IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains

Beck, Joakim; Tamellini, Lorenzo; Tempone, Raul

dc.contributor.author	Beck, Joakim
dc.contributor.author	Tamellini, Lorenzo
dc.contributor.author	Tempone, Raul
dc.date.accessioned	2019-05-06T08:05:34Z
dc.date.available	2019-01-10T13:54:33Z
dc.date.available	2019-05-06T08:05:34Z
dc.date.issued	2019-03-28
dc.identifier.citation	Beck J, Tamellini L, Tempone R (2019) IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains. Computer Methods in Applied Mechanics and Engineering 351: 330–350. Available: http://dx.doi.org/10.1016/j.cma.2019.03.042.
dc.identifier.issn	0045-7825
dc.identifier.doi	10.1016/j.cma.2019.03.042
dc.identifier.uri	http://hdl.handle.net/10754/630793
dc.description.abstract	This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis (IGA) techniques. Introducing IGA solvers to the MISC algorithm is very natural since they are tensor-based PDE solvers, which are precisely what is required by the MISC machinery. Moreover, the combination-technique formulation of MISC allows the straightforward reuse of existing implementations of IGA solvers. We present numerical results to showcase the effectiveness of the proposed approach.
dc.description.sponsorship	The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Uncertainty quantification for complex systems: theory and methodologies” supported by EPSRC, UK Grant No. EP/K032208/1, where work on this paper was undertaken. Part of this research was carried out while the authors visited the Banff International Research Station for Mathematical Innovation and Discovery (BIRS), for the workshop “Computational Uncertainty Quantification” in October 2017 (https://www.birs.ca/events/2017/5-day-workshops/17w5072) organized by Serge Prudhomme, Roger Ghanem, Mohammad Motamed, and Raúl Tempone. The hospitality and support of BIRS is acknowledged with gratitude. This work was supported by the KAUST, Saudi Arabia Office of Sponsored Research (OSR) under award numbers URF/1/2281-01-01 and URF/1/2584-01-01 in the KAUST Competitive Research Grants Program-Rounds 3 and 4, respectively. Lorenzo Tamellini also received support from the European Union's Horizon 2020 research and innovation program through the Grant No. 680448 “CAxMan”, and by the GNCS 2018 project “Metodi non conformi per equazioni alle derivate parziali”.
dc.publisher	Elsevier BV
dc.relation.ispartofseries	ArXiv e-prints
dc.relation.url	https://www.sciencedirect.com/science/article/pii/S0045782519301811
dc.rights	NOTICE: 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, [351, , (2019-03-28)] DOI: 10.1016/j.cma.2019.03.042 . © 2019. 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.subject	Combination-technique
dc.subject	Isogeometric analysis
dc.subject	Multilevel methods
dc.subject	Sparse grids
dc.subject	Stochastic collocation methods
dc.subject	Uncertainty quantification
dc.title	IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains
dc.type	Article
dc.contributor.department	Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.department	Applied Mathematics and Computational Science Program
dc.identifier.journal	Computer Methods in Applied Mechanics and Engineering
dc.eprint.version	Post-print
dc.contributor.institution	Consiglio Nazionale delle Ricerche - Istituto di Matematica Applicata e Tecnologie Informatiche “E. Magenes” (CNR-IMATI), Via Ferrata 1, Pavia, 27100, , Italy
dc.contributor.institution	Alexander von Humboldt Professor in Mathematics of Uncertainty Quantification, RWTH Aachen University, Aachen, 52062, , Germany
dc.identifier.arxivid	1810.01661
kaust.person	Beck, Joakim
kaust.person	Tempone, Raul
kaust.grant.number	URF/1/2281-01-01
kaust.grant.number	URF/1/2584-01-01
refterms.dateFOA	2019-01-10T13:54:34Z
dc.date.published-online	2019-03-28
dc.date.published-print	2019-07
dc.date.posted	2018-10-03