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    A hybrid collocation-perturbation approach for PDEs with random domains

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    Type
    Article
    Authors
    Castrillón-Candás, Julio E. cc
    Nobile, Fabio
    Tempone, Raul cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Stochastic Numerics Research Group
    Date
    2021-05-02
    Online Publication Date
    2021-05-02
    Print Publication Date
    2021-06
    Embargo End Date
    2022-05-02
    Permanent link to this record
    http://hdl.handle.net/10754/669431
    
    Metadata
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    Abstract
    Consider a linear elliptic PDE defined over a stochastic stochastic geometry a function of N random variables. In many application, quantify the uncertainty propagated to a quantity of interest (QoI) is an important problem. The random domain is split into large and small variations contributions. The large variations are approximated by applying a sparse grid stochastic collocation method. The small variations are approximated with a stochastic collocation-perturbation method and added as a correction term to the large variation sparse grid component. Convergence rates for the variance of the QoI are derived and compared to those obtained in numerical experiments. Our approach significantly reduces the dimensionality of the stochastic problem making it suitable for large dimensional problems. The computational cost of the correction term increases at most quadratically with respect to the number of dimensions of the small variations. Moreover, for the case that the small and large variations are independent the cost increases linearly.
    Citation
    Castrillón-Candás, J. E., Nobile, F., & Tempone, R. F. (2021). A hybrid collocation-perturbation approach for PDEs with random domains. Advances in Computational Mathematics, 47(3). doi:10.1007/s10444-021-09859-6
    Sponsors
    This material is based upon work supported by the National Science Foundation under Grant No. 1736392. Research reported in this technical report was supported in part by the National Institute of General Medical Sciences (NIGMS) of the National Institutes of Health under award number 5R01GM131409-03.
    Publisher
    Springer Science and Business Media LLC
    Journal
    Advances in Computational Mathematics
    DOI
    10.1007/s10444-021-09859-6
    Additional Links
    https://link.springer.com/10.1007/s10444-021-09859-6
    ae974a485f413a2113503eed53cd6c53
    10.1007/s10444-021-09859-6
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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