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Article: Generation of tetrahedral mesh of variable element size by sphere packing over an unbounded 3D domain

TitleGeneration of tetrahedral mesh of variable element size by sphere packing over an unbounded 3D domain
Authors
KeywordsDelaunay triangulation
Descend by rotation
Frontal surface
Sphere packing
Tetrahedral mesh
Unbounded 3D domain
Issue Date2005
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cma
Citation
Computer Methods In Applied Mechanics And Engineering, 2005, v. 194 n. 48-49, p. 5002-5018 How to Cite?
AbstractThis paper describes an algorithm for the generation of tetrahedral mesh of specified element size over an unbounded three-dimensional domain. Starting from an arbitrary point in space (defined as the origin) and guided by the concept of advancing front, spheres of size compatible with the specified element size are packed tightly together one by one to form a cluster of spheres of different sizes. The compactness of the cluster of spheres is achieved by packing spheres at a site closest to the origin in a densest manner with tangent but no overlapping with as many other spheres as possible. In view of these criteria, a rotational mechanism between spheres is innovated, which allows the newly inserted sphere to follow the path by rotation between existing spheres until the lowest point is reached. The centres of the packing spheres provide ideal locations for Delaunay point insertion to form a triangulation of tetrahedral elements of size compatible with the specified value. Spheres of random size distribution or of size specified by a node spacing function are packed by the proposed algorithm. In all test examples, high-quality tetrahedral elements of size consistent with the specified node spacing are generated. The process is fast and robust, and the time complexity for mesh generation is expected to be almost linear; however, in the present implementation, a quasi-linear time relationship is observed as a search for the nearest node on the front is proposed in the sphere packing process. The memory requirement has been kept to a minimum as no additional data structure other than the adjacency relationship of the tetrahedral elements as required by the Delaunay triangulation is stored. The structure of the advancing frontal surface needs not be explicitly constructed nor updated as it is simply not required in the sphere packing process. © 2005 Elsevier B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/70906
ISSN
2015 Impact Factor: 3.467
2015 SCImago Journal Rankings: 2.952
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorLo, SHen_HK
dc.contributor.authorWang, WXen_HK
dc.date.accessioned2010-09-06T06:27:10Z-
dc.date.available2010-09-06T06:27:10Z-
dc.date.issued2005en_HK
dc.identifier.citationComputer Methods In Applied Mechanics And Engineering, 2005, v. 194 n. 48-49, p. 5002-5018en_HK
dc.identifier.issn0045-7825en_HK
dc.identifier.urihttp://hdl.handle.net/10722/70906-
dc.description.abstractThis paper describes an algorithm for the generation of tetrahedral mesh of specified element size over an unbounded three-dimensional domain. Starting from an arbitrary point in space (defined as the origin) and guided by the concept of advancing front, spheres of size compatible with the specified element size are packed tightly together one by one to form a cluster of spheres of different sizes. The compactness of the cluster of spheres is achieved by packing spheres at a site closest to the origin in a densest manner with tangent but no overlapping with as many other spheres as possible. In view of these criteria, a rotational mechanism between spheres is innovated, which allows the newly inserted sphere to follow the path by rotation between existing spheres until the lowest point is reached. The centres of the packing spheres provide ideal locations for Delaunay point insertion to form a triangulation of tetrahedral elements of size compatible with the specified value. Spheres of random size distribution or of size specified by a node spacing function are packed by the proposed algorithm. In all test examples, high-quality tetrahedral elements of size consistent with the specified node spacing are generated. The process is fast and robust, and the time complexity for mesh generation is expected to be almost linear; however, in the present implementation, a quasi-linear time relationship is observed as a search for the nearest node on the front is proposed in the sphere packing process. The memory requirement has been kept to a minimum as no additional data structure other than the adjacency relationship of the tetrahedral elements as required by the Delaunay triangulation is stored. The structure of the advancing frontal surface needs not be explicitly constructed nor updated as it is simply not required in the sphere packing process. © 2005 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.rightsComputer Methods in Applied Mechanics and Engineering. Copyright © Elsevier BV.en_HK
dc.subjectDelaunay triangulationen_HK
dc.subjectDescend by rotationen_HK
dc.subjectFrontal surfaceen_HK
dc.subjectSphere packingen_HK
dc.subjectTetrahedral meshen_HK
dc.subjectUnbounded 3D domainen_HK
dc.titleGeneration of tetrahedral mesh of variable element size by sphere packing over an unbounded 3D domainen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0045-7825&volume=194&issue=48-49&spage=5002&epage=5018&date=2005&atitle=Generation+of+tetrahedral+mesh+of+variable+element+size+by+sphere+packing+over+an+unbounded+3D+domainen_HK
dc.identifier.emailLo, SH:hreclsh@hkucc.hku.hken_HK
dc.identifier.authorityLo, SH=rp00223en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.cma.2004.11.022en_HK
dc.identifier.scopuseid_2-s2.0-24044449651en_HK
dc.identifier.hkuros103719en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-24044449651&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume194en_HK
dc.identifier.issue48-49en_HK
dc.identifier.spage5002en_HK
dc.identifier.epage5018en_HK
dc.identifier.isiWOS:000231860700008-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridLo, SH=7401542444en_HK
dc.identifier.scopusauthoridWang, WX=8695906800en_HK

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