Application Of Time Domain Discontinuous Galerkin Method In Dispersion Materials

With the development of science and technology,they often face complex electromagnetic environment and multi-scale equipment and other issues,so people have higher and higher requirements for high-performance electromagnetic simulation technology.In the numerical calculation method,the time domain method includes information at each moment in time.Based on this information,the wide-band frequency domain information can be obtained through the Fourier transform.Therefore,the transient and wide-band characteristics in the complex electromagnetic environment can be obtained.Good solution.In the process of meshing,non-structural meshes can more accurately fit complex geometric models,and thus can well solve the fine structure meshing in multi-scale equipment.To solve the complex electromagnetic environment and multi-scale equipment problems must meet the above two requirements,the time domain discontinuous Galerkin method(DGTD)just can solve this problem.This article will use the DGTD algorithm to solve the electromagnetic scattering characteristics of nano-gold ball as the goal,mainly to study the basic theoretical derivation of DGTD algorithm in vacuum and its simple application,so as to further study the application of DGTD algorithm in nano-optics.The main job overview is as follows:1.Starting from Maxwell's equations in vacuum,a tetrahedral mesh is used to divide the meshes.The discontinuous Galerkin method is used to obtain the semi-discrete form of Maxwell's equations.The time is discretized using the display time format(such as the leapfrog time format).Get the fully discretized form of Maxwell's equation in vacuum.2.Using the numerical flux method,the specific expressions of perfect electric boundary conditions(PEC)and first-order absorption boundary conditions(ABC)in the DGDT method are derived.The validity of the boundary conditions was verified by the simulation of the lowest sub-mode field in the resonant cavity and the simulation of metal ball scattering.3.The Drude dispersion model is used to fit the dielectric properties of nano-gold spheres.Starting from the Maxwell equations in the dispersive medium,the fully discretized form of the Maxwell equations in the dispersive medium can be spatially discretized by the discontinuous Galerkin method.The display time format is time-discrete,and the correctness of the dispersion model is verified by the simulation of the nano-gold resonator and the plasma sheath.4.In order to ensure the versatility of the code,a generalized dispersion model was introduced,and then the dielectric properties of the nano-gold spheres were fitted by selecting specific coefficients.The general dispersion model was verified by the simulation of scattering of nano-gold resonators and nano-gold spheres.