Research On Time-Domain Meshless Method In Computational Electromagnetics

For nearly sixty years,computational electromagnetics members have not stopped to put forth new ideas,and have developed a great variety and a considerable number of numerical methods.These powerful electromagnetic computation methods have not only promoted scientific development of electromagnetism,optics,remote sensing imaging and other fields,but also drived technological progress in many industries such as electronics,communications,and computers.According to the spatial discretization ways,electromagnetic numerical methods could be divided into two categories: the mesh-based methods and the node-based meshless methods.Compare to the conventional mesh-based methods,meshless methods have some unique advantages including better capability of complex boundary modeling and local structure re-discretization.Therefore,in the recent years,meshless methods have attracted more and more attention,and research on it has become more and more active.Time-domain meshless methods in computational electromagnetics are researched in this dissertation,including the unifying computational platform based on meshless method,the unconditionally stable time-domain meshless method,and the fast time-domain meshless method based on the wave equation.The main contents are divided into three parts that are shown as follows.In the first part,the unifying computational platform based on meshless method is studied.Firstly,the method of weighted residuals(MWR)and its simple application are introduced.Selection criteria of expansion and testing function of the MWR are analyzed,and the MWR derives and generalizes other numerical methods are also shown.Secondly,a new electromagnetic numerical method is introduced,which is the meshless method based on node discretization.Thirdly,a unifying computational platform is developed and proposed which is based on the MWR and framed by meshless method.By employing this unifying platform,computational electromagnetics members can understand existing numerical methods more intuitively,open up a new vision for proposing new algorithms,and have a new thinking for hybridization and co-simulation of different methods.Finally,two simulation experiments are applyed to verify the effectiveness of the proposed computational platform.In the second part,the unconditionally stable time-domain radial point interpolation meshless(RPIM)method is studied.Firstly,to remove time-step limitation that causes by nodal spacing,the locally one-dimensional(LOD)scheme is introduced into the conventional time-domain RPIM method,and then the LOD-RPIM method with unconditional stability is developed and proposed.Due to the introduction of the LOD scheme,time discretization step is not limited by nodal spacing and then choosen by simulation accuracy requirement.Numerical experiments results not only testify the time-domain unconditional stability of the LOD-RPIM method,but also show that the computational cost of the proposed method is lower than the alternating-directionimplicit RPIM mthod when obtains a similar solution accuracy.Then,to extend the application scope of the LOD-RPIM method to model open-region structures and radiation problems,the perfectly matched layer(PML)scheme is introduced,and the split-field PML scheme for the unconditionally stable time-domain LOD-RPIM method is proposed.A simulation experiment of current source radiation in free space is employed to validate wave absorption ability of the proposed PML scheme.In the third part,the novel and fast time-domain meshless method based on the wave eqaution is studied.Firstly,to extend the application scope of the wave-equationbased meshless method to open-domain structures and radiation problems modeling,and by introducing the auxiliary variables and the auxiliary differential equations,the convolution PML(CPML)scheme for the time-domain wave-equation-based meshless method is studied and proposed.By applying numerical experiments,the absorption performance of the proposed scheme is verified,the performance influences of different CPML parameters is analyzed and then the parameters suggestion is given.Meanwhile,with the introduction of this method to the FDTD method based on the wave equation,the wave-equation-based FDTD method CPML ABC scheme is developed and validated.Then,start with the time-domain wave equation and by applying the eigenmode analysis,the transfer function between the excitation source and time-domain field is obtained.In the meantime,the transfer function for different media is proved to be stable over time.Consequently,based on time-independent spatial eigenmode expansion,the time-domain meshless method with analytical property is developed and proposed.By conducting a few numerical experiments,the proposed method is validated to be with better solution accuracy,which is due to time discretization error is removed.