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

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dc.contributor.advisorSorensen, Danny C.en_US
dc.creatorChaturantabut, Saifonen_US
dc.date.accessioned2011-07-25T01:39:32Zen_US
dc.date.available2011-07-25T01:39:32Zen_US
dc.date.issued2009en_US
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.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH. SCI. 2009 CHATURANTABUTen_US
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>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/61925en_US
dc.language.isoengen_US
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.en_US
dc.subjectMathematicsen_US
dc.subjectComputer scienceen_US
dc.titleDimension reduction for unsteady nonlinear partial differential equations via empirical interpolation methodsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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