Development and application of a novel class of hierarchical tangential vector finite elements for electromagnetics

Tangential vector finite elements (TVFEs) overcome most of the shortcomings of node-based finite elements for electromagnetic simulations. For a triangular element, this paper proposes a class of hierarchical TVPEs that differ from traditional TVFEs. The hierarchical nature of the proposed TVFEs makes them ideally suited for employing an efficient selective field expansion (the lowest order TVFE employed within part of the computational domain and a higher order TVFE employed within the remaining part of the computational domain). This is an attractive feature not shared by nonhierarchical TVFEs for which a more traditional approach (the same TVFE employed throughout the computational domain) must be applied. For determining the scattering by composite cylinders, this paper argues that the performance (in terms of accuracy, memory, and, in most cases, CPU time) of the proposed class of hierarchical TVFEs when applying selective field expansion is superior to that of the lowest order TVFE and a traditional nonhierarchical TVFE. This is the case when an artificial absorber as well as a boundary integral is used for truncating the computational domain. A guideline is given as to how lowest and higher order TVFEs shall be combined for optimal performance of the proposed class of hierarchical TVFEs.