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dc.contributor.authorBeck, Joakim
dc.contributor.authorSangalli, Giancarlo
dc.contributor.authorTamellini, Lorenzo
dc.date.accessioned2018-03-06T06:50:08Z
dc.date.available2018-03-06T06:50:08Z
dc.date.issued2018-02-28
dc.identifier.citationBeck J, Sangalli G, Tamellini L (2018) A sparse-grid isogeometric solver. Computer Methods in Applied Mechanics and Engineering. Available: http://dx.doi.org/10.1016/j.cma.2018.02.017.
dc.identifier.issn0045-7825
dc.identifier.doi10.1016/j.cma.2018.02.017
dc.identifier.urihttp://hdl.handle.net/10754/627225
dc.description.abstractIsogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90’s in the context of the approximation of high-dimensional PDEs.The tests that we report show that, in accordance to the literature, a sparse-grid construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
dc.description.sponsorshipGiancarlo Sangalli and Lorenzo Tamellini were partially supported by the European Research Council through the FP7 ERC consolidator grant n. 616563HIGEOM and by the GNCS 2017 project “Simulazione numerica di problemi di Interazione Fluido-Struttura (FSI) con metodi agli elementi finiti ed isogeometrici”. Lorenzo Tamellini also received support from the scholarship “Isogeometric method” granted by the Università di Pavia and by the European Union’s Horizon 2020 research and innovation program through the grant no. 680448 CAxMan. Joakim Beck received support from the KAUST CRG3 Award Ref:2281 and the KAUST CRG4 Award Ref:2584.
dc.publisherElsevier BV
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0045782518300975
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, 28 February 2018. DOI: 10.1016/j.cma.2018.02.017. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectIsogeometric analysis
dc.subjectB-splines
dc.subjectNURBS
dc.subjectSparse grids
dc.subjectCombination technique
dc.titleA sparse-grid isogeometric solver
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalComputer Methods in Applied Mechanics and Engineering
dc.eprint.versionPost-print
dc.contributor.institutionConsiglio Nazionale delle Ricerche - Istituto di Matematica Applicata e Tecnologie Informatiche “E. Magenes” (CNR-IMATI), Via Ferrata 1, 27100, Pavia, Italy
dc.contributor.institutionDipartimento di Matematica “F. Casorati”, Università di Pavia, Via Ferrata 5, 27100, Pavia, Italy
kaust.personBeck, Joakim
kaust.grant.numberCRG3 Award Ref:2281
kaust.grant.numberCRG4 Award Ref:2584
refterms.dateFOA2020-02-28T00:00:00Z
dc.date.published-online2018-02-28
dc.date.published-print2018-06


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