Two Dimensional Electromagnetic Waves Simulation Based On Regular Grid Immersed Finite Element Method

In the motion simulation of charged particles, the PIC algorithm is widely used because of its simple structure and intuitive results. The simulation field must be discretized with regular grids because the information interaction between the particle simulation and electromagnetic solving is very frequent. Although finite difference method can meet the requirements, and it can solve electromagnetic scattering and radiation problem in composite material, finite difference method will in poor solution accuracy when complex structured interface problem is concern. Although finite element method can solve complex structured interface problem, it cannot satisfy the requests of regular grid when the particle simulation is concerned. In the previous PIC algorithm, the electromagnetic field model was solved by the immersed finite element method, but the immersed finite element method can only solve the space electrostatic field, which don’t change through the time, and cannot solve the coupling effect between the space electric field and the magnetic field. In this paper, a time-domain finite immersed element method is developed, which makes it possible to study the motion of charged particles in electromagnetic environment.First, this paper established the two-dimensional electrostatic field model with composite material, in the solution we use regularized grids to mesh the field, the base function selecting bilinear function. In order to improve the algorithm accuracy at boundary the base function in interface grids are fragmented base function. In which we focused on the boundary condition in the interface of two media. The approximate mesh method is compared with the immersed method, and the result shows that the solution accuracy of the immersed finite element method is better.Then, based on the two wave equations of TM and TE, the new boundary condition of the wave equation in the finite element is derived, and the boundary conditions of the object with no surface charge and the surface current are discussed. Based on the traditional immersed finite element method, constructing of the stiffness matrix and time dispersed method are studied. "Newmark-β" method is used in the simulation. And the complete electromagnetic distribution is solved by the results of TE and TM wave solution. Finally, Dirichlet boundary condition is used to constructed line source of TM wave. TM wave scattering of cylindrical objects is calculated, the results is that with lossy medium scattering object, TM wave near the surface will be weakened, while the electric field will be strengthened. By comparing with the traditional finite element method and immersed finite element method, the correctness of the algorithm is proved.At last, the simulation of charged particles is introduced into the algorithm, and the electromagnetic field is interpolated to the position of the particle, and the motion equation of the charged particle is solved. It was found that the charged particles in the time domain electromagnetic space will produce significant drift, that is to say, when the space electromagnetic fluctuation is large or particle mass is small, the electromagnetic fluctuations cannot be simply ignored.