A hybrid finite element method for electromagnetics with applications in time-domain

Doctoral thesis, 2007

In this thesis, a new hybrid method that combines the Finite Element Method (FEM) with the Finite-Difference in Time-Domain (FDTD) method is presented. Tetrahedrons in the unstructured FEM region are connected directly to the hexahedrons in the structured FDTD region. The discontinuity in the tangential electric field inherent to this type of discretization is treated rigorously by means of Nitsche's method. It is possible to prove that the hybrid is stable for time steps that satisfy the Courant criterion for the FDTD region. The hybridization combines the efficiency of the FDTD scheme with the flexibility of the FEM that efficiently models curved boundaries and fine details to high accuracy. This allows the hybrid to treat a wide range of problems and here it is applied to resonant cavities, scattering and antenna problems. For scattering analysis of periodic structures at oblique incidence, a new technique is proposed that constructs the broad-band incident wave as a spectrum of plane waves, such that simple periodic boundary conditions may be used. Furthermore, we consider shape and material optimization by means of continuum design sensitivity analysis and the adjoint problem.