Research On Rigorous Modeling And Fast Algorithms For 3D Electromagnetic Problem For Composite Conducting And Dielectric Targets

The rigorous modeling and high efficient calculation of electromagnetic radiation and scattering from complex electrically-large targets is studied in this dissertation. It is discussed from three points. First, accurate geometrical and electromagnetic modeling for complex targets; secondly, the details of effectively solving the integral equations by fast numerical methods; thirdly, analyzing the fast algorithms for complex irregular objects.Firstly, the crux techniques of the basic method for solving the integral equations-method of moment (MoM) have been studied. Curvilinear triangular patches and curvilinear RWG basis function are used to model the shape of the curved surface and the current distribution on the curved surface, respectively. A Duffy's transformation method is used to solve the singularity of integral equation and the general minimum residual method (GMRES) is used to solve linear equations. Numerical examples validate our codes.Then, the surface integral equations (SIEs) for composite conducting and dielectric objects are presented. Some formulations of SIEs are derived from equivalent principle. A new CFIE-JMCFIE formulation is proposed and compared with other equations from iterative characteristics and the applicability. CFIE-JMCFIE requires fewer iterations than other formulations because its impedance matrix is diagonally dominant and has low condition number. A treatment for SIEs and basis functions on the junctions of composite objects with multiple metallic and dielectric regions is discussed. A new contact region method (CRM) is proposed to simplify the treatment for complex composite objects.As key techniques for solving the scattering by electrically-large object efficiently, extensive study of the multilevel fast multipole algorithm (MLFMA) based on CFIE-JMCFIE has been carried out. The principles and the numerical realization in dielectric regions of MLFMA have been described. The numerical examples show that MLFMA with block-diagonal preconditioner can solve electrically-large problems accurately and efficiently. Where after, some other preconditioners based on MLFMA have been studied. A new grouped sparse approximate inverse (SAI) preconditioner is proposed to save the construction cost significantly and reduce the iteration number.For the sake of reducing unknowns, a higher order MLFMA, using the maximally orthogonalized higher order hierarchical vector basis functions based on modified Legendre polynomials, is proposed. To improve the efficiency of higher order MLFMA with large patches, a detailed discussion for grouping and parameters and the referenced principle are given. Through reasonably chousing the order of basis function and the size of the patches, higher order MLFMA can solve scattering problem for composite objects efficiently and accurately.Aimed at resolving the scattering by composite object with open metallic structure with high efficient solution, a new IEFIE-IPMCHW formulation has been proposed. By adding the principal value term into EFIE-PMCHW operator, a well-conditioned IEFIE-IPMCHW operator is constructed. To achieve a reasonable accuracy, several update steps for the current vector are required. This method attains much faster convergence of iterations than conventional methods, particularly for 3-D structures with open or sharp surface.Finally, detailed work has been done for the problems of complicated objects attached with wires, such as wire monopoles on platform. A surface/surface junction mode has been used to model the wire/surface junction. When the monopole is added or moved on the surface, accurate results of impedance and radiation properties have been achieved and only a few triangular patches need to be resegmented near the attachment point. Then, a Costa's junction basis function is described. An iterative MoM-PO method and a preconditioned MLFMA are employed to solve the electrically-large problems, respectively.As a basic research work for electromagnetic radiation and scattering characteristics of the 3-D electrically-large objects with arbitrary shape and materials, this research work presented in the dissertation provides the powerful way in rigorous modeling and effective solution, as well as a solid foundation for the further development in this subject.