Theoretical Modeling And Efficient Algorithm Research On Electromagnetic Scattering From Inhomogeneous And Complex Structures

The rigorous modeling and high efficient calculation of electromagnetic (EM) radiation and scattering from electrically-large inhomogeneous and complex structures are studied in this dissertation. With the deep research on equivalent modeling, discretization of Maxwell's equation, matrix solution and time-frequency domain transformation, one by one, we have mainly discussed the effective electromagnetic modeling and fast numerical calculation of radiation and scattering from electrically-large conductors, thin dielectric structures and coatings; arbitrary conductor-dielectric composers and their multi-region problems. Consequently, we provide a solid foundation for the final goal of integrated modeling and high-precision simulation of inhomogeneous and complex structures.In the first, the commonly used numerical algorithms for solving and analyzing the EM characteristics of complex structures are introduced. Specially, the numerical solution and critical techniques of integral equation method have been systematically stated. The surface integral equation (SIE), volume integral equation (VIE) and hybrid volume-surface integral equation are established according the equivalence principle. Then, the RWG basis functions, curvilinear RWG basis functions and SWG basis functions are introduced to express the equivalent currents on conductor and dielectrics, respectively. After that, the integral equations are discretized to linear equations with Galerkin method. The singularity and near singularity of Green's function are treated by adding and subtracting a singular term. Finally, the linear equations are efficiently solved with multilevel fast multipole algorithm (MLFMA) and iteration methods.In order to reduce the number of unknowns and efficiently computing the scattering from electrically-large conductors, we defined the phase-extracted (PE) basis functions based on the deeply understanding of induced current's physic properties. Starting from the Maxwell's equations and boundary conditions, the mathematical verification of phase extraction is presented and the validate conditions are discussed. The PE basis functions not only describe the slowly varying magnitude but also the fast changing phase of induced current, so they can reside on large, higher order interpolation patches, such as curvilinear triangular patches. Consequently, we can use a few number of PE basis functions to accurately reconstruct the induced current on PEC (Perfect Electric Conductors) surfaces. The saving of basis functions dramatically reduces the computer resource requirement. Furthermore, the coefficients of PE basis function vary slowly with the frequency. Therefore they have excellent performances in wideband calculation coupled with the frequency sampling the current interpolation techniques.The accurate electromagnetic modeling and efficient scattering calculation of thin dielectric structures and thin dielectric coatings is always a challenge. For these special structures, we proposed the multilayer thin-dielectric-sheets (TDS) approximation and the generalized thin-dielectric-coating approximation owing to the characteristics that the field is continuous and changes slowly along the normal direction. These approximation models reduce the number of unknowns as well as the complexity of electromagnetic modeling, and they are easy to be solved with available fast algorithms, such as MLFMA. The multilayer TDS approximation simplifies the mesh generation and numerical integration of the volume integral equation. And the generalized thin-dielectric-coating approximation can solve arbitrary thin coating problems with the same computational complexity as pure PEC targets. In engineering applications, they can be used to efficiently obtain the radiation and scattering from radomes, coated aircraft, and other electrically-large objects.Aimed at resolving the radiation and scattering from arbitrary composite objects, multiple targets and finite periodic structures, a multi-solver based generalized impedance boundary condition (MS-GIBC) is proposed and finally a domain decomposing method (DDM) is achieved. The scattering from complex structures is equivalent to the radiation of equivalent sources (electric current and magnetic current) resided on their boundaries. A generalized impedance boundary condition (GIBC) is established between the equivalent magnetic current and electric current. Different solvers, such as boundary integral equation (BIE) or finite element method (FEM), can be adopted in different domain to construct the GIBC. Finally, we only need to solve the boundary integral equations concerning equivalent current at each boundary. Moreover, it is very convenient to use multilevel fast multipole algorithm and various preconditioners to accelerate the solution process. Multilevel fast multipole algorithm is a most efficient algorithm in EM calculation. It successfully reduces the computational complexity to O ( N log N ) by dividing a scatterer into many groups and calculating the coupling of groups in far region with aggregation, translation and disaggregation. However, fine structures and 3D dielectric objects usually give rise to too many grids and lead to a large number of unknowns in each group. This will burden the computer calculation and reduce the efficiency of MLFMA. For the sake of further improving its efficiency, we compressed the rank-deficient matrices in MLFMA through the truncated singular value decomposition (TSVD). The proposed TSVD-MLFMA approach compresses the memory requirement of impedance matrix, aggregation matrix and disaggregation matrix, as well as reduces the iteration time.At the end, the time domain response of complex structures excited by pulse signal is discussed with frequency domain methods. The wideband time domain response can be efficiently solved now with Fourier transform, current interpolation, and the approximation models and fast algorithms proposed in this dissertation. As a basic research on the electromagnetic radiation and scattering of 3-D electrically-large objects with arbitrary shape and materials, our research presented in the dissertation provides a powerful approach in rigorous modeling and effective solution, as well as a solid foundation for the further development in this subject. The corresponding program codes have been developed for each numerical algorithm with parallel computing technique. These codes are easy to be used and further developed. Numerical examples validate their correction and efficiency.