Handle URI:
http://hdl.handle.net/10754/624060
Title:
Multilevel quadrature of elliptic PDEs with log-normal diffusion
Authors:
Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus
Abstract:
We apply multilevel quadrature methods for the moment computation of the solution of elliptic PDEs with lognormally distributed diffusion coefficients. The computation of the moments is a difficult task since they appear as high dimensional Bochner integrals over an unbounded domain. Each function evaluation corresponds to a deterministic elliptic boundary value problem which can be solved by finite elements on an appropriate level of refinement. The complexity is thus given by the number of quadrature points times the complexity for a single elliptic PDE solve. The multilevel idea is to reduce this complexity by combining quadrature methods with different accuracies with several spatial discretization levels in a sparse grid like fashion.
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
Issue Date:
7-Jan-2015
Type:
Poster
Appears in Collections:
Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

Full metadata record

DC FieldValue Language
dc.contributor.authorHarbrecht, Helmuten
dc.contributor.authorPeters, Michaelen
dc.contributor.authorSiebenmorgen, Markusen
dc.date.accessioned2017-06-05T08:35:47Z-
dc.date.available2017-06-05T08:35:47Z-
dc.date.issued2015-01-07-
dc.identifier.urihttp://hdl.handle.net/10754/624060-
dc.description.abstractWe apply multilevel quadrature methods for the moment computation of the solution of elliptic PDEs with lognormally distributed diffusion coefficients. The computation of the moments is a difficult task since they appear as high dimensional Bochner integrals over an unbounded domain. Each function evaluation corresponds to a deterministic elliptic boundary value problem which can be solved by finite elements on an appropriate level of refinement. The complexity is thus given by the number of quadrature points times the complexity for a single elliptic PDE solve. The multilevel idea is to reduce this complexity by combining quadrature methods with different accuracies with several spatial discretization levels in a sparse grid like fashion.en
dc.titleMultilevel quadrature of elliptic PDEs with log-normal diffusionen
dc.typePosteren
dc.conference.dateJanuary 6-9, 2015en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)en
dc.conference.locationKAUSTen
dc.contributor.institutionUniversity of Baselen
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