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Article: Hybrid-trefftz six-node triangular finite element models for helmholtz problem

TitleHybrid-trefftz six-node triangular finite element models for helmholtz problem
Authors
KeywordsDisplacement-frame
Finite element
Helmholtz
Hybrid-trefftz
Triangular
Issue Date2010
PublisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00466/index.htm
Citation
Computational Mechanics, 2010, v. 46 n. 3, p. 455-470 How to Cite?
AbstractIn this paper, six-node hybrid-Trefftz triangular finite element models which can readily be incorporated into the standard finite element program framework in the form of additional element subroutines are devised via a hybrid variational principle for Helmholtz problem. In these elements, domain and boundary variables are independently assumed. The former is truncated from the Trefftz solution sets and the latter is obtained by the standard polynomial-based nodal interpolation. The equality of the two variables are enforced along the element boundary. Both the plane-wave solutions and Bessel solutions are employed to construct the domain variable. For full rankness of the element matrix, a minimal of six domain modes are required. By using local coordinates and directions, rank sufficient and invariant elements with six plane-wave modes, six Bessel solution modes and seven Bessel solution modes are devised. Numerical studies indicate that the hybrid-Trefftz elements are typically 50% less erroneous than their continuous Galerkin element counterpart.
Persistent Identifierhttp://hdl.handle.net/10722/124021
ISSN
2015 Impact Factor: 2.639
2015 SCImago Journal Rankings: 2.126
ISI Accession Number ID
Funding AgencyGrant Number
Hong Kong Research Grant Council GRFHKU 7167 08E
Funding Information:

The present work is supported by the Hong Kong Research Grant Council GRF Grant HKU 7167 08E. The authors are grateful to Professor Clark Kimberling for pointing out that the points C in Figure 3(d) and 3(e) are commonly known as Fermat points (also known as Torricelli points and the 1st isogonic centers) of the triangles formed by the corner and side nodes, respectively [42].

References

 

DC FieldValueLanguage
dc.contributor.authorSze, KYen_HK
dc.contributor.authorLiu, GHen_HK
dc.date.accessioned2010-10-19T04:33:49Z-
dc.date.available2010-10-19T04:33:49Z-
dc.date.issued2010en_HK
dc.identifier.citationComputational Mechanics, 2010, v. 46 n. 3, p. 455-470en_HK
dc.identifier.issn0178-7675en_HK
dc.identifier.urihttp://hdl.handle.net/10722/124021-
dc.description.abstractIn this paper, six-node hybrid-Trefftz triangular finite element models which can readily be incorporated into the standard finite element program framework in the form of additional element subroutines are devised via a hybrid variational principle for Helmholtz problem. In these elements, domain and boundary variables are independently assumed. The former is truncated from the Trefftz solution sets and the latter is obtained by the standard polynomial-based nodal interpolation. The equality of the two variables are enforced along the element boundary. Both the plane-wave solutions and Bessel solutions are employed to construct the domain variable. For full rankness of the element matrix, a minimal of six domain modes are required. By using local coordinates and directions, rank sufficient and invariant elements with six plane-wave modes, six Bessel solution modes and seven Bessel solution modes are devised. Numerical studies indicate that the hybrid-Trefftz elements are typically 50% less erroneous than their continuous Galerkin element counterpart.en_HK
dc.languageengen_HK
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00466/index.htmen_HK
dc.relation.ispartofComputational Mechanicsen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong Licenseen_HK
dc.subjectDisplacement-frameen_HK
dc.subjectFinite elementen_HK
dc.subjectHelmholtzen_HK
dc.subjectHybrid-trefftzen_HK
dc.subjectTriangularen_HK
dc.titleHybrid-trefftz six-node triangular finite element models for helmholtz problemen_HK
dc.typeArticleen_HK
dc.identifier.emailSze, KY:szeky@graduate.hku.hken_HK
dc.identifier.authoritySze, KY=rp00171en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1007/s00466-010-0494-0en_HK
dc.identifier.scopuseid_2-s2.0-77954959524en_HK
dc.identifier.hkuros191225-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77954959524&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume46en_HK
dc.identifier.issue3en_HK
dc.identifier.spage455en_HK
dc.identifier.epage470en_HK
dc.identifier.eissn1432-0924en_HK
dc.identifier.isiWOS:000277937300007-
dc.publisher.placeGermanyen_HK
dc.description.otherSpringer Open Choice, 01 Dec 2010-
dc.identifier.scopusauthoridSze, KY=7006735060en_HK
dc.identifier.scopusauthoridLiu, GH=35320145100en_HK
dc.identifier.citeulike7017474-

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