IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains
Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
KAUST Grant Number
URF/1/2281-01-01URF/1/2584-01-01
Date
2019-03-28Preprint Posting Date
2018-10-03Online Publication Date
2019-03-28Print Publication Date
2019-07Permanent link to this record
http://hdl.handle.net/10754/630793
Metadata
Show full item recordAbstract
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.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.Sponsors
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”.Publisher
Elsevier BVarXiv
1810.01661Additional Links
https://www.sciencedirect.com/science/article/pii/S0045782519301811ae974a485f413a2113503eed53cd6c53
10.1016/j.cma.2019.03.042