A sparse-grid isogeometric solver

Handle URI:
http://hdl.handle.net/10754/627225
Title:
A sparse-grid isogeometric solver
Authors:
Beck, Joakim; Sangalli, Giancarlo; Tamellini, Lorenzo
Abstract:
Isogeometric 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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Beck 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.
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
KAUST Grant Number:
CRG3 Award Ref:2281; CRG4 Award Ref:2584
Issue Date:
28-Feb-2018
DOI:
10.1016/j.cma.2018.02.017
Type:
Article
ISSN:
0045-7825
Sponsors:
Giancarlo 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.
Additional Links:
http://www.sciencedirect.com/science/article/pii/S0045782518300975
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBeck, Joakimen
dc.contributor.authorSangalli, Giancarloen
dc.contributor.authorTamellini, Lorenzoen
dc.date.accessioned2018-03-06T06:50:08Z-
dc.date.available2018-03-06T06:50:08Z-
dc.date.issued2018-02-28en
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.en
dc.identifier.issn0045-7825en
dc.identifier.doi10.1016/j.cma.2018.02.017en
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.en
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.en
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0045782518300975en
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/en
dc.subjectIsogeometric analysisen
dc.subjectB-splinesen
dc.subjectNURBSen
dc.subjectSparse gridsen
dc.subjectCombination techniqueen
dc.titleA sparse-grid isogeometric solveren
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.eprint.versionPost-printen
dc.contributor.institutionConsiglio Nazionale delle Ricerche - Istituto di Matematica Applicata e Tecnologie Informatiche “E. Magenes” (CNR-IMATI), Via Ferrata 1, 27100, Pavia, Italyen
dc.contributor.institutionDipartimento di Matematica “F. Casorati”, Università di Pavia, Via Ferrata 5, 27100, Pavia, Italyen
kaust.authorBeck, Joakimen
kaust.grant.numberCRG3 Award Ref:2281en
kaust.grant.numberCRG4 Award Ref:2584en
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