Research And Application Of Fast Integral Equation Method Based On Layered Medium Green's Function

Integrated analysis of electromagnetic characteristics between targets and inhomogeneous environment is of great scientific and application significance.Half space and planar-layered medium background is one of the basic research field in composite electromagnetic modeling of the target and the environment.Dyadic Green's function of a planar-layered medium(PLDGF)is established to model of the composite electromagnetic scattering from objects residing in a planar-layered or half-space scenario.Based on this numerical analysis model,this dissertation studies the key techniques and fast solutions of integral equations for scattering and radiation problems in a layered medium.In addition,an integral equation method based on the domain decomposition method(IEDDM)is proposed to analyze the multi-scale electromagnetic problems in the half-space scenario.In the first,to model general dielectric or magnetic objects,the dyadic expression of planar layered media Green's function based on the method of vector wave functions expansion and pilot vector potential approach and duality principle is generalized for both electric and magnetic sources.In view of efficient calculation of the PLDGF,the properties of Sommerfeld integrations(SIs)are analyzed and summarized.Two types efficient methods for evaluation SIs are systematically researched.One is direct numerical calculation,and two efficient algorithms named the weighted averages(WA)algorithm and the generalized pencil of function(GPOF)method are introduced to accelerated the Sommerfeld integral tails.The other one is discrete complex image method(DCIM)which based on three-level algorithms.Secondly,according to the basic theorem of surface equivalence principle,the surface integral equation method is formulated by boundary condition in planar-layered medium.Then,four kinds of basic integral operator are constructed and given.The critical techniques of method of moments(MoM)numerical solution of the integral equation is described in terms of four aspects as geometry modeling,mesh generation,basis functions definition and matrix equation solving.In order to reduce the singularity of the field-type Green's functions,integration by parts is applied wherever possible to transfer the partial derivative from the Green's function to the basis functions,which eventually formed to a matrix-friendly.In this manner,the field type Green's function has the same properties as the common potential type Green's function,thus is easy to be used in the MoM.These studies lay the foundation for the development and implementation of the fast solutions of integral equations.Three types fast solutions of integral equations are adopted in this dissertation to improve the efficiency of the MoM solution of integral equation which based on the half space Green's function.Among them,the pre-corrected fast Fourier transform method(p-FFT)and the half space multilevel fast multipole algorithm(MLFMA)are dependent on the integral kernel,while the multilevel adaptive cross approximation method(ACA)does not depend on the integral kernel.By using matrix transformation method to convert the propagation matrix of half-space Green's function into Toeplitz matrix form,FFT-based methods can be utilized to model the electromagnetic scattering from general three-dimensional(3-D)objects in a half space?A novel diagonal perturbation of dual threshold incomplete LU factorization(ILUT)is presented and investigated as an effective preconditioner to improve convergence property of the half-space EFIE.Thus the high accuracy of EFIE is maintained,yet good calculating efficiency comparable to the combined field integral equation(CFIE)can be achieved.Then,the principle and implementation of MLFMA and MLACA in half space are introduced,and the advantages and disadvantages of the three methods in the background of planar layered media are illustrated and summarized by numerical examples.Most existing literature on DDM only consider electromagnetic phenomenon in an unbounded homogeneous background.In this work,an extension of the IE-DDM is presented for the analysis of EM scattering from multiscale structures above a lossy half space.Firstly,the integral equation domain decomposition method based on the half space Green's function is formulated in detail.Furthermore,block-Jacobi preconditioning with an inner-outer scheme is construct as the iterative solution of the system matrix of IE-DDM.In particular,traditional fast solutions of integral equations are always inefficient for multiscale problems because of the high burden of near-field interactions and slow convergence property.To overcome this difficulty,a novel multiple-grid precorrected fast Fourier transform(MG-p-FFT)auxiliary Cartesian grids with different size,order,location,and spacing,is adopted in each sub-domain independently to account for the self-interactions.Here,the proposed multiple-grid p-FFT scheme outperforms the existing single-grid p-FFT scheme for multiscale problems by reducing the computational time and memory consumption.Secondly,a new integral equation domain decomposition method(IE-DDM)using electric and magnetic current combined-field integral equation(JMCFIE)is proposed for efficient EM analysis of composite objects in half-space.In order to obtain a good approximation of the global solution,both electric and magnetic field interactions are considered at the sub-domain interfaces,in addition to the traditional Robin type transmission conditions.In this manner,the unphysical reflections at sub-domain interfaces can be further suppressed.It is shown that the condition of the new JMCFIE-DDM system is much improved in this new implementation.Accuracy and efficiency of the proposed method are demonstrated through several numerical experiments.The higher-order hierarchical vector bases(HOHVB)based on curvilinear triangular patches is extended to IE-DDM to further improve the efficiency of the analysis of electromagnetic scattering from arbitrary three-dimensional conducting objects in a halfspace.Due to the flexibility of DDM,it allows flexibility of order selection of HOHVB in different subdomains based on the property of each subdomain.Finally,summarize the work of this dissertation,then fully understand “divide and conquer” as the philosophy of IE-DDM,a novel hybrid solver is introduced where HOHVB,MLACA and the half-space MLFMA are integrated seamlessly in the framework of IE-DDM.This hybrid solver sharing the efficiency and flexibility of each method which allows different basis functions and fast solvers to be used in different subdomains,make it is suitable for a wide range of application.Numerical results show that this hybrid solver can reduce both the number of unknowns and the computation and storage complexity.As a basic research on the composite electromagnetic modeling of the target and the environment,this dissertation provides a powerful approach in rigorous modeling and effective solution for composite electromagnetic scattering from objects residing in a planar-layered or half-space scenario.These work also lay a solid foundation for the numerical simulation of the multi-scale and large-scale electromagnetic characteristics in the practical engineering.A set of convenient maintenance numerical codes have been independently developed.Numerical examples verify their accuracy and reliability.