A Full-Wave Discontinuous Galerkin Time-Domain Finite Element Method for Electromagnetic Field Mode Analysis

The accurate analysis and the characterization of guided-wave structures are important steps in the design of microwave and optical systems. A numerical methodology based on a three-dimensional discontinuous Galerkin time-domain (DGTD) finite element method is used to estimate the resonant frequencies of various structures in a single run, with several polychromatic sources (dipole, plane wave, etc). The proposed approach leads to simulations that are fast and accurate, this being the result of the local discretization strategy of the full-wave time-domain Maxwell's equations on unstructured tetrahedral meshes that is easy to parallelize. The stability of the overall numerical scheme is obtained using an upwind numerical flux and an implicit second-order accurate time integration scheme. The numerical methodology is verified based on two problems with closed-form solutions. First, homogeneous and non-homogeneous waveguides are studied using the proposed methodology. The WR-284 waveguide is used, and cut-off frequencies of the first 7 modes are computed and compared with analytical solutions. Propagation characteristics of mode-selective transmission lines (MSTL) are then investigated. These MSTL simulation results are verified using measurement results of fabricated MSTL, microstrip, and RWG prototypes up to 110 GHz. Simulation results show the flexibility, the robustness, and the high accuracy of the proposed numerical strategy.