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Title: Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics
Author(s): Yan, Su
Advisor(s): Jin, Jianming
Department / Program: Electrical & Computer Eng
Discipline: Electrical & Computer Engr
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: M.S.
Genre: Thesis
Subject(s): Accuracy analysis
Buffa-Christiansen functions
extinction theorem
first-kind integral equations
identity operator
magnetic-field integral equation
method of weighted residuals
near-singularity extraction
N-Müller integral equations
numerical accuracy
Rayleigh-Ritz scheme
second-kind integral equations
testing scheme.
Abstract: In computational electromagnetics, the second-kind Fredholm integral equations (IEs) are known to have very fast iterative convergence but rather poor solution accuracy compared with the first-kind Fredholm integral equations. The loss of the numerical accuracy is mainly due to the discretization error of the identity operators involved in second-kind IEs. In the past decade, although much effort has been made to improve the numerical accuracy of the second-kind integral equations, no conclusive understandings and final resolutions are achieved. In this thesis, the widely used surface integral equations in computational electromagnetics are first presented along with the discussions of their respective mathematical and numerical properties. The integral operators involved in these integral equations are investigated in terms of their mathematical properties and numerical discretization strategies. Based on such discussions and investigations, a numerical scheme is presented to significantly suppress the discretization error of the identity operators by using the Buffa-Christiansen (BC) functions as the testing function, leading to much more accurate solutions to the second-kind integral equations for smooth objects in both perfect electric conductor (PEC) and dielectric cases, while maintaining their fast convergence properties. This technique is then generalized for generally shaped objects in both PEC and dielectric cases by using the BC functions as the testing functions, and by handling the near-singularities in the evaluation of the system matrix elements carefully. The extinction theorem is applied for accurate evaluation of the numerical errors in the calculation of scattering problems for generally shaped objects. Several examples are given to investigate and demonstrate the performance of the proposed techniques in the accuracy improvement of the second-kind surface integral equations in both PEC and dielectric cases. The reasons for the accuracy improvement are explained, and several important conclusive remarks are made.
Issue Date: 2012-09-18
URI: http://hdl.handle.net/2142/34442
Rights Information: Copyright 2012 Su Yan
Date Available in IDEALS: 2012-09-18
Date Deposited: 2012-08


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