Skip to content
University of Maryland LibrariesDigital Repository at the University of Maryland
    • Login
    View Item 
    •   DRUM
    • College of Computer, Mathematical & Natural Sciences
    • Computer Science
    • Technical Reports from UMIACS
    • View Item
    •   DRUM
    • College of Computer, Mathematical & Natural Sciences
    • Computer Science
    • Technical Reports from UMIACS
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Efficient Iterative Solvers for Stochastic Galerkin Discretizations of Log-Transformed Random Diffusion Problems

    Thumbnail
    View/Open
    CS-TR-4986.pdf (296.7Kb)
    No. of downloads: 758

    Date
    2011-06-22
    Author
    Ullmann, Elisabeth
    Elman, Howard C.
    Ernst, Oliver G.
    Metadata
    Show full item record
    Abstract
    We consider the numerical solution of a steady-state diffusion problem where the diffusion coefficient is the exponent of a random field. The standard stochastic Galerkin formulation of this problem is computationally demanding because of the nonlinear structure of the uncertain component of it. We consider a reformulated version of this problem as a stochastic convection-diffusion problem with random convective velocity that depends linearly on a fixed number of independent truncated Gaussian random variables. The associated Galerkin matrix is nonsymmetric but sparse and allows for fast matrix-vector multiplications with optimal complexity. We construct and analyze two block-diagonal preconditioners for this Galerkin matrix for use with Krylov subspace methods such as the generalized minimal residual method. We test the efficiency of the proposed preconditioning approaches and compare the iterative solver performance for a model problem posed in both diffusion and convection-diffusion formulations.
    URI
    http://hdl.handle.net/1903/11404
    Collections
    • Technical Reports from UMIACS
    • Technical Reports of the Computer Science Department

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility
     

     

    Browse

    All of DRUMCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister
    Pages
    About DRUMAbout Download Statistics

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility