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Article: Error analysis for the truncation of multipole expansion of vector Green's functions

TitleError analysis for the truncation of multipole expansion of vector Green's functions
Authors
Song, JChew, WC
KeywordsError Analysis
Fast Multipole Algorithms (Fma)
Vector Green's Functions
Issue Date2001
Citation
Ieee Microwave And Wireless Components Letters, 2001, v. 11 n. 7, p. 311-313 How to Cite?
DOI: http://dx.doi.org/10.1109/7260.933781
AbstractOne of the most important mathematical formulas in fast multipole algorithms (FMA) is the addition theorem. In the numerical implementation of the addition theorem, the infinite series should be truncated. In this paper, the number of terms needed for the scalar Green's function is derived, and the error analysis for the truncation error in the multipole expansion of the vector Green's functions is given. We have found that the error term in vector Green's functions is proportional to 1/R. If the scalar Green's function is truncated at the L-th term and the relative error is ε, then the relative error in the dyadic Green's function is ε/4, if it is truncated at the (L + 2)-th term. For the vector Green's function related to MFIE, the relative error is ε/2 if it is truncated at the (L + 1)-th term.
Persistent Identifierhttp://hdl.handle.net/10722/182656
ISSN
1531-1309
2021 Impact Factor: 2.719
2020 SCImago Journal Rankings: 0.940
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorSong, Jen_US
dc.contributor.authorChew, WCen_US
dc.date.accessioned2013-05-02T05:16:18Z-
dc.date.available2013-05-02T05:16:18Z-
dc.date.issued2001en_US
dc.identifier.citationIeee Microwave And Wireless Components Letters, 2001, v. 11 n. 7, p. 311-313en_US
dc.identifier.issn1531-1309en_US
dc.identifier.urihttp://hdl.handle.net/10722/182656-
dc.description.abstractOne of the most important mathematical formulas in fast multipole algorithms (FMA) is the addition theorem. In the numerical implementation of the addition theorem, the infinite series should be truncated. In this paper, the number of terms needed for the scalar Green's function is derived, and the error analysis for the truncation error in the multipole expansion of the vector Green's functions is given. We have found that the error term in vector Green's functions is proportional to 1/R. If the scalar Green's function is truncated at the L-th term and the relative error is ε, then the relative error in the dyadic Green's function is ε/4, if it is truncated at the (L + 2)-th term. For the vector Green's function related to MFIE, the relative error is ε/2 if it is truncated at the (L + 1)-th term.en_US
dc.languageengen_US
dc.relation.ispartofIEEE Microwave and Wireless Components Lettersen_US
dc.subjectError Analysisen_US
dc.subjectFast Multipole Algorithms (Fma)en_US
dc.subjectVector Green's Functionsen_US
dc.titleError analysis for the truncation of multipole expansion of vector Green's functionsen_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.doi10.1109/7260.933781en_US
dc.identifier.scopuseid_2-s2.0-0035401652en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0035401652&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume11en_US
dc.identifier.issue7en_US
dc.identifier.spage311en_US
dc.identifier.epage313en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridSong, J=7404788341en_US
dc.identifier.scopusauthoridChew, WC=36014436300en_US
dc.identifier.issnl1531-1309-

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