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An enhanced volume integral equation method and augmented equivalence principle algorithm for low frequency problems

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Title: An enhanced volume integral equation method and augmented equivalence principle algorithm for low frequency problems
Author(s): Sun, Lin
Director of Research: Chew, Weng Cho
Doctoral Committee Chair(s): Chew, Weng Cho
Doctoral Committee Member(s): Jin, Jianming; Bernhard, Jennifer T.; Wong, Martin D.
Department / Program: Electrical & Computer Eng
Discipline: Electrical & Computer Engr
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Enhanced Volume Integral Equation Method Equivalence Principle Algorithm Augmentation Technique Low Frequency Problems
Abstract: Two techniques based on integral equation methods are addressed. Firstly, a novel volume integral equation method is proposed to characterize the scattering properties of dielectric objects involving inhomogeneous and anisotropic permittivity and permeability. Two algorithms are available: conventional method of moments and reciprocity preserving method. Both of them are applied to both the permittivity and permeability terms. Curl-conforming edge elements are used to model the electric field distributions. Integration by parts is applied to deal with the singularities at the boundary introduced by the discontinuities of the material properties. Duffy's method formulations are derived for all the surface and volume singular integrations. Moreover, the multilevel fast multipole algorithm (MLFMA) is utilized to accelerate the matrix vector product process for large problems. Representative numerical results are shown to be excellent. Secondly, the present equivalence principle algorithm (EPA) is augmented by introducing charge densities as extra unknowns. This helps to separate the vector potential term and scalar potential term and avoid the imbalance at low frequencies. The current continuity constraint is enforced in both the scattering operator and translation operator. These further form a new augmented EPA equation system. With this technique, the low-frequency breakdown of EPA is removed. The augmented system serves not only as a stable low-frequency method, but also as a substitute over the whole frequency band. The new scheme is verified by numerical examples.
Issue Date: 2010-05-14
URI: http://hdl.handle.net/2142/15564
Rights Information: Copyright 2010 Lin Sun
Date Available in IDEALS: 2010-05-14
2012-05-15
Date Deposited: May 2010
 

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