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Article: Four- and eight-node hybrid-Trefftz quadrilateral finite element models for helmholtz problem

TitleFour- and eight-node hybrid-Trefftz quadrilateral finite element models for helmholtz problem
Authors
KeywordsBessel
Finite element
Helmholtz
Hybrid-Trefftz
Plane wave
Quadrilateral
Issue Date2010
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cma
Citation
Computer Methods In Applied Mechanics And Engineering, 2010, v. 199 n. 9-12, p. 598-614 How to Cite?
AbstractIn this paper, four- and eight-node quadrilateral finite element models which can readily be incorporated into the standard finite element program framework are devised for plane Helmholtz problems. In these models, frame (boundary) and domain approximations are defined. The former is obtained by nodal interpolation and the latter is truncated from Trefftz solution sets. The equality of the two approximations are enforced along the element boundary. Both the Bessel and plane wave solutions are employed to construct the domain approximation. For full rankness, a minimal of four and eight domain modes are required for the four- and eight-node elements, respectively. By using local coordinates and directions, rank sufficient and invariant elements with minimal and close to minimal numbers of domain approximation modes are devised. In most tests, the proposed hybrid-Trefftz elements with the same number of nodes yield close solutions. In absolute majority of the tests, the proposed elements are considerably more accurate than their single-field counterparts. © 2009 Elsevier B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/124827
ISSN
2015 Impact Factor: 3.467
2015 SCImago Journal Rankings: 2.952
ISI Accession Number ID
Funding AgencyGrant Number
Research Grant Council of Hong KongHKU 716708E
Funding Information:

This work is funded by the Research Grant Council of Hong Kong under grant HKU 716708E. The correspondence author is grateful to Professor Isaac Harari for the useful discussions during the Trefftz 2008 Workshop held in Leuven, Belgium. Special thanks are given to the reviewers whose comments and suggestions are valuable for enhancing the quality of this paper.

References
Grants

 

DC FieldValueLanguage
dc.contributor.authorSze, KYen_HK
dc.contributor.authorLiu, GHen_HK
dc.contributor.authorFan, Hen_HK
dc.date.accessioned2010-10-31T10:56:26Z-
dc.date.available2010-10-31T10:56:26Z-
dc.date.issued2010en_HK
dc.identifier.citationComputer Methods In Applied Mechanics And Engineering, 2010, v. 199 n. 9-12, p. 598-614en_HK
dc.identifier.issn0045-7825en_HK
dc.identifier.urihttp://hdl.handle.net/10722/124827-
dc.description.abstractIn this paper, four- and eight-node quadrilateral finite element models which can readily be incorporated into the standard finite element program framework are devised for plane Helmholtz problems. In these models, frame (boundary) and domain approximations are defined. The former is obtained by nodal interpolation and the latter is truncated from Trefftz solution sets. The equality of the two approximations are enforced along the element boundary. Both the Bessel and plane wave solutions are employed to construct the domain approximation. For full rankness, a minimal of four and eight domain modes are required for the four- and eight-node elements, respectively. By using local coordinates and directions, rank sufficient and invariant elements with minimal and close to minimal numbers of domain approximation modes are devised. In most tests, the proposed hybrid-Trefftz elements with the same number of nodes yield close solutions. In absolute majority of the tests, the proposed elements are considerably more accurate than their single-field counterparts. © 2009 Elsevier B.V. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cmaen_HK
dc.relation.ispartofComputer Methods in Applied Mechanics and Engineeringen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectBesselen_HK
dc.subjectFinite elementen_HK
dc.subjectHelmholtzen_HK
dc.subjectHybrid-Trefftzen_HK
dc.subjectPlane waveen_HK
dc.subjectQuadrilateralen_HK
dc.titleFour- and eight-node hybrid-Trefftz quadrilateral finite element models for helmholtz problemen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0045-7825&volume=199&issue=9-12&spage=598&epage=614&date=2010&atitle=Four-+and+eight-node+hybrid-Trefftz+quadrilateral+finite+element+models+for+helmholtz+problem-
dc.identifier.emailSze, KY:szeky@graduate.hku.hken_HK
dc.identifier.authoritySze, KY=rp00171en_HK
dc.description.naturepostprint-
dc.identifier.doi10.1016/j.cma.2009.10.012en_HK
dc.identifier.scopuseid_2-s2.0-73449088343en_HK
dc.identifier.hkuros175441en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-73449088343&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume199en_HK
dc.identifier.issue9-12en_HK
dc.identifier.spage598en_HK
dc.identifier.epage614en_HK
dc.identifier.isiWOS:000274572600015-
dc.publisher.placeNetherlandsen_HK
dc.relation.projectDevelopment of wave-based finite element families for plane, axial symmetric and three-dimensional Helmholtz problems.-
dc.identifier.scopusauthoridSze, KY=7006735060en_HK
dc.identifier.scopusauthoridLiu, GH=35320145100en_HK
dc.identifier.scopusauthoridFan, H=7402553644en_HK
dc.identifier.citeulike6065175-

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