Fast Algorithms for Electromagnetic Scattering Analyses
|School||Nanjing University of Technology and Engineering|
|Course||Electromagnetic Field and Microwave Technology|
|Keywords||electromagnetic scattering method of moment non-equispaced fast Fourier transform multilevel fast multipole approach solenoidal basis function finite element method preconditioning technique iterative solvers|
The accurate and efficient analyses of electromagnetic scattering of complex objectswith electrically large size are urgently required by the quick development of technologyfor military and civil use. Fortunately, the combination of the modern computer technologyand the fast algorithm for rigorous full-wave analysis make it possible to givehigh-performance researches for numerous practical problems in a popular personalcomputer, which traditionally can only be analyzed by use of high-frequency approximateapproaches.The dissertation investigates three kinds of fast algorithms to achieve the low memorycost and low operation complexity in the electromagnetic analyses.First is the fast Fourier transform technique. We apply this technique into theimplementation of discrete dipole approximation method, and the method of moment ofvolume integral equation. The FFT technique combined with iterative solvers reported inthe literatures is compared for the ordinary volume integral equation and weakform ones.The second is a newly developed scheme called non-uniform FFT (NUFFT). Itinherits the efficiency of the FFT and removes the limitation of the uniform mesh grid. Theprocedure for the inverse transform is improved. The applications in the analyses ofelectricmagnetic scattering from conductor plates and dielectric objects are discussed. Thememory requirement and computational complexity is O(N) and O(NlogN), respectively.The third fast algorithm investigated is multilevel fast multipole approach (MLFMA).It is powerful and flexible since the arbitrary mesh partition can be permitted. Thedissertation discusses in detail on the implementation of the algorithm, and applies it toanalyze the scattering from the conductor objects, dielectric objects, and microstrip patchantenna. The solenoidal basis functions are adopted in the scattering analysis of dielectricobjects, which lead to a less number of unknowns for the same mesh as in the traditionalSchaubert-Wilton-Glisson basis functions.The vector-edge finite element method combined with boundary integral (FE-BI)technique with MLFMA accelerator is also investigated in the dissertation. This hybridapproach is able to analyze various complicated problems with the advantages of bothFEM and MLFMA. It has been considered as one of the most powerful schemes to theelectromagnetic problems. All the above fast algorithms can only accelerate the speed of every iteration, however,they do not reduce the total iteration number. Among the various Krylov subspace iterativesolvers, different solver for the certain problems is discussed. Some preconditioningschemes are proposed to further reduce the computational time of solvers. A lot ofnumerical examples illustrate the efficiency and accuracy of the fast algorithms studied inthis dissertation.