Research On Electromagnetic Modeling And Local Space-Time Acceleration Technology Of Discontinue Galerkin Time Domain Method

Nowadays,the structures and functions of electromagnetic equipment are becoming increasingly sophisticated and complicated.In order to satisfy the needs of electromagnetic system design and verification,the national defense and industry sections have put forward higher requirements on the accuracy and efficiency of electromagnetic numerical simulation technologies.The computational electromagnetics community has made many useful explorations to meet the challenge.Among them,the discontinuous Galerkin time domain(DGTD)method,as a special finite element time domain(FETD)method,has the general advantages of the traditional FETD method.Moreover,due to the introduction of the numerical flux,the DGTD method allows the elementwise solution and thus is easy to be flexibly parallelized.Due to these good characteristics,the DGTD method is expected to be one of the promising time-domain methods to solve the current challenges.However,the development of the DGTD method at present is not mature enough,and its computational efficiency for complex electromagnetic problems needs to be further improved.This dissertation is to study and develop some key electromagnetic modelling technologies of the DGTD method and its local space-time acceleration schemes for the improvement of its modeling ability and computation efficiency for complex electromagnetic problems.The main research contents of the dissertation include the following parts:1.A fast time step threshold estimation method and an efficient local time stepping(LTS)scheme for Maxwell equation based DGTD(DGTD-ME)method are developed.Basing on the CFL stability condition,a rapid time step threshold estimation method based on local element matrix is developed.Through the three-dimensional electromagnetic numerical tests,the time step threshold estimated by the proposed method can reach 0.91 times of the accurate value.Compared with the method by the widely used reported method,the calculation efficiency can achieve a speedup of about 18.69 times.Subsequently,the LTS technique for the DGTD-ME method with leapfrog stepping scheme is developed by the time proximity solution approximation method with a well designed stepping sequence,which is suitable for arbitrarily multiple sub-regions.With considering the feature of the proposed LTS strategy,an automatic division process of sub-regions is realized in terms of the time step threshold of each element calculated by the proposed estimation method.Finally,the LTS scheme for the DGTD-ME method is achieved.Numerical examples show that the proposed LTS scheme can deal with the practical multi-scale electromagnetic problems whose element time step threshold ratio is up to 1151.7 times in the whole calculation domain.Compared with the calculation efficiency of the scheme with the global uniform time step,the speedup of the proposed method can reach 13.41 times.2.Fast estimation methods for penalty factor and time step threshold for wave equation based DGTD(DGTD-WE)method are developed.Starting from the semi-discrete global matrix equation of the DGTD-WE method,the properties of each matrix are analyzed,which reveals the effect of penalty factor on the stability of the DGTD-WE system.With this analysis,the stability condition of the DGTD-WE method is deduced.Subsequently,each global matrix is decomposed into the sum of a series of matrices defined on local elements based on the matrix equation of DGTD-WE method.And then the penalty factor threshold is determined by solving the local matrix spectral radius.Due to the local matrix based solution,the proposed estimation method can obtain a high computational efficiency compared with the method by solving global matrices spectral radius.The numerical example of a metal cavity shows that the estimated penalty factor threshold is about 1.09～1.34 times the accurate value.With the obtained threshold of the penalty factor,a fast estimation method for the element time step threshold of the DGTD-WE method is realized by a similar global matrix decomposition method.The numerical results show that the estimated time step threshold by proposed method is about 0.85～0.93 times the accuracy value.3.An LTS scheme based on the DGTD-WE method is developed.The linear interpolation technique is adopted,and a suitable sub-region stepping sequence is developed,thus achieving multiple sub-regions with arbitrary integer time step ratio in the LTS scheme.Some criterions for the division of sub-regions are proposed to reduce the interpolation operation of the sub-domain boundary elements and partition more elements into a subdomain with a larger time step for good computational efficiency.Finally,combining the penalty factor and time step threshold estimation method above-mentioned,a LTS scheme based on DGTD-WE method is achieved.Numerical examples show that the scheme has good stability and energy conservation characteristics.And it can achieve significant efficiency acceleration of the 6 times speedup,compared to the scheme using the global uniform time step for multi-scale practical electromagnetic problems.4.An hp-adaptive scheme based on the nodal DGTD-ME method is developed.A template matrix method for tetrahedron element subdivision and coarsen is designed.Based on the template,a fast calculation method for the numerical flux on the adjacent common surface which is non-conformal or/and with different basis order is proposed.Then,the error indicators based on the reference solution method for hp-adaption are adopted,and a fast calculation scheme is developed to realize the computation of the error indicators.It can obtain up to 10 times acceleration as compared with the direct calculation method.Finally,a reasonable hp-adaptive strategy is proposed,and an efficient hp-adaptive nodal DGTDME method is achieved.Numerical examples show that,comparing the nodal DGTD-ME method without the hp-adaptivity scheme,it can consume less computation time to obtain the simulation result with almost same accuracy.5.The impedance transmission boundary for the DGTD-WE method is developed.Starting from the basic constraints on the impedance boundary,the numerical flux of the impedance transmission boundary in the DGTD-WE method is deduced.Subsequently,with the impedance boundary condition,the graphene devices are modeled by using the vector fitting technology and auxiliary differential equation method.Numerical examples show the good ability of graphene device modeling by using impedance transmission boundary based on the DGTD-WE method.6.A DGTD method with the consideration of Maxwell’s equations divergence clearing is developed.Starting from the pure hyperbolic Maxwell’s equations system with damped terms(DPHM),the governing equations and the numerical fluxes of basic boundary conditions of the DPHM based DGTD(DGTD-DPHM)method are derived,respectively.Then,with the leapfrog stepping method,the full discrete equation of the DGTD-DPHM method is given,thus giving rise to the DGTD-DPHM method.In the numerical examples,the influence of the coupling factors for the divergence clearing effect are studied,and the good divergence clearing performance of the DGTD-DPHM method is demonstrated.