| With the rapid growth of modern weapons and electronic devices,such as highpower vacuum electronic devices,warships,armored missiles and other systems,they are playing an important role in the microwave device design,satellite communication,radar and other fields.In fact,the surfaces of these weapons and equipments may be set up on various kinds of antennas,sensors and other small devices,and at the same time,the composition of media materials are often different,which makes the physical characteristics of the whole equipments more complex,as a result,these structures have geometric and material multi-scale characteristics.In addition,in the modern battlefield,as the number of electromagnetic radiation sources increases rapidly for different battlefield functions,the electromagnetic environment becomes increasingly complicated in the battlefield.Especially the electromagnetic pulse field formed by high-power microwaves and other strong electromagnetic pulses may be fatal to multiscale equipment.Therefore,in order to ensure that the multi-scale equipment can give full play to its combat effectiveness in the complex electromagnetic environment,it is urgent to study its electromagnetic parameters.However,the existing numerical calculation methods are often unable to meet the requirements of high performance and high precision on the 3D electromagnetic simulations for multi-scale problems in the current complex environment.Therefore,it is urgent to carry out more accurate and efficient algorithm for multi-scale problems in complex electromagnetic environment,so as to lay a reliable theoretical foundation for simulation analysis softwares.The research works of this dissertation are focused on the simulation analysis of multi-scale problems on the frequency domain and time domain in the complex electromagnetic environment.The main content and innovation works can be summarized as the following five aspects.1.Take the input/output window of microwave tube as the research object,based on the vector finite element method,an adaptive fast sweep method is proposed by combining with model reduction.This method mainly includes the following three techniques: 1)Chebyshev function approximation method is used to obtain the expansion subspace of the reduced order model,which avoids the time-consuming and complex operation of Taylor series expansion.2)The error determination conditions of inner and outer nesting are proposed so as to seek for the best reduced order space quickly and accurately.3)The convergence radius is defined,and an effective selfadaptive sweep technique is proposed to obtain the response parameters for the full frequency band.2.The discontinuous Galerkin time domain(DGTD)method is studied systematically for solving the three-dimensional time-domain Maxwell's equations.Tetrahedral elements are used for region discretization.Then a semi-discrete DGTD formulation can be acquired by combining the simple node scalar basis functions with numerical fluxes.In the case of time discretization,the fully discrete formulation of DGTD is obtained by applying an explicit time scheme.Then the field of each element can be iterated according to the cellular property of DGTD.In addition,this dissertation gives in detail the boundary treatments,various excitation source forms,imposing source approach in the DGTD and stability analysis.Through numerical examples,the accuracy of the algorithm is verified,which lays a solid theoretical foundation for the later research of explicit and implicit algorithm.3.In order to reduce the degrees of freedom(DOFs)in DGTD,by combining with the implicit time scheme,a hybridizable discontinuous Galerkin time-domain(imHDGTD)method is proposed to solve the three-dimensional time-domain Maxwell's equations based on the frequency-domain hybridizable discontinuous Galerkin(HDG)method.This method mainly includes the following five techniques: 1)After tetrahedral discretization,the same hierarchical scalar basis functions are used for the volume and surface elements so as to prepare for matrix preprocessing.2)In the case of spatial discretization,hybrid variables are introduced into the face element to replace the numerical fluxes of DGTD.According to the conservativity condition,a global linear system is finally formulated.Since the variable of global system is only related to hybrid variables,the number of DOFs can be greatly reduced.3)The unconditionally stable Crank–Nicolson(CN)time scheme is used in the time discretization of global linear system,which can effectively expand time step of the explicit time scheme for the fine grids,and then the full discretization formulation of imHDGTD has been derived.4)In this dissertation,the hybrid variables is regarded as the constants to be solved,so as to reduce the computational consumption of time iteration on hybrid variables.Once the hybrid variables is calculated from the global linear system,the field value of each element can be obtained according to the local linear system.5)In addition to the absorbing boundary condition(ABC)boundary formulation commonly used in the HDG algorithm,the Perfectly Matched Layer(PML)boundary formulation is also derived in imHDGTD and successfully applied to waveguide transmission problems.4.For the implicit time scheme,in order to reduce the complexity caused by solving the global matrix(along with the increase of grid and order numbers,there may be an ill-conditioned matrix),a kind of effective matrix solving technology is first-time proposed in the time-domain imHDGTD method.Through the hierarchical characteristics of the basis functions,the p-type multigrid preconditioner is proposed to accelerate the solution of the global linear system in the imHDGTD.At present,for the passive Maxwell's equations,almost sources are imposed at the boundary when using the HDG method.Considering that the types of excitation sources are diverse in the actual electromagnetic problems.Therefore,based on time-domain Maxwell's equations with sources,this dissertation extends the previous imHDGTD research works,and further give specific processing techniques for different current and magnetic current sources.5.In order to further improve the computational performance of the time-domain algorithm for solving complex multi-scale problems,this dissertation combines the advantages of explicit ex DGTD and implicit imHDGTD,and further proposes a novel three-dimensional explicit-implicit time-domain electromagnetic numerical method(eximHDGTD).The method mainly includes the following four techniques: 1)According to the size of the discrete grid,the whole computational region is divided into coarse mesh and fine mesh.The ex DGTD method is used in coarse grid area,and the imHDGTD method is used in fine grid area.2)In terms of time iteration,the Verlet time format is used to avoid the time step of the full explicit time scheme being limited by the stability of the fine mesh size,and it also avoids generating the system matrix with very large dimension caused by the full implicit time scheme.3)For the boundary formulation,note that the PML and ABC boundaries are the first time applied in the proposed ex-imHDGTD algorithm.4)For the ways of imposing the excitation,both the total field method and the total-fileld/scattered-field method are separately applied in the new explicit-implicit algorithm.Finally,through the complex waveguide and aircraft examples,it is verified that the proposed algorithm has the fewer DOFs.Compared with ex DGTD,imHDGTD and traditional explicit-implicit DGTD methods,the overall simulation memory and calculation time can be greatly reduced when using the ex-imHDGTD method.This provides an analytical method for solving multi-scale problems in time-domain electromagnetics. |
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