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dc.contributor.supervisor Okhmatovski, Vladimir (Electrical and Computer Engineering) en_US
dc.contributor.author Aronsson, Jonatan
dc.date.accessioned 2013-08-23T13:36:51Z
dc.date.available 2013-08-23T13:36:51Z
dc.date.issued 2010 en_US
dc.date.issued 2009 en_US
dc.date.issued 2011 en_US
dc.identifier.citation J. Aronsson, K. Butt, I. Jeffrey, and V. Okhmatovski, The Barnes-Hut Hierarchical Center-of-Charge Approximation for Fast Capacitance Extraction in MultilayeredMedia, IEEE Transactions on Microwave Theory and Techniques, vol. 58, pp. 1175-1188, 2010 en_US
dc.identifier.citation J. Aronsson, I. Jeffrey, and V. Okhmatovski, Generalization of the Barnes-Hut Algorithm for the Helmholtz Equation in Three Dimensions, IEEE Antennas and Wireless Propagation Letters, vol. 8, pp. 425-428, 2009 en_US
dc.identifier.citation J. Aronsson, and V. Okhmatovski, Vectorial Low-Frequency MLFMA for the Combined Field Integral Equation, IEEE Antennas and Wireless Propagation Letters, vol. 10, pp. 532-535, 2011 en_US
dc.identifier.uri http://hdl.handle.net/1993/22086
dc.description.abstract Tree-based methods have wide applications for solving large-scale problems in electromagnetics, astrophysics, quantum chemistry, fluid mechanics, acoustics, and many more areas. This thesis focuses on their applicability for solving large-scale problems in electromagnetics. The Barnes-Hut (BH) algorithm and the Fast Multipole Method (FMM) are introduced along with a survey of important previous work. The required theory for applying those methods to problems in electromagnetics is presented with particular emphasis on the capacitance extraction problem and broadband full-wave scattering. A novel single source approximation is introduced for approximating clusters of electrostatic sources in multi-layered media. The approximation is derived by matching the spectra of the field in the vicinity of the stationary phase point. Combined with the BH algorithm, a new algorithm is shown to be an efficient method for evaluating electrostatic fields in multilayered media. Specifically, the new BH algorithm is well suited for fast capacitance extraction. The BH algorithm is also adapted to the scalar Helmholtz kernel by using the same methodology to derive an accurate single source approximation. The result is a fast algorithm that is suitable for accelerating the solution of the Electric Field Integral Equation (EFIE) for electrically small structures. Finally, a new version of FMM is presented that is stable and efficient from the low frequency regime to mid-range frequencies. By applying analytical derivatives to the field expansions at the observation points, the proposed method can rapidly evaluate vectorial kernels that arise in the FMM-accelerated solution of EFIE, the Magnetic Field Integral Equation (MFIE), and the Combined Field Integral Equation (CFIE). en_US
dc.publisher IEEE en_US
dc.publisher IEEE en_US
dc.publisher IEEE en_US
dc.subject electromagnetics en_US
dc.subject tree-based algorithms en_US
dc.subject Barnes-Hut en_US
dc.subject Fast Multipole Algorithm en_US
dc.title Novel tree-based algorithms for computational electromagnetics en_US
dc.degree.discipline Electrical and Computer Engineering en_US
dc.contributor.examiningcommittee LoVetri, Joe (Electrical and Computer Engineering) Thulasiraman, Parimala (Computer Science) Balasubramaniam, Shanker (Michigan State University) en_US
dc.degree.level Doctor of Philosophy (Ph.D.) en_US
dc.description.note October 2013 en_US


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