• Login
    View Item 
    •   DSpace@RPI Home
    • Rensselaer Libraries
    • RPI Theses Online (Complete)
    • View Item
    •   DSpace@RPI Home
    • Rensselaer Libraries
    • RPI Theses Online (Complete)
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Novel multiscale finite element methods for deterministic and stochastic time-harmonic wave equations

    Author
    Jagalur Mohan, Jayanth
    View/Open
    172706_JagalurMohan_rpi_0185E_10365.pdf (11.58Mb)
    Other Contributors
    Oberai, Assad; Shephard, M. S. (Mark S.); De, Suvranu; McLaughlin, Joyce; Li, Fengyan;
    Date Issued
    2014-05
    Subject
    Mechanical engineering
    Degree
    PhD;
    Terms of Use
    This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.;
    Metadata
    Show full item record
    URI
    https://hdl.handle.net/20.500.13015/1121
    Abstract
    We extend and analyze the VMS method to partial differential equations with stochastic coefficients. For a natural choice of an "optimal" coarse-scale solution and L2-orthogonal stochastic basis functions, we demonstrate that the fine-scale stochastic Green's function is intimately linked to its deterministic counterpart. Further, we prove whenever the deterministic fine-scale function vanishes, the stochastic fine-scale function satisfies a weaker, and discrete notion of vanishing stochastic coefficients. Using the theoretical insights, we argue how approximations to enable a practical implementation of the VMS method can be made. Subsequently, on select model problems we demonstrate how we gain improved statistics of the solution at a much lower computational cost.; Multiscale phenomena are integral to most processes which can be modeled as wave propagation problems. The goal of this work is to explore the use of variational multiscale (VMS) techniques for deterministic and stochastic time-harmonic wave propagation problems.; We construct a non-overlapping domain decomposition method for time-harmonic Maxwell's equations. Using perfectly matched layers to enforce pseudo-differential interface conditions; we capture the outgoing wave from one sub-domain, and enforce it as an incoming wave to the corresponding adjacent neighbor. We demonstrate numerically how this turns out to be a computationally inexpensive method with fast convergence.; We prove the efficacy of the Galerkin least squares (GLS) technique for time-harmonic Maxwell equations. The GLS method can be categorized under the ambit of the VMS framework. A modified variational formulation constructed by appending the weighted coarse-scale residual characterizes the new method. Using a dispersion analysis procedure we design the parameter weighting the residual, and show how the dispersion error can be nulled with ;a-priori knowledge of the direction of propagation of the wave, and in general reduced for an arbitrary direction of propagation. The claims are illustrated using numerical examples.;
    Description
    May 2014; School of Engineering
    Department
    Dept. of Mechanical, Aerospace, and Nuclear Engineering;
    Publisher
    Rensselaer shePolytechnic Institute, Troy, NY
    Relationships
    Rensselaer Theses and Dissertations Online Collection;
    Access
    Restricted to current Rensselaer faculty, staff and students. Access inquiries may be directed to the Rensselaer Libraries.;
    Collections
    • RPI Theses Online (Complete)

    Browse

    All of DSpace@RPICommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    Login

    DSpace software copyright © 2002-2022  DuraSpace
    Contact Us | Send Feedback
    DSpace Express is a service operated by 
    Atmire NV