The Discontinuous Galerkin Time Domain (DGTD) method is an extremely popular numerical algorithm due to its ability to handle general non-conformal meshes, its flexibility with respect to choice of time stepping scheme, and its amenability to parallelization which makes it perfectly suited for high-performance computing (HPC) architectures. CEARL researchers have developed state-of-the-art extensions of the DGTD method in electromagnetics by incorporating periodic boundaries for obliquely incident radiation, the generalized dispersion model (GDM) for handling materials with arbitrary dispersion, and hybrid local time stepping schemes for increase efficiency.  

PFEBI analyzes the scattering or radiation from a doubly periodic structure. This periodic structure can be an Frequency Selective Surface (FSS) or an infinite antenna array. In both cases, the structure can be composed of (1) one or more homogeneous dielectric slabs (isotropic media) or anisotropic or bi-anisotropic media, (2) one or more inhomogeneous dielectric slabs (isotropic media) or inhomogeneous anisotropic or inhomogeneous bi-anisotropic media and (3) one or more metal/surface impedance screens. For dielectric materials (isotropic materials) or anisotropic or bi-anisotropic, it can be either lossy or losses or dispersive materials. Magnetic materials (isotropic materials) can be treated as well. For metal screens, it can be perfectly electric conducting or lossy. Lossy metal screens are treated by surface impedance screens.

The rapid development of various types of lenses devices requires accurate and efficient numerical methods for evaluating their performance. However, performing 3D full-wave simulations on electrically large lenses designs remains a challenge when using commercially available software due to the huge memory requirements and long computation times. It has been demonstrated that different body-of-revolution (BOR) techniques, including the method of moments (MoM), finite-element method (FEM), and finite-difference time-domain (FDTD) method, can be utilized for analysis of 3D objects with rotational symmetry. Compared to the MoM and FEM, the BOR-FDTD algorithm does not require solving a large system of equations. Therefore, BOR-FDTD is an efficient and well suited method for analysis of 3D axisymmetric  devices, such as lenses. 

High-frequency asymptotic methods based on ray tracing are well known techniques in the computational electromagnetics community for efficiently modeling complex environments at high frequencies. Ray methods such as Uniform Theory of Diffraction (UTD) and Physical Theory of Diffraction (PTD) provide significant reductions in both memory and computation time when treating electrically large objects. In asymptotic methods, the scattering contributions such as reflection, wedge and corner diffraction are a local phenomenon that depends on the geometry of the object at the point of interest. The practical applicability of these methods is related to the solution of canonical problems that locally approximate the actual structure at specular points.