Analysis-suitable G1 multi-patch parametrizations for C1 isogeometric spaces
| hal.structure.identifier | Modélisation Mathématique pour l'Oncologie [MONC] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Université de Bordeaux [UB] | |
| dc.contributor.author | COLLIN, Annabelle | |
| hal.structure.identifier | Università degli Studi di Pavia [Italia] = University of Pavia [Italy] = Université de Pavie [Italie] [UNIPV] | |
| dc.contributor.author | SANGALLI, Giancarlo | |
| hal.structure.identifier | University of Linz - Johannes Kepler Universität Linz [JKU] | |
| dc.contributor.author | TAKACS, Thomas | |
| dc.date.accessioned | 2024-04-04T03:12:45Z | |
| dc.date.available | 2024-04-04T03:12:45Z | |
| dc.date.issued | 2016-10-01 | |
| dc.identifier.issn | 0167-8396 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193894 | |
| dc.description.abstractEn | One 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.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | Analysis-suitable G1 multi-patch parametrizations for C1 isogeometric spaces | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math] | |
| dc.identifier.arxiv | 1509.07619 | |
| bordeaux.journal | Computer Aided Geometric Design | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01404076 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01404076v1 | |
| bordeaux.COinS | ctx_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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