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Analysis-suitable G1 multi-patch parametrizations for C1 isogeometric spaces

hal.structure.identifierModélisation Mathématique pour l'Oncologie [MONC]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierUniversité de Bordeaux [UB]
dc.contributor.authorCOLLIN, Annabelle
hal.structure.identifierUniversità degli Studi di Pavia [Italia] = University of Pavia [Italy] = Université de Pavie [Italie] [UNIPV]
dc.contributor.authorSANGALLI, Giancarlo
hal.structure.identifierUniversity of Linz - Johannes Kepler Universität Linz [JKU]
dc.contributor.authorTAKACS, Thomas
dc.date.accessioned2024-04-04T03:12:45Z
dc.date.available2024-04-04T03:12:45Z
dc.date.issued2016-10-01
dc.identifier.issn0167-8396
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193894
dc.description.abstractEnOne key feature of isogeometric analysis is that it allows smooth shape functions. Indeed, when isogeometric spaces are constructed from p-degree splines (and extensions, such as NURBS), they enjoy up to C p1 continuity within each patch. However, global continuity beyond C 0 on so-called multi-patch geometries poses some significant diculties. In this work, we consider planar multi-patch domains that have a parametrization which is only C 0 at the patch interface. On such domains we study the h-refinement of C 1-continuous isogeometric spaces. These spaces in general do not have optimal approximation properties. The reason is that the C 1-continuity condition easily over-constrains the solution which is, in the worst cases, fully locked to linears at the patch interface. However, recently [21] has given numerical evidence that optimal convergence occurs for bilinear two-patch geometries and cubic (or higher degree) C 1 splines. This is the starting point of our study. We introduce the class of analysis-suitable G 1 geometry parametrizations, which includes piecewise bilinear parametrizations. We then analyze the structure of C 1 isogeometric spaces over analysis-suitable G 1 parametrizations and, by theoretical results and numerical testing, discuss their approximation properties. We also consider examples of geometry parametrizations that are not analysis-suitable, showing that in this case optimal convergence of C 1 isogeometric spaces is prevented.
dc.language.isoen
dc.publisherElsevier
dc.title.enAnalysis-suitable G1 multi-patch parametrizations for C1 isogeometric spaces
dc.typeArticle de revue
dc.subject.halMathématiques [math]
dc.identifier.arxiv1509.07619
bordeaux.journalComputer Aided Geometric Design
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01404076
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01404076v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Computer%20Aided%20Geometric%20Design&rft.date=2016-10-01&rft.eissn=0167-8396&rft.issn=0167-8396&rft.au=COLLIN,%20Annabelle&SANGALLI,%20Giancarlo&TAKACS,%20Thomas&rft.genre=article


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