Research On Efficient Numerical Simulation Technique Of Complex Electromagnetic Problems

Electromagnetic technology has been widely used in many military and civilian fields,such as radar systems,electronic countermeasures,satellite positioning and miniaturized electronic devices.The electromagnetic numerical simulation technology can save the cost of electromagnetic research and shorten the design cycle,so it has become more and more important in electromagnetic research.However,there are many kinds of electromagnetic problems in practical engineering.They have very complex geometric structure and material structure,so that the electromagnetic numerical simulation technology is facing many challenges in practical application.Therefore,for complex electromagnetic problems,the study of efficient numerical algorithms to reduce the computational memory and improve the efficiency of simulation analysis is the urgent need for electromagnetic numerical simulation technology in practical engineering applications.In addition,solving the practical engineering problems with the electromagnetic numerical technology needs to rely on the simulation software platform,so it is also important to develop the self-controlled electromagnetic simulation software.Therefore,the study of efficient electromagnetic numerical algorithms,combined with computer technology to develop electromagnetic simulation software,is of great significance and value to our engineering application and development of electromagnetic technology.In this dissertation,it mainly focuses on the efficient numerical simulation technology of complex electromagnetic problems.Study the corresponding efficient electromagnetic numerical methods for different kinds of complex electromagnetic problems,and on this basis,further develop the electromagnetic simulation software.The main research contents and contributions of the work are listed as follow:1.In the first section,the efficient finite element method and its application in opendomain electromagnetic problems are studied.Firstly,the finite element theory of electromagnetic radiation and scattering analysis is studied,and the hierarchical vector basis function is used in the finite element analysis.Since the finite element matrix solution is the most time-consuming part in the whole finite element numerical solution process,and the preprocessing technology is the key to improve the efficiency of iterative matrix solving,the p-type multiplicative Schwarz preconditioner and the multifrontal block incomplete Cholesky preconditioner are further studied to improve the solving efficiency.In the aspect of truncation boundary,the perfect matching layer boundary is further studied,which has higher precision than first order absorbing boundary.In addition,in order to improve the capability of of finite element method to solve the largescale electromagnetic problems,the domain decomposition(DD)technique based on internal penalty(IP)for finite element method is studied.It further improves the computational efficiency and reduces memory consumption of finite element method.Finally,the solution of far-field post-processing parameters of the electromagnetic radiation and scattering problems are studied.This part of research work is further applied to the development of finite element solving function for the high frequency electromagnetic simulation software.2.The second section mainly studies the application of high efficiency moment method in electrically large objects.Firstly,the reasons for this section’s research are explained,which are mainly to overcome the low solution efficiency of solving complex electrically large objects by finite element method,such as the electromagnetic scattering of aircraft and ships in military radar band.In the aspect of algorithm research,the principle of electromagnetic integral equation is studied firstly,and then the principle of moment method,basis function and matrix discrete form are studied in detail.The twostep preconditioner and GMRES iterative solution techniques are studied in the matrix solution of moment method.In addition,in order to reduce the memory consumption and improve the computational efficiency of the moment method,the efficient IE-FFT method is studied.In the iterative solution part of IE-FFT,Open MP based parallel is further used to accelerate the matrix vector product and Fast Fourier Transform.This part of research work is further applied to the development of integral equation solving function of highfrequency electromagnetic simulation software.3.In the third section,the study of discontinuous Galerkin time domain method(DGTD)which is one of electromagnetic time domain algorithms is provided.Firstly,the theory of DGTD method is studied,including the DG weak form of Maxwell’s equations,numerical fluxes,space semi-discrete scheme and time discrete scheme.Then,the boundary condition of DGTD method and the excitation source in time domain are studied.In order to improve the efficiency of DGTD method,the non-conforming meshes and local time stepping method based on DGTD are studied.Then,the application of DGTD method in nanophotonics is studied.The SO-DGTD method based on Drude model and the DGTD method based on non-local dispersion model are studied and derived,which can be applied to the electromagnetic numerical simulation of nano-metal dispersive materials.This part of research work provides a theoretical basis for the research and development of time domain solver of high-frequency electromagnetic simulation software.4.The fourth section is mainly about the design of high frequency electromagnetic simulation software.This section is mainly developed a high frequency electromagnetic simulation software based on the efficient finite element method and the efficient moment method in the previous studies.At present,the software has been equipped with 3D entity modeling,material setting,mesh division,boundary and excitation setting,simulation analysis and post-processing display and other functions,which can be applied to the simulation of various kinds of complex electromagnetic radiation and scattering problems.In the future works,the software functions will be further improved,and the time domain solver will be developed.Finally,the works of this dissertation are summarized and discussed,and based on the current studies,the future research work is discussed and prospected.