Research On Efficient Calculation Method Of Layered Medium Green's Function

According to the demands and requirements of practical engineering applications,in whether military or civilian and commercial area,many researches on electromagnetic radiation and scattering of targets existing in complex electromagnetic environment are increasingly concerned and popular.Different from the researches on the electromagnetic characteristics of targets in free space,in the background of sophisticated environment,only when the influence of the complex physical process between the environment and the target on the electromagnetic characteristics of the target must be fully considered can the target be accurately and effectively modeled and numerically calculated.The planar layered medium model is one of the simplest and most effective methods for integrated modeling of target and complex environment,additionally,layered medium Green's function(LMGF)is the cornerstone and core of plane layered medium modeling.In fact,the effects of layered background environment on the electromagnetic characteristics of specific targets are all included in LMGF.In computational electromagnetics,the definition of LMGF is that the point source response(field or potential)is generated by arbitrary polarization source with unit intensity at a certain point in stratified medium.The concrete forms of LMGF are different owing to different mathematical definitions or integral equations.The expression of field-type LMGF is derived by the theory of vector wave function and pilot vector potential in this thesis.In order to reduce the singularity of integral kernels,the matrix-friendly layered medium Green's function with low singularity is derived based on mathematical vector identity and integration theory by part.Compared with free-space Green's function,the calculation of LMGF is involved Sommerfeld integrals which usually have a slow convergence when direct numerical quadrature is utilized.Consequently,it is vitally significant and urgently-needed to develop an efficient and accurate method for LMGF calculation.Then,the characteristics of Sommerfeld integrals are summarized and retrospected,the efficient and fast calculation method of Sommerfeld integrals is given focus.Afterwards,spatial tabulation and interpolation method(TIM)is studied to calculate LMGF effectively in the thesis.Lagrange interpolation method(LIM)?Gaussian basis function interpolation(GIM)and Newton interpolation method(NIM)are utilized,which need to be in combination with direct numerical integration method in the usage process.Several numerical examples show that TIM can evidently improve the computational efficiency of LMGF by minimizing the calculation times of Sommerfeld integrals.Secondly,a fully connected neural network based on optimization algorithm(FNNMEA)is proposed to accelerate the calculation of LMGF in consideration of neural network's powerful nonlinear fitting capability,computational efficiency and favorable generalization capability.LMGF obtained by direct numerical integration method is used as the training set to train the fully connected neural network(FNN)to characterize the LMGF.Due to the randomness of the optimization algorithm,the prediction results of LMGF are unstable and the efficiency is relatively low.Next,least squares support vector machine(LSSVM)is further studied to accelerate LMGF in this thesis because LSSVM is based on the principle of structural risk minimization and has fewer super parameters.The cross-validation method is introduced to determine the hyperparameters.Compared with FNN and FNN-MEA by several numerical examples and the performance evaluation index of neural network,the calculation accuracy and efficiency of LMGF in LSSVM are improved in LSSVM.