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Article: A novel approach for evaluating hypersingular and strongly singular surface integrals in electromagnetics

TitleA novel approach for evaluating hypersingular and strongly singular surface integrals in electromagnetics
Authors
KeywordsElectromagnetic Scattering
Integral Equations
Singular Integrals
Stokes' Theorem
Issue Date2010
Citation
Ieee Transactions On Antennas And Propagation, 2010, v. 58 n. 11, p. 3593-3601 How to Cite?
AbstractSolving electromagnetic (EM) problems by integral equation methods requires an accurate and efficient treatment for the singular integral kernels related to the Green's function. For surface integral equations (SIEs), there are L and K operators which include hypersingular integrals (HSIs) and strongly singular integrals (SSIs), respectively. The HSIs are generated from the double gradient of the Green's function while the SSIs come from the single gradient of the Green's function. Although the HSIs could be reduced to weakly singular integrals (WSIs) in the method of moments (MoM) implementation with divergence conforming basis function such as the Rao-Wilton-Glisson (RWG) basis function, they do appear in Nystrm method (NM) or boundary element method (BEM) and one has to tackle them. The SSIs always exist in the K operator and could also exist in the L operator when the testing function is not the RWG-like basis function. The treatment for the HSIs and SSIs is essential because they have a significant influence on the numerical solutions. There have been many publications dealing with the singular integrals, but they mainly focus on the WISs or SSIs, and the HSIs were seldom addressed. In this work, we develop a novel approach for evaluating those HSIs and SSIs based on the Stokes' theorem. The derived formulas are much simpler and more friendly in implementation since no polar coordinates or extra coordinate transformation are involved. Numerical experiments are presented to demonstrate the effectiveness of the approach. © 2010 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/182776
ISSN
2015 Impact Factor: 2.053
2015 SCImago Journal Rankings: 2.130
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorTong, MSen_US
dc.contributor.authorChew, WCen_US
dc.date.accessioned2013-05-02T05:16:48Z-
dc.date.available2013-05-02T05:16:48Z-
dc.date.issued2010en_US
dc.identifier.citationIeee Transactions On Antennas And Propagation, 2010, v. 58 n. 11, p. 3593-3601en_US
dc.identifier.issn0018-926Xen_US
dc.identifier.urihttp://hdl.handle.net/10722/182776-
dc.description.abstractSolving electromagnetic (EM) problems by integral equation methods requires an accurate and efficient treatment for the singular integral kernels related to the Green's function. For surface integral equations (SIEs), there are L and K operators which include hypersingular integrals (HSIs) and strongly singular integrals (SSIs), respectively. The HSIs are generated from the double gradient of the Green's function while the SSIs come from the single gradient of the Green's function. Although the HSIs could be reduced to weakly singular integrals (WSIs) in the method of moments (MoM) implementation with divergence conforming basis function such as the Rao-Wilton-Glisson (RWG) basis function, they do appear in Nystrm method (NM) or boundary element method (BEM) and one has to tackle them. The SSIs always exist in the K operator and could also exist in the L operator when the testing function is not the RWG-like basis function. The treatment for the HSIs and SSIs is essential because they have a significant influence on the numerical solutions. There have been many publications dealing with the singular integrals, but they mainly focus on the WISs or SSIs, and the HSIs were seldom addressed. In this work, we develop a novel approach for evaluating those HSIs and SSIs based on the Stokes' theorem. The derived formulas are much simpler and more friendly in implementation since no polar coordinates or extra coordinate transformation are involved. Numerical experiments are presented to demonstrate the effectiveness of the approach. © 2010 IEEE.en_US
dc.languageengen_US
dc.relation.ispartofIEEE Transactions on Antennas and Propagationen_US
dc.subjectElectromagnetic Scatteringen_US
dc.subjectIntegral Equationsen_US
dc.subjectSingular Integralsen_US
dc.subjectStokes' Theoremen_US
dc.titleA novel approach for evaluating hypersingular and strongly singular surface integrals in electromagneticsen_US
dc.typeArticleen_US
dc.identifier.emailChew, WC: wcchew@hku.hken_US
dc.identifier.authorityChew, WC=rp00656en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1109/TAP.2010.2071370en_US
dc.identifier.scopuseid_2-s2.0-78149441153en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-78149441153&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume58en_US
dc.identifier.issue11en_US
dc.identifier.spage3593en_US
dc.identifier.epage3601en_US
dc.identifier.isiWOS:000283940100019-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridTong, MS=11839685700en_US
dc.identifier.scopusauthoridChew, WC=36014436300en_US

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