Fast Evaluation And Multiresolution Basis Based High Efficient Algorithm Of Electromagnetic Scattering Problems

The electromagnetic (EM) scattering characteristic of target has wide application in areas of radar system design and target identification, stealth and anti-stealth technology of military weapon, and EMC in complex environment etc. As the advancement of the computer technology and numerical methods, the EM numerical simulation technologies have became important tools for analyzing the EM scattering characteristic of target. The EM numerical methods can be categorized into asymptotic high-frequency (HF) methods and low-frequency (LF) numerical methods. This thesis mainly focused on the application of the two kinds of methods in the fast calculation of EM scattering problems.The HF methods neglect most of the EM coupling by utlizing the asymptotic localizing principle, thus they have advantages in fast computation and low computer requirement. Therefore, the HF methods provide high efficient tools in fast evaluation of the EM scattering problems. The classical HF methods are introduced and compared systematically, and their basic principles, formulations and applications in realistic engineering are also provided in this thesis. Also, the validations of the HF methods in analyzing the scattering problems are discussed through numerical results. Especially, the widely used shooting and bouncing ray (SBR) method is particularly studied. An improved acceleration technique based on monostatic bistatic equivalence principle is proposed for the SBR simulation in the monostatic radar cross section (RCS) prediction. An EM simulation software is also developed based on the SBR algorithm. The time-domain versions of several classical HF methods are also studied, and their corresponding formulations are deduced. Also, the time-domain SBR (TD-SBR) method is taken as an example to demonstrate the realization procedure for the time-domain HF methods in realistic engineering.Although the HF methods have advantages in the fast calculation of EM scattering problems, their calculation error is large in the analysis of electrical small objects and objects contain electrical small structures. Therefore, the researches of the LF numerical methods are of great significance. The method of moments (MoM) is a typical LF numerical method and has a strong practicability, since it doesn't need to introduce the truncation boundary condition and generates fewer unknowns. Therefore, the multiresolution (MR) basis and MR preconditioning technique applicable in MoM are researched in this thesis. Compared with the MoM matrix generated from classical RWG basis, the matrix generated from the MR basis can be highly sparsified and has better condition number. Therefore, the MR basis and MR preconditioning technique can be effectively applied in the fast calculation of EM scattering problems. The MR basis can be classified into mesh-dividing based basis and mesh-grouping based basis, and the two kinds of MR bases and their preconditioning techniques are fully studied in this thesis.Firstly, the mesh-dividing based MR basis is studied and the corresponding MR preconditioner is constructed. The mesh-dividing based MR basis can be easily constructed. However, the modeling ability the MR basis is restricted by the shape of the coarse mesh. A perturbation from the principle value term of the magnetic field integral equation (MFIE) operator is introduced to improve the MR preconditioner. The MR basis is generalized to the curvilinear MR basis, and the constructed curvilinear MR basis has better modeling ability and fast convergence rate for iterative solvers. The corresponding MR preconditioner is combined with the FMM algorithm to analyze EM scattering problems. Also, the MR preconditioner has been applied to accelerate the hybrid PO-MoM method effectively.Secondly, the mesh-grouping based MR basis is studied. Compared with the mesh-dividing based MR basis, the mesh-grouping MR based basis has better modeling ability. A geometric strategy is proposed to construct the mesh-dividing based MR basis. Compared with the MR basis generated with algebra strategy, the MR basis generated with geometric strategy can be constructed in a much easier fashion and provide more direct physical meanings. A comparison is given for the MR bases generated with the two strategies, and both of the generated MR bases are applied in the analysis of low-frequency problems. A redundant loop basis is proposed as the solenoidal part of MR basis to improve the performance of MR basis for closed surfaces. Also, the MR preconditioner is proposed to be combined with the MDA-SVD algorithm for fast analyzing the densely discretized scatters. As a result, the problems of the dense and ill-conditioned matrix arise from the dense discretizations are solved.