The New Basis Functions Of Three-dimensional Electromagnetic Scattering, And Fast Iterative Technique

The fast analysis of the scattering characteristic of three dimension structure has always been intensive research in computational methods for electromagnetics. This thesis focuses on the method of new basis function and fast iteration technique. The content includes: the multiresolution basis function and its application to the multilevel fast multipole algorithm (MLFMA); the Loop-Tree basis function and the incomplete Cholesky (IC) factorization precondition applied to FMA; the PE-CRWG basis function and its application to multi-region iterative method (MRI) MLFMA and the modified technique based on the MRI-MLFMA.Firstly, the integral equation methods for electromagnetic problems are briefly introduced. Numerical methods for integral equation—moment of method (MoM) and the fast solving technique-MLFMA are introduced as well. Then, the preconditonal technique in analysis of electromagnetics scattering characteristic is presented.Secondly, the multiresolution (MR) basis function based on the mesh refinement and its construction method are studied. The MR basis function based on the RWG basis function defined on the planar triangle and its Galerkin Method are successfully realized. The diagonal precondition which making use of the good spectral properties is realized in MoM and MLFMA. The iteration speed is remarkably improved.Thirdly, as the traditional RWG basis function and Galerkin Method result into numerical unbalance between vector potential and scalar potential, the scalar potential term dominates over the vector potential term. This is the reason for low-frequency breakdown. The Loop-Tree basis function is adopted to overcome the problem, however, this would lead to bad spectral properties of impedance matrix and slow iteration speed. The IC precondition technique is applied to the integral equation to improve the spectral properties and accelerate the iteration speed of matrix equation.Finally, in order to improve the memory requirement and computational speed in the Multi-region iterative method (MRI)-MLFMA, a novel basis function defined on a large patch—Phase-Extracted (PE) basis function is introduced, which could allow very few unknown to attain appropriate solution of electrically-large object . The modified technique of using different combining factor in different regions is also studied in MRI according to the coupling intensity or geometric characteristics. The speed is greatly improved for solving the matrix equation with the reasonable precision requirement.