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Article: A succinct way to diagonalize the translation matrix in three dimensions

TitleA succinct way to diagonalize the translation matrix in three dimensions
Authors
KeywordsIntegral Equation
Numerical Methods
Translation Matrix
Issue Date1997
PublisherJohn Wiley & Sons, Inc. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/37176
Citation
Microwave And Optical Technology Letters, 1997, v. 15 n. 3, p. 144-147 How to Cite?
AbstractThe diagonalization of the translation matrix is crucial in reducing the solution time in the fast multipole method. The translation matrix can be related, to the matrix representation of the translation operators in the translation group in group theory. Therefore, these matrices can be diagonalized with a proper choice of basis representation. Here, a different and succinct way to diagonalize the translation operator in three dimensions for the Helmholtz equation involving a general number of multipoles is demonstrated. The derivation is concise, and can be related to a set of similarity transforms equivalent to the change of basis representation for the translation group. The result can be used for scattering calculations related to the wave equation as found in electrodynamics, elastodynamics, and acoustics, where the fast multipole method is used. © 1997 John Wiley & Sons, Inc.
Persistent Identifierhttp://hdl.handle.net/10722/182577
ISSN
2015 Impact Factor: 0.545
2015 SCImago Journal Rankings: 0.372
References

 

DC FieldValueLanguage
dc.contributor.authorChew, WCen_US
dc.contributor.authorKoc, Sen_US
dc.contributor.authorSong, JMen_US
dc.contributor.authorLu, CCen_US
dc.contributor.authorMichielssen, Een_US
dc.date.accessioned2013-05-02T05:15:57Z-
dc.date.available2013-05-02T05:15:57Z-
dc.date.issued1997en_US
dc.identifier.citationMicrowave And Optical Technology Letters, 1997, v. 15 n. 3, p. 144-147en_US
dc.identifier.issn0895-2477en_US
dc.identifier.urihttp://hdl.handle.net/10722/182577-
dc.description.abstractThe diagonalization of the translation matrix is crucial in reducing the solution time in the fast multipole method. The translation matrix can be related, to the matrix representation of the translation operators in the translation group in group theory. Therefore, these matrices can be diagonalized with a proper choice of basis representation. Here, a different and succinct way to diagonalize the translation operator in three dimensions for the Helmholtz equation involving a general number of multipoles is demonstrated. The derivation is concise, and can be related to a set of similarity transforms equivalent to the change of basis representation for the translation group. The result can be used for scattering calculations related to the wave equation as found in electrodynamics, elastodynamics, and acoustics, where the fast multipole method is used. © 1997 John Wiley & Sons, Inc.en_US
dc.languageengen_US
dc.publisherJohn Wiley & Sons, Inc. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/37176en_US
dc.relation.ispartofMicrowave and Optical Technology Lettersen_US
dc.subjectIntegral Equationen_US
dc.subjectNumerical Methodsen_US
dc.subjectTranslation Matrixen_US
dc.titleA succinct way to diagonalize the translation matrix in three dimensionsen_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.scopuseid_2-s2.0-0031167993en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0031167993&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume15en_US
dc.identifier.issue3en_US
dc.identifier.spage144en_US
dc.identifier.epage147en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridChew, WC=36014436300en_US
dc.identifier.scopusauthoridKoc, S=7003829699en_US
dc.identifier.scopusauthoridSong, JM=7404788341en_US
dc.identifier.scopusauthoridLu, CC=7404804587en_US
dc.identifier.scopusauthoridMichielssen, E=7005196479en_US

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