Expansion of periodic boundary condition for 3-D FEM analysis using edge elements

The application of periodic boundary conditions in the analysis of three-dimensional magnetic fields by finite element methods (FEMs) leads to a substantial reduction of computation labor and storage. The expansion of the condition for magnetostatic curl-curl formulation with the magnetic vector potential employing edge tetrahedral elements is discussed. Differences between the definitions of the condition for nodal and edge elements are examined. The vectorial nature of edge elements is emphasized and associated difficulties in the formulation and application of the condition are carefully analyzed and overcome. Details for computer implementation are given and a simple test problem to verify the validity of the software is proposed. Advantages gained when the condition is used for TEAM Workshop problem 13 as an example are shown