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dc.contributor.authorHaji Ali, Abdul Lateef
dc.contributor.authorNobile, Fabio
dc.contributor.authorTamellini, Lorenzo
dc.contributor.authorTempone, Raul
dc.date.accessioned2016-03-30T07:26:10Z
dc.date.available2016-03-30T07:26:10Z
dc.date.issued2016-03-28
dc.identifier.citationMulti-Index Stochastic Collocation for random PDEs 2016 Computer Methods in Applied Mechanics and Engineering
dc.identifier.issn00457825
dc.identifier.doi10.1016/j.cma.2016.03.029
dc.identifier.urihttp://hdl.handle.net/10754/603944
dc.description.abstractIn this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.
dc.language.isoen
dc.publisherElsevier BV
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0045782516301141
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 March 2016. DOI: 10.1016/j.cma.2016.03.029
dc.subjectUncertainty Quantification
dc.subjectRandom PDEs
dc.subjectMultivariate approximation
dc.subjectSparse grids
dc.subjectStochastic Collocation methods
dc.subjectMultilevel methods
dc.subjectCombination technique
dc.titleMulti-Index Stochastic Collocation for random PDEs
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
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.institutionCSQI - MATHICSE, École Polytechnique Fédérale de Lausanne, Station 8, CH 1015, Lausanne, Switzerland
dc.contributor.institutionDipartimento di Matematica “F. Casorati”, Università di Pavia, Via Ferrata 5, 27100 Pavia, Italy
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
dc.identifier.arxivid1508.07467
kaust.personHaji Ali, Abdul Lateef
kaust.personTempone, Raul
refterms.dateFOA2018-03-28T00:00:00Z
dc.date.published-online2016-03-28
dc.date.published-print2016-07


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