A direct three-dimensional finite element method for the solution of electromagnetic fields in cavities

A new variational finite element method that directly solves the magnetic or electric field in three-dimensional cavities is proposed. The novelty is in the way the boundary conditions are implemented and the manner in which the H- and E-field vectors are rendered nondivergent. Principal vector boundary conditions and the zero divergence condition are treated as constraints and implemented by a technique based on connection matrices. The formulation is based on a curvilinear brick-type finite element with 27 interpolation nodes.