Improved Double-Arctan Transformation for the Stable Evaluation of Nearly Hypersingular Integrals in SIE

Ren, Y; Chen, Y; Liu, Y; Meng, M

Improved Double-Arctan Transformation for the Stable Evaluation of Nearly Hypersingular Integrals in SIE

Ren, Y Chen, Y Liu, Y

Meng, M

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Publisher:: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Publication Type:: Journal Article
Citation:: IEEE Transactions on Antennas and Propagation, 2020, 68, (9), pp. 6850-6855
Issue Date:: 2020-09-01

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Field	Value	Language
dc.contributor.author	Ren, Y
dc.contributor.author	Chen, Y
dc.contributor.author	Liu, Y https://orcid.org/0000-0001-5466-0184
dc.contributor.author	Meng, M
dc.date.accessioned	2021-02-12T22:38:02Z
dc.date.available	2021-02-12T22:38:02Z
dc.date.issued	2020-09-01
dc.identifier.citation	IEEE Transactions on Antennas and Propagation, 2020, 68, (9), pp. 6850-6855
dc.identifier.issn	0018-926X
dc.identifier.issn	1558-2221
dc.identifier.uri	http://hdl.handle.net/10453/146060
dc.description.abstract	© 1963-2012 IEEE. The evaluation of singular or near-singular integrals is one of the key techniques in the integral equation method. Based on the previously proposed double-arctan transformation (DAT) for the nearly hypersingular integrals in curved surface modeling, this work presents new transformation methods to improve the accuracy and stability of DAT for the following two situations, i.e., the field point is: 1) extremely close to the source surface and 2) extremely close to the boundary of the source surface. The original DAT fails in these two situations and, hence, limits its applications. The reasons that cause such an instability are studied. Two additional transformations are introduced to make the DAT stable for these two cases. For situation I, the exponential transformation (ET) is adopted to optimize the distribution of the Gaussian quadrature points. For situation II, the shape-function transformation (SFT) is further proposed to remove the nearly angular singularity. We denote the newly developed DAT with ET and SFT as the improved DAT (IDAT) in this communication. The typical testing cases are provided to validate the proposed method.
dc.language	English
dc.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
dc.relation.ispartof	IEEE Transactions on Antennas and Propagation
dc.relation.isbasedon	10.1109/TAP.2020.2985504
dc.rights	© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.	en_US
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0906 Electrical and Electronic Engineering, 1005 Communications Technologies
dc.subject.classification	Networking & Telecommunications
dc.title	Improved Double-Arctan Transformation for the Stable Evaluation of Nearly Hypersingular Integrals in SIE
dc.type	Journal Article
utslib.citation.volume	68
utslib.for	0906 Electrical and Electronic Engineering
utslib.for	1005 Communications Technologies
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
pubs.organisational-group	/University of Technology Sydney
utslib.copyright.status	closed_access	*
dc.date.updated	2021-02-12T22:37:29Z
pubs.issue	9
pubs.publication-status	Published
pubs.volume	68
utslib.citation.issue	9

Abstract:

© 1963-2012 IEEE. The evaluation of singular or near-singular integrals is one of the key techniques in the integral equation method. Based on the previously proposed double-arctan transformation (DAT) for the nearly hypersingular integrals in curved surface modeling, this work presents new transformation methods to improve the accuracy and stability of DAT for the following two situations, i.e., the field point is: 1) extremely close to the source surface and 2) extremely close to the boundary of the source surface. The original DAT fails in these two situations and, hence, limits its applications. The reasons that cause such an instability are studied. Two additional transformations are introduced to make the DAT stable for these two cases. For situation I, the exponential transformation (ET) is adopted to optimize the distribution of the Gaussian quadrature points. For situation II, the shape-function transformation (SFT) is further proposed to remove the nearly angular singularity. We denote the newly developed DAT with ET and SFT as the improved DAT (IDAT) in this communication. The typical testing cases are provided to validate the proposed method.

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http://hdl.handle.net/10453/146060