Study Of Spectral-Element Time-Domain Method In Efficient Electromagnetic Simulation

With the development of science and technology,the study of complex electromagnetic problems is moving towards multi-scale and multi-physics applications.How to analyze these problems accurately and efficiently with numerical methods is becoming a great challenge for computational electromagnetics.The spectral-element time-domain method(SETD),a combination of the spectral method and finite-element time-domain method(FETD),has the advantage of flexible modeling and spectral accuracy.In this dissertation,based on the spectral-element time-domain method,some efficient electromagnetic simulation methods are proposed.The main research work and results are summarized as follows:In the first part of this dissertation,the basic principle of the spectral-element time-domain method is studied and the derivations of formula are given respectively based on the Maxwell equation and wave equation.Then the stability is analyzed.The parallel technique is introduced and efficient concurrent design is described.The parallel efficiency can be seen from the numerical examples.Finally,the paralleled SETD method is used to simulate the airtight communication capsule UWB channel.The simulation results are compared with those from the experiments,which can further verify the efficiency of the parallel method.In the second part of this dissertation,the unconditionally stable SETD method is introduced with the Newmark-Beta scheme.Based on that,a hybrid explicit-implicit SETD method is proposed for the multi-scale problems.The central-difference is applied for the coarse region with large cells and the Newmark-Beta scheme is for the fine region with small cells.Then a large size of time step can be selected in the whole domain instead of the one limited by the smallest cell.When solving the matrix equation formed by the implicit scheme,two approaches are employed.One uses the sparse matrix solver UMFPACK directly and the other involves an explicit and iterative process which is called iterative Newmark-Beta scheme.The efficiency of the two methods are compared from the numerical examples.At last,the explicit-implicit SETD method is used to analyze the dispersive media to verify the efficiency,which has attracted much attention recently.In the third part of this dissertation,the discontinuous Galerkin SETD method(DG-SETD)is considered,which is based on the variable E and B.Different mesh sizes are allowed for different subregions.The nonconformal interface is handled and the upwind flux is introduced,which makes the discretization more flexible.Then a modified discontinuous Galerkin FETD is proposed,which is called continuous-discontinuous Galerkin finite-element time-domain method(CDG-FETD).This method is aimed at exploiting the advantages of reduced number of unknowns for continuous Galerkin method and block-diagonal property of discontinuous Galerkin method.At last,based on the disconnuous Galerkin technique,the SETD and the CDG-FETD are hybrided to further make use of the advantages of both.The local time stepping scheme is also employed to save simulation time.In the fourth part of this dissertation,the efficient SETD method is studied for the analysis of the nonlinear microwave circuits and the synchronous field-circuit coupling is established.At first,the output response for the microwave circuits is given with the semiconductor device's equivalent physical model and equivalent circuit model.After that,the real physical model for the semiconductor device is introduced to solve the drift-diffusion equation.The electothermal characterisitic of the microwave circuit is demonstrated.Finally,the discontinuous Galerkin technique is also used in the simulation of the semiconductor's physical model.Basis functions with different orders are applied for different regions,which can greatly save the time.In conclusion,the efficient electromagnetic simulation algorithms are developed in detail.For the large scale electromagnetic problems,the effective parallel technique is proposed.For the multi-scale problem,the explicit-implicit scheme is proposed.For the problem with complex geometry,the SETD and DG-FETD are hybrided.For the simulation of nonlinear microwave circuits,the synchronous field-circuit coupling and electrothermal simution based on the semiconductor's physical model are proposed.The accuracy and the efficiency of the proposed methods in this dissertation are demonstrated in numerical results.