Exclusion of false modes from solution of three-dimensional spectral problems of electrodynamics by the finite element method

Two mathematical models for the solution of three-dimensional (3D) vector eigenvalue problems are described. Both models are based on the variational finite element method and guarantee that no false modes are present in the eigenfrequency spectrum. The parameters of the chains of coupled one-gap and two-gap resonators of a complex configuration are calculated to estimate the accuracy and universality of the models.