Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

You searched for subject:(Rayleigh Ritz scheme). One record found.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters


University of Illinois – Urbana-Champaign

1. Yan, Su. Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics.

Degree: MS, 1200, 2012, University of Illinois – Urbana-Champaign

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. Advisors/Committee Members: Jin, Jianming (advisor).

Subjects/Keywords: 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.

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Yan, S. (2012). Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics. (Thesis). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34442

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Yan, Su. “Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics.” 2012. Thesis, University of Illinois – Urbana-Champaign. Accessed February 24, 2020. http://hdl.handle.net/2142/34442.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Yan, Su. “Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics.” 2012. Web. 24 Feb 2020.

Vancouver:

Yan S. Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics. [Internet] [Thesis]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Feb 24]. Available from: http://hdl.handle.net/2142/34442.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Yan S. Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics. [Thesis]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34442

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.