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A quasi-optimal sparse grids procedure for groundwater flows

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Název: A quasi-optimal sparse grids procedure for groundwater flows
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
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  – Url: https://doi.org/10.1007/978-3-319-01601-6_1#
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  Data: A quasi-optimal sparse grids procedure for groundwater flows
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  Data: <searchLink fieldCode="AR" term="%22Beck%2C+Joakim%22">Beck, Joakim</searchLink><br /><searchLink fieldCode="AR" term="%22Nobile%2C+Fabio%22">Nobile, Fabio</searchLink><br /><searchLink fieldCode="AR" term="%22Tamellini%2C+Lorenzo%22">Tamellini, Lorenzo</searchLink><br /><searchLink fieldCode="AR" term="%22Tempone%2C+Raul%22">Tempone, Raul</searchLink>
– Name: Author
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  Data: Azaïez, Mejdi<br />El Fekih, Henda<br />Hesthaven, Jan S.
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  Data: Springer
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  Label: Publication Year
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  Data: 2013
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  Data: Ecole Polytechnique Fédérale Lausanne (EPFL): Infoscience
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  Data: <searchLink fieldCode="DE" term="%22Uncertainty+quantification%22">Uncertainty quantification</searchLink><br /><searchLink fieldCode="DE" term="%22PDEs+with+random+data%22">PDEs with random data</searchLink><br /><searchLink fieldCode="DE" term="%22linear+elliptic+equations%22">linear elliptic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Darcy+equation%22">Darcy equation</searchLink><br /><searchLink fieldCode="DE" term="%22lognormal+permeability%22">lognormal permeability</searchLink><br /><searchLink fieldCode="DE" term="%22Karhunen-Loeve%22">Karhunen-Loeve</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+Collocation+methods%22">Stochastic Collocation methods</searchLink><br /><searchLink fieldCode="DE" term="%22Sparse+grids+approximation%22">Sparse grids approximation</searchLink>
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  Data: 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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  Data: 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
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  Data: 10.1007/978-3-319-01601-6_1
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  Data: https://doi.org/10.1007/978-3-319-01601-6_1<br />https://infoscience.epfl.ch/handle/20.500.14299/91421<br />https://hdl.handle.net/20.500.14299/91421
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        Value: 10.1007/978-3-319-01601-6_1
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      – Text: unknown
    Subjects:
      – SubjectFull: Uncertainty quantification
        Type: general
      – SubjectFull: PDEs with random data
        Type: general
      – SubjectFull: linear elliptic equations
        Type: general
      – SubjectFull: Darcy equation
        Type: general
      – SubjectFull: lognormal permeability
        Type: general
      – SubjectFull: Karhunen-Loeve
        Type: general
      – SubjectFull: Stochastic Collocation methods
        Type: general
      – SubjectFull: Sparse grids approximation
        Type: general
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      – TitleFull: A quasi-optimal sparse grids procedure for groundwater flows
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            NameFull: Beck, Joakim
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