Application And Analysis Of DGTD Algorithm In Electromagnetic Problems

The traditional methods applied to electromagnetic problems, such as finite element method(FEM) and finite difference time domain(FDTD), are facing many challenges for solving large-scale electromagnetic problems. As more and more electromagnetic problems tend to be large-scale and complicated, it’s of great significance to seek out a higher efficient algorithm. In this paper, the discontinuous Galerkin time domain method(DGTD), which is combining the advantages of FEM and finite volume method(FVM), is suitable for calculating complex multi-scale electromagnetic problems. It has the advantages of unstructured grids, higher-order basis functions with high precision and inherent parallelism. In this study, the core is the application and analysis of DGTD algorithm in electromagnetic problems for one-dimensional and two-dimensional Maxwell equations in time-domain, discussing and analyzing the stability with different order of the basis functions, as well as the impact on the results accuracy by different mesh density and orders.This paper introduces the basic principles and key technologies of the traditional FEM and Finite Volume Time Domain(FVTD) methods, including the concept of Galerkin method and numerical flux. Considering the above-mentioned aspects, we propose the fundamental principle and key technologies of DGTD, including semi-discrete equation, calculation of the mass matrices and stiffness matrices, the basis function, discrete points in the unit, the concept of numerical flux, as well as the processing of the partial derivatives of time. We study the DGTD method and its key technologies of one-dimensional and two-dimensional Maxwell equations in time-domain. The paper uses the higher-order Legendre polynomial as the basis functions of every unit, and Legendre-Gauss-Lobatto discrete points as the integration points within the cell, and solves the partial derivative of time with 4-order low storage Runge-Kutta method.In the end, two waveguide problems in one dimension and two dimension for verifying the correctness of the algorithm are calculated with the method of DGTD. The first step is to achieve a one-dimensional numerical simulation with Matlab, verifying the feasibility of DGTD method and the correctness of the program. Then generate grid data of the model with the Gmsh software, calculate the electromagnetic fields of waveguide cross-section, and mapped the electromagnetic field distribution, the time curves of electromagnetic under the different orders of the basis functions and the resonance frequency. The time, the error of the calculation results and the storage of this calculation which are with the change of grid density and function’s order, are studied, getting the calculation efficiency under different conditions.