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    Multilevel quadrature of elliptic PDEs with log-normal diffusion

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    Type
    Poster
    Authors
    Harbrecht, Helmut
    Peters, Michael
    Siebenmorgen, Markus
    Date
    2015-01-07
    Permanent link to this record
    http://hdl.handle.net/10754/624060
    
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    Abstract
    We apply multilevel quadrature methods for the moment computation of the solution of elliptic PDEs with lognormally distributed diffusion coefficients. The computation of the moments is a difficult task since they appear as high dimensional Bochner integrals over an unbounded domain. Each function evaluation corresponds to a deterministic elliptic boundary value problem which can be solved by finite elements on an appropriate level of refinement. The complexity is thus given by the number of quadrature points times the complexity for a single elliptic PDE solve. The multilevel idea is to reduce this complexity by combining quadrature methods with different accuracies with several spatial discretization levels in a sparse grid like fashion.
    Conference/Event name
    Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
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    Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

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