Plane Wave Discontinuous Galerkin methods for scattering by periodic structures

Abstract: This thesis explores the application of Plane Wave Discontinuous Galerkin (PWDG) methods for the numerical simulation of electromagnetic scattering by periodic structures. Periodic structures play a pivotal role in various engineering and scientific applications, including antenna design, metamaterial characterization, and photonic crystal analysis. Understanding and accurately predicting the scattering behavior of electromagnetic waves from such structures is crucial in optimizing their performance and advancing technological advancements. The thesis commences with an overview of the theoretical foundations of electromagnetic scattering by periodic structures. This theoretical dissertation serves as the basis for formulating the PWDG method within the context of wave equation. The DtN operator is presented and it is used to derive a suitable boundary condition. The numerical implementation of PWDG methods is discussed in detail, emphasizing key aspects such as basis function selection and boundary conditions. The algorithm's efficiency is assessed through numerical experiments. We then present the DtN-PWDG method, which is discussed in detail and is used to derive numerical solutions of the scattering problem. A comparison with the finite element method (FEM) is presented. In conclusion, this thesis demonstrates that PWDG methods are a powerful tool for simulating electromagnetic scattering by periodic structures.