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Title: Development and application of hybrid finite methods for solution of time dependent maxwell's equations
Keywords: Computational Electromagnetics, FDTD, FETD, Hybrid Methods, Antenna Modeling, Maxwell's Equations
Issue Date: 22-Nov-2007
Citation: NEELAKANTAM V. VENKATARAYALU (2007-11-22). Development and application of hybrid finite methods for solution of time dependent maxwell's equations. ScholarBank@NUS Repository.
Abstract: In this thesis, improvements to the finite element time domain (FETD) method, the finite difference time domain (FDTD) method and the hybrid FETD-FDTD method are proposed along with the application of the hybrid method for modeling and simulation of electromagnetic radiation from antennas. Firstly, a solution for the problem of weak instability inherent to the FETD method using edge element basis functions, manifesting in the electric field solution as a gradient vector field that grows linearly with time is discussed. A novel method to eliminate the occurrence of such weak-instability using divergence-free constraint equations is proposed. The method is directly extended to eliminate appearance of non-physical modes in the eigenvalue modeling of electromagnetic resonators. An efficient implementation of the constraint equation using tree-cotree decomposition of the finite element mesh and by constructing the discrete gradient and integration matrices is proposed. Secondly, the concept of hanging variables is extended to the FETD method specifically in the context of rectangular and hexahedral elements. Due to the Galerkin-type treatment of the hanging variables, the resulting FETD method has the same conditions of stability as those of the regular FETD method. Based on this method, an FDTD subgridding method with provable numerical stability is proposed. Numerical examples indicating the potential of the subgridding method with different refinement ratios are demonstrated. Thirdly, the extension of the hybrid FETD-FDTD method using hierarchical higher order vector basis functions in the FETD region is presented. The formulation in the FETD region allows for the modeling of ports with transverse electromagnetic mode of excitation. Finally, the successful application of the developed numerical technique in the computation of the modal reflection coefficient, input impedance and radiation pattern of real-world antennas and other benchmark problems is presented.
Appears in Collections:Ph.D Theses (Open)

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