| Nowadays,Microstrip antennas are widely used in the fields of aviation,automotive,and satellite communication owing to their attractive features such as compact-size,low-cost,high-efficiency and relatively low requirements in their fabrication and integration.However,in recent years,all kinds of complex microstrip antennas pose new challenges to the finite element method and other full-wave analysis methods.Finite Element Method(FEM)is a numerical method for global dispersion.Due to its strong adaptability of complex structure,definite solution for complex media problems and sparse solving matrix,it is an indispensable method in the full-wave analysis of microstrip antennas.However,it often needs to introduce extra unknowns in the calculation of open-domain problems such as microstrip antenna,which increases the calculation cost.Meanwhile,when the traditional FEM deals with the wide-band response problem of microstrip antenna,it needs to re-establish the finite element equation at each frequency point and calculate repeatedly.The time cost produced by this is often unacceptable in practical engineering.And in face of large-scale array structures,the traditional FEM is difficult to solve the problem limited by computer hardware.In order to solve the above problems,this thesis first introduces the FEM analysis model and solving equation of microstrip antenna,and then elaborates the basic idea of model order reduction(MOR)and the realization process of FEM system model order reduction in detail.The second-order Arnoldi algorithm based on Krylov subspace is used to form a reduced model to represent the original FEM model.During the whole frequency sweep process,the reduced model only needs to be solved,and then the solution of the original system model is recovered through the corresponding relationship,which greatly improves the solving efficiency and has a high accuracy.However,in the process of forming the reduced model,the original scale FEM equation still needs to be solved once.In the face of large-scale problems such as antenna arrays,the traditional FEM is faced with great challenges,so this thesis also introduces the Finite Element Tearing and Interconnecting method(FETI).Based on the idea of domain decomposition,the FETI divides the original solution domain into several subdomains,each of which is solved independently,and imposes specific boundary conditions on the interface of the subdomains to ensure the uniqueness of the solution.The FETI transforms the original problem of solving large-scale matrix in three-dimensional space into the problem of solving two-dimensional plane equations on the interface and the subdomainint in three-dimensional sapce,which effectively reduces the computer memory occupation and computing time in the process of calculating.Finally,several examples of typical microstrip antennas are given to demonstrate the correctness and effectiveness of the proposed method. |
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