Accurate and efficient simulation of antennas using hierarchical mixed-order tangential vector finite elements for tetrahedra

Hierarchical mixed-order tangential vector finite elements (TVFEs) for tetrahedral elements are attractive for accurate and efficient finite-element method simulation of complicated electromagnetic problems. They provide versatility in the geometric modeling of physical structures, guarantee solutions free of spurious modes, and allow local increase of resolution by selective expansion of the unknown electromagnetic field, i.e., by combination of mixed-order TVFEs of different orders within a computational domain. For a realistic antenna radiation problem, this paper demonstrates that field expansion using lowest and higher order hierarchical mixed-order TVFEs selectively is vastly superior [in terms of accuracy, memory, as well as central processing unit (CPU)-time] to field expansion using a lowest order mixed-order TVFE only.