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dc.contributor.authorCastrillón-Candás, Julio E.
dc.contributor.authorNobile, Fabio
dc.contributor.authorTempone, Raul
dc.date.accessioned2021-06-07T07:04:01Z
dc.date.available2021-06-07T07:04:01Z
dc.date.issued2021-05-02
dc.identifier.citationCastrillón-Candás, J. E., Nobile, F., & Tempone, R. F. (2021). A hybrid collocation-perturbation approach for PDEs with random domains. Advances in Computational Mathematics, 47(3). doi:10.1007/s10444-021-09859-6
dc.identifier.issn1572-9044
dc.identifier.issn1019-7168
dc.identifier.doi10.1007/s10444-021-09859-6
dc.identifier.urihttp://hdl.handle.net/10754/669431
dc.description.abstractConsider a linear elliptic PDE defined over a stochastic stochastic geometry a function of N random variables. In many application, quantify the uncertainty propagated to a quantity of interest (QoI) is an important problem. The random domain is split into large and small variations contributions. The large variations are approximated by applying a sparse grid stochastic collocation method. The small variations are approximated with a stochastic collocation-perturbation method and added as a correction term to the large variation sparse grid component. Convergence rates for the variance of the QoI are derived and compared to those obtained in numerical experiments. Our approach significantly reduces the dimensionality of the stochastic problem making it suitable for large dimensional problems. The computational cost of the correction term increases at most quadratically with respect to the number of dimensions of the small variations. Moreover, for the case that the small and large variations are independent the cost increases linearly.
dc.description.sponsorshipThis material is based upon work supported by the National Science Foundation under Grant No. 1736392. Research reported in this technical report was supported in part by the National Institute of General Medical Sciences (NIGMS) of the National Institutes of Health under award number 5R01GM131409-03.
dc.publisherSpringer Science and Business Media LLC
dc.relation.urlhttps://link.springer.com/10.1007/s10444-021-09859-6
dc.rightsArchived with thanks to Advances in Computational Mathematics
dc.titleA hybrid collocation-perturbation approach for PDEs with random domains
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.contributor.departmentStochastic Numerics Research Group
dc.identifier.journalAdvances in Computational Mathematics
dc.rights.embargodate2022-05-02
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics and Statistics, Boston University, 111 Cummington Mall, Boston, MA, 02215, USA
dc.contributor.institutionÉcole Politechnique Fédérale Lausanne, CSQI-MATHICSE, Station 8, CH1015, Lausanne, Switzerland
dc.identifier.volume47
dc.identifier.issue3
kaust.personTempone, Raul
dc.identifier.eid2-s2.0-85105186192
dc.date.published-online2021-05-02
dc.date.published-print2021-06


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