Research On Fast Frequency Sweep Algorithms In Electromagnetic Finite Elements Method

In order to meet the increasing demand of electromagnetic design,the requirement of computer aided engineering software(CAE)is increasing rapidly.As a high-precision numerical analysis method of electromagnetic problems,finite element method is widely used as the basis of all kinds of CAE software.At the same time,the frequency response is often paid attention to in the design of filters,antennas and other devices.For all kinds of wideband and ultra-wideband microwave devices,Efficiency of the discrete frequency sweep is too low,and the traditional fast frequency sweep is limited to narrow-band signals.In this paper,the commonly used post-processing parameters of the model are obtained by using the electromagnetic finite element method,such as scattering parameters and impedance parameters.And the corresponding frequency response curves are obtained by rational function approximation.As a generalized fast frequency sweep method,this method has the advantages of being suitable for broadband problems and high speed.So it has high practical value.This paper discusses the application of Vector Fitting(VF)algorithm and AAA(adaptive Antoulas-Anderson)algorithm in frequency scanning,and gives their specific implementation methods.The judgment and imposition of various characteristics when it is used in the scattering system are further studied.Through the comparison and analysis of examples,it is proved that the AAA algorithm has better convergence than the VF algorithm,but it is faced with great difficulties that the system characteristics are difficult to impose,which limits its further application.The main work and innovation of this paper are as follows:1.The finite element method of electromagnetic field is studied,its basic principle and derivation process are mastered,and its implementation method is briefly described.Based on the finite element field solution,the calculation principle of port scattering parameters is studied,and other post-processing parameters are obtained.2.The characteristics of the linear time-invariant system are analyzed,such as the scattering system or impedance system of microwave devices in linear lossless media.Aiming at the two cases of scattering system and impedance system,the stability,causality,realness and passivity are discussed,and the correlation and judging conditions of vari-ous characteristics are analyzed.Finally,the definitions of Positive Realness and Bounded Realnesss are given.3.VF algorithm is used to realize frequency scanning.The original VF algorithm is modified to accelerate the convergence and calculation speed.And it is extended to the multi-port system.The imposed methods of realness,causality and stability,as well as the judgment conditions of passivity are given.Realized the use of VF algorithm to quickly obtain the frequency response of the scattering system.4.The AAA algorithm proposed in recent years is introduced,and its format is modi-fied to apply to vector values and matrix values.The transformation relationship between rational barycentric form and state space representation is established.The imposed for-mat of its realness and the method of judging passivity are given.And a post-processing method based on projecting the transfer function onto the stability space is used to impose stability.The application of this method in the frequency scanning of scattering system is realized.5.A simple and effective adaptive sampling method is given,which is applied to the electromagnetic CAE software EMLAB developed by the author’s team.Based on EM-LAB,some examples are modeled and simulated.And the convergence,accuracy and system characteristics imposed by VF algorithm and AAA algorithm are compared.It is concluded that AAA algorithm has better convergence,but it is more difficult to impose system characteristics.The application of this algorithm in the field of electromagnetic simulation still has great research and development prospects.