Rapid Finite Element Analysis Of Microwave Passive Components

The finite element method(FEM)is more important and more widely in the field of electromagnetic field,and the accuracy of the calculated results becomes an important indicator to measure whether they are valid or not.In order to obtain higher precision,the finite element method chooses the refinement grid and the high order basis function to simulate the microwave device.However,although this method can obtain high precision results,the dimension of the corresponding finite element matrix will also increase,resulting in additional memory consumption and time consumption in the solving process.For the sake of high precision results while reducing the consumption of computer resources and achieving the purpose of rapid analysis of devices,this paper takes the vector finite element method based on the second order hierarchical basis function as the research subject,and focuses on the fast finite element analysis method of resonator cavity and waveguide.And the main content of this paper is divided into three parts.Firstly,the Ritz method and Galerkin method,which are the two methods of finite element method for electromagnetic boundary value problem,are introduced.Meanwhile,the realization steps and calculation formulas of finite element method are derived and analyzed,and the selection of basis function is discussed.Finally,in order to verify the accuracy of the finite element method proposed in this paper,the eigenvalues of rectangular cavity and cylindrical cavity are calculated by using the finite element method based on the vector hierarchical basis function,and the calculated results are consistent with the theoretical values.Secondly,Galerkin finite element method based on the second order hierarchical basis function is used to study the eigenproblems of resonant cavity under the condition of loss and no-loss.Under the condition of no loss,the spurious dc mode appears when the governing equation does not satisfy the electric field divergence equation when calculating the eigenvalue of the resonator with the traditional finite element method,thus increasing the solving time and memory consumption.In order to make a fast eigenanalysis of the resonator,the Galerkin weak form of the divergence equation of the electric field is considered while solving the governing equation,so that the spurious dc mode can be removed by using the characteristics of the second order hierarchical basis function.On the other hand,the nonlinear eigenproblem of lossy resonant cavity is transformed into linear eigenproblem to accelerate the solving process.Then,some resonant cavity models are used to calculate the parameters of the eigenproblem and compared with the commercial software,HFSS,and the result is accurate and efficient,and the time computation is greatly reduced.In the end,the Galerkin weak form of waveguide transmission problem based on the above methods is derived,the finite element model of multi-port network with single port excitation is also discussed,and the realization method of S parameter is expounded.In addition,the waveguide model is used for calculation and verification.In order to respond quickly to the S parameter with wide band,this paper further studies the fast sweep algorithm of asymptotic wave estimation(AWE),and the result of the final model is consistent with that of HFSS.