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MATHICSE Technical Report : A quasi-optimal sparse grids procedure for groundwater flows

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Název: MATHICSE Technical Report : A quasi-optimal sparse grids procedure for groundwater flows
Autoři: Beck, Joakim, Nobile, Fabio, Tamellini, Lorenzo, Tempone, Raúl
Přispěvatelé: MATHICSE-Group
Informace o vydavateli: MATHICSE
Écublens
Rok vydání: 2019
Sbírka: Ecole Polytechnique Fédérale Lausanne (EPFL): Infoscience
Témata: Uncertainty Quantification, PDEs with random data, linear elliptic equations, Darcy equation, lognormal permeability, Karhunen-Loève, 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 ap- proximation 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 construc- tion of such quasi-optimal grid and show its effectivenenss on a numerical ex- ample. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution and ; CSQI ; MATHICSE Technical Report Nr. 46.2012 November 2012
Druh dokumentu: report
Jazyk: unknown
Relation: https://infoscience.epfl.ch/record/263218/files/46.2012_JB-FN-LT-RT.pdf; #PLACEHOLDER_PARENT_METADATA_VALUE#; https://infoscience.epfl.ch/handle/20.500.14299/153689
DOI: 10.5075/epfl-MATHICSE-263218
Dostupnost: https://doi.org/10.5075/epfl-MATHICSE-263218
https://infoscience.epfl.ch/handle/20.500.14299/153689
https://hdl.handle.net/20.500.14299/153689
Přístupové číslo: edsbas.23537318
Databáze: BASE
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  – Url: https://doi.org/10.5075/epfl-MATHICSE-263218#
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  Data: MATHICSE Technical Report : 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+Raúl%22">Tempone, Raúl</searchLink>
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  Data: MATHICSE<br />Écublens
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  Data: 2019
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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-Loève%22">Karhunen-Loève</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>
– Name: Abstract
  Label: Description
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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 ap- proximation 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 construc- tion of such quasi-optimal grid and show its effectivenenss on a numerical ex- ample. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution and ; CSQI ; MATHICSE Technical Report Nr. 46.2012 November 2012
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  Data: https://infoscience.epfl.ch/record/263218/files/46.2012_JB-FN-LT-RT.pdf; #PLACEHOLDER_PARENT_METADATA_VALUE#; https://infoscience.epfl.ch/handle/20.500.14299/153689
– Name: DOI
  Label: DOI
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  Data: 10.5075/epfl-MATHICSE-263218
– Name: URL
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  Data: https://doi.org/10.5075/epfl-MATHICSE-263218<br />https://infoscience.epfl.ch/handle/20.500.14299/153689<br />https://hdl.handle.net/20.500.14299/153689
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      – SubjectFull: Uncertainty Quantification
        Type: general
      – SubjectFull: PDEs with random data
        Type: general
      – SubjectFull: linear elliptic equations
        Type: general
      – SubjectFull: Darcy equation
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      – SubjectFull: lognormal permeability
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      – SubjectFull: Karhunen-Loève
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      – SubjectFull: Stochastic Collocation methods
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      – SubjectFull: Sparse grids approximation
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      – TitleFull: MATHICSE Technical Report : A quasi-optimal sparse grids procedure for groundwater flows
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              Y: 2019
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