Higher order method of moments for current flow modelling of sector shaped conductors and scattering by dielectric cylinder
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Date
2018
Authors
Hosen, Mohammad Shakander
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Abstract
Design of complex multi conductor transmission lines (MTLs) depends on the knowl- edge of per unit length (p.u.l.) inductance and resistance along with p.u.l. capacitance and conductance. In order to calculate with controlled precision p.u.l. inductance and resistance of complex MTLs of arbitrary cross-section higher order numerical methods are required. Such method based on Higher Order (HO) Method of Moment (MoM) solution of Surface Volume Surface Electric Field Integral Equation (SVS- EFIE) is proposed in this thesis. The cross-section of the MTLs is discretized with higher order quadrilateral elements to reduce the error associated with the geometry representation. The unknown currents are approximated by high order polynomial basis functions for accurate representation of their sophisticated behaviour according to the skin- and proximity-effects. Memory requirement for the proposed method is shown to be substantially smaller than that of the HO Finite Element Method (FEM) due to discretization of only the MTLs cross-section and not the surrounding volume. Analogous SVS-EFIE is shown in the thesis to be solved with HO-MoM to calculate the scattered field with high accuracy inside 2-D dielectric scatterers of arbitrary shape under TM-polarization.Various obstacles in achieving error controlled HO-MoM solution of SVS-EFIE are overcome in this thesis. In order to get error controlled solution of the sought fields, singularity extraction is performed on 1-D and 2-D HO elements when calculating the integrals related to HO-MoM discretization. As the HO FEM must truncate its mesh within a certain region around the object of interest in order to perform one-to-one comparison of the fields computed using the HO- MoM solution of the SVS-EFIE against HO-FEM the same region of interest must be considered. In this work a grounded cylindrical cavity of large radius surrounding MTLs is introduced for truncation of the FEM mesh. To enforce the same boundary condition in the HO-MoM solution the Green’s function of the cylindrical cavity is analytically derived and used in the SVS-EFIE formulation.
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Keywords
Higher order Method of Moments, Singularity extraction, Green function of cylindrical cavity, Electromagnetic scattering