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

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dc.contributor.advisorSorensen, Danny C.
dc.creatorChaturantabut, Saifon
dc.date.accessioned2011-07-25T01:39:32Z
dc.date.available2011-07-25T01:39:32Z
dc.date.issued2009
dc.description.abstractThis 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.
dc.format.mimetypeapplication/pdf
dc.identifier.callnoTHESIS MATH. SCI. 2009 CHATURANTABUT
dc.identifier.citationChaturantabut, Saifon. "Dimension reduction for unsteady nonlinear partial differential equations via empirical interpolation methods." (2009) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/61925">https://hdl.handle.net/1911/61925</a>.
dc.identifier.urihttps://hdl.handle.net/1911/61925
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectMathematics
dc.subjectComputer science
dc.titleDimension reduction for unsteady nonlinear partial differential equations via empirical interpolation methods
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematical Sciences
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
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