Exploring Matrix Generation Strategies in Isogeometric Analysis

Angelos Mantzaflaris 1 Bert Jüttler 2
1 RICAM - Johann Radon Institute for Computational and Applied Mathematics
2 Institute of Applied Geometry [Linz]
Abstract : An important step in simulation via isogeometric analysis (IGA) is the assembly step, where the coefficients of the final linear system are generated. Typically, these coefficients are integrals of products of shape functions and their derivatives. Similarly to the finite element analysis (FEA), the standard choice for integral evaluation in IGA is Gaussian quadrature. Recent developments propose different quadrature rules, that reduce the number of quadrature points and weights used. We experiment with the existing methods for matrix generation. Furthermore we propose a new, quadrature-free approach, based on interpolation of the geometry factor and fast look-up operations for values of B-spline integrals. Our method builds upon the observation that exact integration is not required to achieve the optimal convergence rate of the solution. In particular, it suffices to generate the linear system within the order of accuracy matching the approximation order of the discretization space. We demonstrate that the best strategy is one that follows the above principle, resulting in expected accuracy and improved computational time.
Keywords : isogeometric analysis stiffness matrix mass matrix numerical integration quadrature
Type de document :
Chapitre d'ouvrage
Michael Floater, Tom Lyche, Marie-Laurence Mazure, Knut Mørken, Larry L. Schumaker. Mathematical Methods for Curves and Surfaces, 8177, Springer, pp.364-382, 2014, 978-3-642-54381-4. 〈10.1007/978-3-642-54382-1〉
Liste complète des métadonnées

Littérature citée [21 références]  Voir  Masquer  Télécharger
https://hal.inria.fr/hal-00816141
Contributeur : Angelos Mantzaflaris <>
Soumis le : vendredi 19 avril 2013 - 19:48:45
Dernière modification le : lundi 23 juin 2014 - 20:27:32
Document(s) archivé(s) le : lundi 3 avril 2017 - 07:56:25

Fichier

oslo_paper_2012.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Angelos Mantzaflaris, Bert Jüttler. Exploring Matrix Generation Strategies in Isogeometric Analysis. Michael Floater, Tom Lyche, Marie-Laurence Mazure, Knut Mørken, Larry L. Schumaker. Mathematical Methods for Curves and Surfaces, 8177, Springer, pp.364-382, 2014, 978-3-642-54381-4. 〈10.1007/978-3-642-54382-1〉. 〈hal-00816141〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

173

Téléchargements de fichiers

257

Contact


archive-ouverte@inria.fr