Discontinuous Galerkin Time‐Domain Method in Electromagnetics: From Nanostructure Simulations to Multiphysics Implementations

Abstract

In the last few decades, the discontinuous Galerkin time-domain (DGTD) method has become widely popular in various fields of engineering due the fact that it benefits from computational advantages that come with finite volume and finite element formulations. Similarly, in the field of computational electromagnetics, the superiority of the DGTD method has been quickly recognized after first few works on its formulation and 1 implementation to solve Maxwell equations. With further developments in more recent years, the DGTD method has become one of the preeminent solutions to tackle a wide variety of challenging large scale electromagnetic problems including those that require multiphysics modeling.This chapter starts with a brief introduction to the DGTD method. This introduction provides the fundamentals of numerical flux, discretization techniques that rely on vector and nodal basis functions, and incorporation of absorbing boundary conditions. This is followed by descriptions of a time-domain boundary integral(TDBI) scheme, which replaces absorbing boundary conditions within the DGTD method, and a multi-step time integration technique, which uses different time step sizes for the DGTD and TDBI parts. Numerical results show that both techniques significantly improve the efficiency, accuracy, and stability of the traditional DGTD method. Then, the chapter continues with the applications of the DGTD method to several real-life practical problems. More specifically, it describes various novel techniques developed to enable the application of the DGTD method to electromagnetic analysis of nanostructures and graphene-based devices, and multiphysics simulation of optoelectronic antennas and source generators. For each application, several numerical examples are provided to demonstrate the accuracy, efficiency, and robustness of the developed techniques.