Study On Key Technologies Of Efficient Electromagnetic Computation Based On Integral Equation Methods

It has important theoretical significance and application value to obtain electromagnetic characteristic of special structure in many frequencies with microwave,millimeter wave and light band,and in various fields like frequency selective surfaces,antenna,super surface and solar cells.Taking advantage of the intrinsic characteristics of these special structures,this dissertation is committed to study the rapid and accurate electromagnetic simulation methods.Frequency domain integral equation methods are mainly studied with periodic green function,multilevel fast multipole and equivalence principle domain decomposition.Firstly,the periodic green function with its fast algorithm is combined with various kinds of integral equations to analyse the electromagnetic problems from the 2D planar periodic structures with homogeneous/inhomogeneous,isotropic/anisotropic medium.Secondly,the plane wave approximate diagonalization of low frequency fast multipole algorithm is studied to solve rapidly the multiscale structure with dense grid.Thirdly,the domain decomposition algorithm based on spherical equivalent principles is studied to analyse efficiently the randomly distributed metal-dielectric composite bodies of revolution.At last,the time domain volumesurface integral equation method in marching-on-in-time scheme is studied to obtain rapidly the broadband electromagnetic scattering form the metal-dielectric composite body of revolution.The first part is some basic theories of this dissertation,which are the basic electromagnetic theory based on the integral equation methods.According to the electromagnetic theory and periodic boundary conditions,the two-dimensional plane periodic green function in the free space is derived in detail.And then the scalar Green function in free space is expanded by using the addition theorem and the plane wave expansion theory,which is the fundamental formula of the high frequency multilevel fast multipole.Finally,the basic implementation process of the equivalence principle domain decomposition algorithm is introduced.In addition,several kinds of electromagnetic parameters are introduced.The second part of this dissertation focuses on the integral equation method with its fast algorithm to analyse the 2D planar periodic structures with homogeneous/inhomogeneous,isotropic/anisotropic medium.First of all,the Ewald transformation and linear interpolation are combined to calculate the 2D periodic Green function quickly and accurately.And the implementation procedure is introduced in detail.Taking the inhomogeneous and anisotropic medium into consideration,the volume-surface integral equation with the 2D periodic Green function is proposed.Meanwhile,the region block-diagonal precondition is employed to improve the condition number of matrices.Next,the surface integral equation with the 2D periodic Green function is also developed to solve the periodic structure with homogeneous or block-homogeneous medium.In such way,the total number of unknown can be reduced and the whole computing resources can be further saved.The third part of this dissertation concentrates on a fast algorithm to analyze the structure with fine grid problems.The proposed method is based on an approximate diagonalization of plane wave expansion to solve the low-frequency breakdown problem of fast multipole algorithm.At first,the approximate diagonalization is introduced into the electric field integral equation.And it is demonstrated that the different groupings for the vector and scalar potential in far field can improve the accuracy.Meanwhile the computational complexity of the algorithm is analyzed.After that,the implementation of the approximate diagonalization in homogeneous medium space is also studied.So the volume integral equation and surface integral equation are also combined with the proposed fast algorithm to analyze dielectric structures.At the same time the proposed method can be combined with the high frequency fast multipole algorithm in a very convenient way.And thus it can be developed to analyze the multiscale problems by accelerating the near field calculation.In the last part of this dissertation,the electromagnetic scattering characteristics of bodies of revolution are investigated.Firstly,the electromagnetic scattering from multiple non-coaxial metal and homogeneous bodies of revolution is considered by using spherical equivalent source domain decomposition algorithm.By using the domain decomposition,the appropriate integral equations can be chosen according to the structure properties.All the unknowns can be transferred to the equivalence surface,and then the general equations are established on the equivalence surfaces.Secondly,the broadband electromagnetic scattering from the composite metal and inhomogeneous body of revolution is obtained by using time domain volume-surface integral equation in marching-on-in-degree scheme.To reduce the storage requirements and filling time of the impedance matrix,the rotational symmetry is employed.Similarly like the unknowns defined on the generatix of metallic surface,the unknowns for inhomogeneous regions are just introduced on the tangent plane.To express these unknowns in space,hybrid basis functions based on triangle and rectangle are adopted.