On the Equivalence of Finite Difference and Finite Element Formulations in Magnetic Field Analysis

摘要

Numerical 3D formulations using scalar Ω 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.