Stochastic collocation method for computing eigenspaces of parameter-dependent operators

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorGrubišić, Luka
dc.contributor.authorSaarikangas, Mikael
dc.contributor.authorHakula, Harri
dc.contributor.departmentUniversity of Zagreb
dc.contributor.departmentDepartment of Mathematics and Systems Analysis
dc.date.accessioned2023-01-18T09:19:58Z
dc.date.available2023-01-18T09:19:58Z
dc.date.issued2023-01
dc.descriptionFunding Information: The work of L.G. has been supported by the Croatian Science Foundation Grant IP-2019-04-6268. We gratefully acknowledge the support. Publisher Copyright: © 2022, The Author(s).
dc.description.abstractWe consider computing eigenspaces of an elliptic self-adjoint operator depending on a countable number of parameters in an affine fashion. The eigenspaces of interest are assumed to be isolated in the sense that the corresponding eigenvalues are separated from the rest of the spectrum for all values of the parameters. We show that such eigenspaces can in fact be extended to complex-analytic functions of the parameters and quantify this analytic dependence in a way that leads to convergence of sparse polynomial approximations. A stochastic collocation method on an anisoptropic sparse grid in the parameter domain is proposed for computing a basis for the eigenspace of interest. The convergence of this method is verified in a series of numerical examples based on the eigenvalue problem of a stochastic diffusion operator.en
dc.description.versionPeer revieweden
dc.format.extent26
dc.format.extent85-110
dc.format.mimetypeapplication/pdf
dc.identifier.citationGrubišić , L , Saarikangas , M & Hakula , H 2023 , ' Stochastic collocation method for computing eigenspaces of parameter-dependent operators ' , Numerische Mathematik , vol. 153 , no. 1 , pp. 85-110 . https://doi.org/10.1007/s00211-022-01339-3en
dc.identifier.doi10.1007/s00211-022-01339-3
dc.identifier.issn0029-599X
dc.identifier.issn0945-3245
dc.identifier.otherPURE UUID: 1ed34c01-345d-44b8-8e1e-d7ad71826f23
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dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/98175327/Stochastic_collocation_method_for_computing_eigenspaces_of_parameter_dependent_operators.pdf
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/118802
dc.identifier.urnURN:NBN:fi:aalto-202301181158
dc.language.isoenen
dc.publisherSPRINGER
dc.relation.ispartofseriesNumerische Mathematiken
dc.relation.ispartofseriesVolume 153, issue 1en
dc.rightsopenAccessen
dc.titleStochastic collocation method for computing eigenspaces of parameter-dependent operatorsen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
dc.type.versionpublishedVersion
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