Finite‐element solution of three‐dimensional resonator problems. Novel rectangular parallelepiped elements

New rectangular parallelepiped elements are proposed for analyses by finite elements for problems of three‐dimensional resonators. Earlier methods of finite‐element analysis confirmed the generation of nonphysical spurious solutions which are mixed with physical solutions. New first‐order and second‐order rectangular parallelepiped elements are proposed and the formulations of these finite elements are derived. One of the characteristics of these new elements is that tangential components are used for the electromagnetic fields on the surface of the elements as an unknown parameter. As concrete examples, they are applied to a cubic resonator and a rectangular resonator which contained a dielectric material. It was confirmed that except for a few zero eigenvalues, all nonzero eigenvalues corresponded to resonant modes. Specifically, if new rectangular parallelepiped elements are used, it is shown that no generation of spurious solutions occurs with nonzero eigenvalues.