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MATHICSE Technical Report : Comparison of Clenshaw-Curtis and Leja quasi-optimal sparse grids for the approximation of random PDEs

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Title: MATHICSE Technical Report : Comparison of Clenshaw-Curtis and Leja quasi-optimal sparse grids for the approximation of random PDEs
Authors: Nobile, Fabio, Tamellini, Lorenzo, Tempone, Raúl
Contributors: MATHICSE-Group
Publisher Information: MATHICSE
Écublens
Publication Year: 2019
Collection: Ecole Polytechnique Fédérale Lausanne (EPFL): Infoscience
Subject Terms: Uncertainty Quantication, PDEs with random data, linear elliptic equations, Stochastic Collocation methods, Sparse grids approximation, Leja points, Clenshaw{Curtis points)
Description: In this work we compare numerically different families of nested quadrature points, i.e. the classic Clenshaw{Curtis and various kinds of Leja points, in the context of the quasi-optimal sparse grid approximation of random elliptic PDEs. Numerical evidence suggests that the performances of both families are essentially comparable within such framework. ; CSQI ; MATHICSE Technical Report Nr. 41.2014 September 2014
Document Type: report
Language: unknown
Relation: https://infoscience.epfl.ch/record/263229/files/41.2014_FN-LT-RTnew.pdf; #PLACEHOLDER_PARENT_METADATA_VALUE#; https://infoscience.epfl.ch/handle/20.500.14299/153709
DOI: 10.5075/epfl-MATHICSE-263229
Availability: https://doi.org/10.5075/epfl-MATHICSE-263229
https://infoscience.epfl.ch/handle/20.500.14299/153709
https://hdl.handle.net/20.500.14299/153709
Accession Number: edsbas.7F79104D
Database: BASE
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  – Url: https://doi.org/10.5075/epfl-MATHICSE-263229#
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  Data: MATHICSE Technical Report : Comparison of Clenshaw-Curtis and Leja quasi-optimal sparse grids for the approximation of random PDEs
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  Data: <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-Group
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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+Quantication%22">Uncertainty Quantication</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="%22Stochastic+Collocation+methods%22">Stochastic Collocation methods</searchLink><br /><searchLink fieldCode="DE" term="%22Sparse+grids+approximation%22">Sparse grids approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Leja+points%22">Leja points</searchLink><br /><searchLink fieldCode="DE" term="%22Clenshaw{Curtis+points%29%22">Clenshaw{Curtis points)</searchLink>
– Name: Abstract
  Label: Description
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  Data: In this work we compare numerically different families of nested quadrature points, i.e. the classic Clenshaw{Curtis and various kinds of Leja points, in the context of the quasi-optimal sparse grid approximation of random elliptic PDEs. Numerical evidence suggests that the performances of both families are essentially comparable within such framework. ; CSQI ; MATHICSE Technical Report Nr. 41.2014 September 2014
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  Data: https://infoscience.epfl.ch/record/263229/files/41.2014_FN-LT-RTnew.pdf; #PLACEHOLDER_PARENT_METADATA_VALUE#; https://infoscience.epfl.ch/handle/20.500.14299/153709
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  Data: 10.5075/epfl-MATHICSE-263229
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  Data: https://doi.org/10.5075/epfl-MATHICSE-263229<br />https://infoscience.epfl.ch/handle/20.500.14299/153709<br />https://hdl.handle.net/20.500.14299/153709
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        Value: 10.5075/epfl-MATHICSE-263229
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    Subjects:
      – SubjectFull: Uncertainty Quantication
        Type: general
      – SubjectFull: PDEs with random data
        Type: general
      – SubjectFull: linear elliptic equations
        Type: general
      – SubjectFull: Stochastic Collocation methods
        Type: general
      – SubjectFull: Sparse grids approximation
        Type: general
      – SubjectFull: Leja points
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      – SubjectFull: Clenshaw{Curtis points)
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      – TitleFull: MATHICSE Technical Report : Comparison of Clenshaw-Curtis and Leja quasi-optimal sparse grids for the approximation of random PDEs
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            NameFull: Nobile, Fabio
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            NameFull: Tamellini, Lorenzo
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            NameFull: Tempone, Raúl
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              Type: published
              Y: 2019
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