The Study Of Key Technique In Discontinuous Galerkin Time Domain

Discontinuous Garlekin Time Domain is a class of Finite Element Method,which combines the advantages of Finite Element Method(FEM)and Finite Volume Method(FVM).It has the merit of unstructured meshes,using high-order function to improve accuracy.This method can change value of the adjacent by using numerical flux to realize domain decomposition method in cel-level,avoiding solving a large sparse matrix,and improving the efficiency of computation.As a new algorithm,this algorithm will play an important role in electromagnetic applications including electromagnetic scattering and complex environment,so it is necessary to study some key problems in electromagnetic analysis in detail.In this paper,the first-order Maxwel's curl equations are chosen as the governing equation of DGTD method,with using tetrahedron which is beneficial to flexible modeling.And this method still adapts hierarchal vector basis functions to improve accuracy.In order to solve multi-scale problem,hybrid explicit-implicit DGTD is used to enhance the efficiency.Additionally,this paper introduces plane wave,making UPML(Uniaxial Perfectly Matched Layer)boundary condition.For the source of antennas,the paper imports rectangular waveguide port,coaxial port and lumped port.For loading problem,the paper realizes the loading of resistor,capacitor and inductor.Specific work is summarized as follows:(1)Hybrid explicit-implicit DGTD is mainly use in solving multi-scale problem,and the computational domain can be divided by different mesh sizes.For multi-scale problems,the model may contain small structures,which may have tens or hundreds of wavelength differences,compared to the operating frequency.In this case,traditional explicit solutions,such as the leapfrog algorithm,are used with low efficiency,due to the existence of CourantFriedrichs-Lewy stability conditions,the maximum time step is related to the minimum split size of the model.The smaler the minimum mesh size,the smaler the time step,which increases the computation time.With hybrid explicit-implicit DGTD,implicit DGTD can be used in areas where precise segmentation is required,and explicit DGTD is used in coarsely divided regions.The time step of implicit method is no longer affected by the minimum mesh size,which is unconditionally stable.Therefore,the dense-section partition and the coarse-section partition can use the same time step,thereby reducing the computation time.(2)For the DGTD method to solve the scattering problem,the total field/scattering field boundary condition(TF/SF)is used to introduce the incident wave,and the uniaxial perfectly matched layer(UPML)is used as the truncation boundary condition.And the outermost layers of PML is added a layer of one order absorption boundary conditions to better absorb incident waves.Using the near-far field extrapolation method,the far-field value can be obtained and used to attain the target scattering characteristics.(3)For the DGTD method to calculate the radiation problem,this paper introduces three ways of forcing source.For the rectangular waveport and the coaxial waveport,the total field/scatter field boundary condition is used for introducing.The boundary conditions are used to implement the lumped port.These excitations can be used as feeds to the antennas to solve the antenna radiation problem.(4)For the problem of DGTD solving lumped components,this paper introduces the addition of resistance,capacitance and inductance components by introducing impedance boundary conditions.The radiation pattern of the loop antenna loaded with the lumped elements is calculated.