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    Dimension reduction for unsteady nonlinear partial differential equations via empirical interpolation methods

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    Author
    Chaturantabut, Saifon
    Date
    2009
    Advisor
    Sorensen, Danny C.
    Degree
    Master of Arts
    Abstract
    This thesis evaluates and compares the efficiencies of techniques for constructing reduced-order models for finite difference (FD) and finite element (FE) discretized systems of unsteady nonlinear partial differential equations (PDEs). With nonlinearity, the complexity for solving the reduced-order system constructed directly from the well-known Proper Orthogonal Decomposition (POD) technique alone still depends on the dimension of the original system. Empirical Interpolation Method (EIM), proposed in [2], and its discrete variation, Discrete Empirical Interpolation Method (DEIM), introduced in this thesis, are therefore combined with the POD technique to remove this inefficiency in the nonlinear terms of FE and FD cases, respectively. Numerical examples demonstrate that both POD-EIM and POD-DEIM approaches not only dramatically reduce the dimension of the original system with high accuracy, but also remove the dependence on the dimension of the original system as reflected in the decrease computational time compared to the POD approach.
    Keyword
    Mathematics; Computer science
    Citation
    Chaturantabut, Saifon. "Dimension reduction for unsteady nonlinear partial differential equations via empirical interpolation methods." (2009) Master’s Thesis, Rice University. http://hdl.handle.net/1911/61925.
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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892