A quasi-optimal sparse grids procedure for groundwater flows
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| Název: | A quasi-optimal sparse grids procedure for groundwater flows |
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| Autoři: | Beck, Joakim, Nobile, Fabio, Tamellini, Lorenzo, Tempone, Raul |
| Přispěvatelé: | Azaïez, Mejdi, El Fekih, Henda, Hesthaven, Jan S. |
| Informace o vydavateli: | Springer |
| Rok vydání: | 2013 |
| Sbírka: | Ecole Polytechnique Fédérale Lausanne (EPFL): Infoscience |
| Témata: | Uncertainty quantification, PDEs with random data, linear elliptic equations, Darcy equation, lognormal permeability, Karhunen-Loeve, Stochastic Collocation methods, Sparse grids approximation |
| Popis: | In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work "On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods" to a Darcy problem where the permeability is modeled as a lognormal random field. We propose an explicit a-priori/a-posteriori procedure for the construction of such quasi-optimal grid and show its effectivenenss on a numerical example. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution and an efficient nested quadrature rule with respect to the Gaussian weight. ; CSQI ; Invited Paper. Also available as MATHICSE-report 46-2012 |
| Druh dokumentu: | conference object |
| Jazyk: | unknown |
| Relation: | https://infoscience.epfl.ch/record/185908/files/beck.nobile.tam.tempgroundwater_1.pdf; https://infoscience.epfl.ch/record/185908/files/csqi-darcy-lognormal-code.zip; Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012; Lecture Notes in computational Science and Engineering; 95; International Conference on Spectral and High-Order Methods 2012 (ICOSAHOM'12); #PLACEHOLDER_PARENT_METADATA_VALUE#; https://infoscience.epfl.ch/handle/20.500.14299/91421 |
| DOI: | 10.1007/978-3-319-01601-6_1 |
| Dostupnost: | https://doi.org/10.1007/978-3-319-01601-6_1 https://infoscience.epfl.ch/handle/20.500.14299/91421 https://hdl.handle.net/20.500.14299/91421 |
| Přístupové číslo: | edsbas.C1D95BBF |
| Databáze: | BASE |
Nájsť tento článok vo Web of Science | Abstrakt: | In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work "On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods" to a Darcy problem where the permeability is modeled as a lognormal random field. We propose an explicit a-priori/a-posteriori procedure for the construction of such quasi-optimal grid and show its effectivenenss on a numerical example. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution and an efficient nested quadrature rule with respect to the Gaussian weight. ; CSQI ; Invited Paper. Also available as MATHICSE-report 46-2012 |
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| DOI: | 10.1007/978-3-319-01601-6_1 |