Research On Efficient Time-domain Discontinuous Galerkin Method For Nonlinear Electromagnetic Problem

With the increasing complexity of electromagnetic environment and the gradual improvement of working frequency of engineering problems,the nonlinear problem in electromagnetic analysis has attracted extensive attention,which challenges the calculation speed,accuracy and scale of traditional electromagnetic numerical methods and commercial electromagnetic simulation software.In nonlinear problems,nonlinear microwave circuit system and nonlinear medium are one of the hot research directions.The nonlinear microwave circuit is gradually developing towards miniaturization,high integration and modularization.With the continuous improvement of the power and frequency of the incident source,the nonlinear effect of the microwave circuit becomes more and more obvious.The nonlinear medium problem is that the polarizability is not linear with the electric field,but related to the higher power of the electric field.The nonlinear convergence will affect the selection of the time step of the algorithm.In order to obtain the global stability condition,it is often necessary to increase the calculation time cost.Compared with the frequency domain method,the time domain differential method has certain advantages in analyzing nonlinear microwave circuit systems and nonlinear media problems.A single simulation can obtain all the information in a wide frequency band.Therefore,based on Maxwell’s spinor equation,this paper proposes an efficient acceleration scheme corresponding to it.The first part of this paper mainly studies the basic method of discontinuous Galerkin finite element in time domain.Due to the discontinuous Galerkin technique,tetrahedral subdivision,hexahedral subdivision and tetrahedral hybrid subdivision can be selected in the model subdivision.The tetrahedral hybrid subdivision method allows non conformal discretization and increases the flexibility of hybrid modeling.The arbitrary higher derivative(ADER)time difference scheme is introduced into the difference scheme,and the spatial partial derivative is used to replace the time partial derivative expanded by Taylor formula.The mass matrix of the semi discrete scheme formed by this method is a block diagonal matrix,which has great advantages over the traditional time-domain method in matrix inversion and efficient parallel.According to the above advantages,the numerical analysis method in this paper adopts the discontinuous Galerkin finite element method in time domain.The second part of this paper mainly studies the time-domain discontinuous Galerkin efficient method of nonlinear microwave circuit system.Because the electromagnetic field part is linear in the field circuit collaborative simulation analysis,and the concentrated element in the field circuit coupling part is nonlinear,it needs to be solved by Newton iterative method,and the global time step is limited by the stability condition of the nonlinear part,The efficiency of the algorithm is further reduced.In order to solve the above difficulties,this paper proposes an efficient solution scheme,namely multi-level local time stepping scheme,which allows us to divide the solution region into nonlinear region and linear region.The linear region can also adaptively select the corresponding time stepping according to the stability conditions of the discrete element.Finally,the antenna and microwave circuit system are analyzed.The signal source and internal resistance of the antenna are extracted by using Thevenin theorem and curve fitting technology,combined with the time-domain discontinuous Galerkin finite element method to analyze the system.The third part of this paper mainly analyzes the nonlinear dispersive media.The above multi-level local time stepping technology is used to solve the nonlinear dispersive media.Because the matrix remains highly parallel after the introduction of multi-level local time part technology,arbitrary dispersion model and high-efficiency parallel technology are introduced to further improve the computational efficiency of nonlinear media.