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Comparison of Clenshaw-Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs

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Titel: Comparison of Clenshaw-Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs
Autoren: Nobile, Fabio, Tamellini, Lorenzo, Tempone, Raul
Weitere Verfasser: Kirby, Robert M., Berzins, Martin, Hesthaven, Jan S.
Verlagsinformationen: Springer
Publikationsjahr: 2014
Bestand: Ecole Polytechnique Fédérale Lausanne (EPFL): Infoscience
Schlagwörter: Uncertainty Quantification, PDEs with random data, linear elliptic equations, Stochastic Collocation methods, Sparse grids approximation, Leja points, Clenshaw–Curtis points
Beschreibung: In this work we compare 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 both families perform comparably within such framework. ; CSQI
Publikationsart: conference object
Sprache: unknown
ISBN: 978-3-319-19800-2
3-319-19800-9
ISSN: 1439-7358
Relation: https://infoscience.epfl.ch/record/201919/files/2015_Nobile_Tamellini_Tempone_LNCSE_Comparison.pdf; https://infoscience.epfl.ch/record/201919/files/icosahom2014-proceedings.zip; Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014; Lecture Notes in Computational Science and Engineering; 106; International Conference on Spectral and High-Order Methods 2014 (ICOSAHOM'14); #PLACEHOLDER_PARENT_METADATA_VALUE#; https://infoscience.epfl.ch/handle/20.500.14299/107171; WOS:000368440400044
DOI: 10.1007/978-3-319-19800-2_44
Verfügbarkeit: https://doi.org/10.1007/978-3-319-19800-2_44
https://infoscience.epfl.ch/handle/20.500.14299/107171
https://hdl.handle.net/20.500.14299/107171
Dokumentencode: edsbas.9643F450
Datenbank: BASE
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  – Url: https://doi.org/10.1007/978-3-319-19800-2_44#
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  Label: Title
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  Data: Comparison of Clenshaw-Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs
– Name: Author
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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+Raul%22">Tempone, Raul</searchLink>
– Name: Author
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  Data: Kirby, Robert M.<br />Berzins, Martin<br />Hesthaven, Jan S.
– Name: Publisher
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  Data: Springer
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  Label: Publication Year
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  Data: 2014
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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="%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%22">Clenshaw–Curtis points</searchLink>
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  Data: In this work we compare 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 both families perform comparably within such framework. ; CSQI
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  Data: 978-3-319-19800-2<br />3-319-19800-9
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  Data: 1439-7358
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  Data: https://infoscience.epfl.ch/record/201919/files/2015_Nobile_Tamellini_Tempone_LNCSE_Comparison.pdf; https://infoscience.epfl.ch/record/201919/files/icosahom2014-proceedings.zip; Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014; Lecture Notes in Computational Science and Engineering; 106; International Conference on Spectral and High-Order Methods 2014 (ICOSAHOM'14); #PLACEHOLDER_PARENT_METADATA_VALUE#; https://infoscience.epfl.ch/handle/20.500.14299/107171; WOS:000368440400044
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  Data: 10.1007/978-3-319-19800-2_44
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  Data: https://doi.org/10.1007/978-3-319-19800-2_44<br />https://infoscience.epfl.ch/handle/20.500.14299/107171<br />https://hdl.handle.net/20.500.14299/107171
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        Value: 10.1007/978-3-319-19800-2_44
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    Subjects:
      – SubjectFull: Uncertainty Quantification
        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
        Type: general
      – SubjectFull: Clenshaw–Curtis points
        Type: general
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      – TitleFull: 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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