| In a typical computational electromagnetics problem, there exist three different length scales: the physical size of the fine geometrical features, the typical wavelength, and the overall physical size. Depending on the ratio of these length scales, the problems can be roughly categorized into three classes: the intermediate-scale problems, the small-scale problems and the large-scale problems. There are many problems where large-scale, small-scale and intermediate scale objects coexist, thus posing a significant computational challenge to any single computational method if it is utilized alone. In this thesis, we develop a hybrid PSTD-FDTD method which combines the Discontinuous Galerkin Pseudo-Spectral Time-Domain (DG-PSTD) method with both the Conformal Alternate Direction Implicit Finite Difference Time-Domain (ADI-CFDTD) method and the Conformal Finite Difference Time-Domain (CFDTD) method in order to solve mixed-scale broadband problems efficiently. In particular, the ADI-CFDTD method is an unconditionally stable time-domain method with second-order spatial accuracy, and allows the time step to be increased beyond the Courant-Friedrichs-Levy limit. In this hybrid technique, the ADI-CFDTD method is applied to regions with fine structures and relatively small computation volumes, while the CFDTD method is applied to electrically intermediate regions with second-order spatial accuracy. The PSTD method, on the other hand, can treat complex objects with exponential accuracy. It is accurate and efficient for regions with large, relatively homogeneous materials. The interface conditions between different regions are obtained by correctly accounting for the fluxes across the boundary through up-wind boundary conditions. Numerical verifications and applications demonstrate the advantage and the effectiveness of this hybrid PSTD-FDTD method. |
