Computation of 3-D electromagnetic cavity resonances using hexahedral vector finite elements with hierarchical polynomial basis functions

Finite element method (FEM) solutions to 3-D electromagnetic field problems based on vector (edge) finite elements have proved to be free of inherent shortcomings of traditionally used scalar (node-based) finite elements. We propose a FEM technique based on using curl-conforming vector hierarchical polynomial basis functions in hexahedral finite elements and implement it in analysis of 3-D electromagnetic cavities. The field expansions automatically satisfy continuity boundary conditions for tangential fields on surfaces shared by adjacent hexahedrons in a FEM mesh. Hierarchical basis functions allow elements of different orders to be incorporated into a mesh. Polynomial degrees can be high, so electrically large finite elements can be used (large-domain FEM technique). This dramatically reduces the overall number of unknowns for a given problem.