description of magnetic field sources arising from the classical mmf distribution approach and when expressed in terms of edge values of vector potential T0 is emphasized. Comparisons are made between results obtained using FDM and FEM for both scalar and vector potential formulations. Forces in systems containing permanent magnets and torques in permanent magnet machines are calculated and compared using both approaches for scalar and vector formulations. A unified form of the stress tensor has been applied to FDM and FEM.