Dimension Reduction for Unsteady Nonlinear Partial Differential Equations via Empirical Interpolation Methods

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dc.contributor.authorChaturantabut, Saifonen_US
dc.date.accessioned2018-06-19T17:45:10Zen_US
dc.date.available2018-06-19T17:45:10Zen_US
dc.date.issued2009-10en_US
dc.date.noteOctober 2009en_US
dc.descriptionThis work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/61925en_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.extent148 ppen_US
dc.identifier.citationChaturantabut, Saifon. "Dimension Reduction for Unsteady Nonlinear Partial Differential Equations via Empirical Interpolation Methods." (2009) <a href="https://hdl.handle.net/1911/102137">https://hdl.handle.net/1911/102137</a>.en_US
dc.identifier.digitalTR09-36en_US
dc.identifier.urihttps://hdl.handle.net/1911/102137en_US
dc.language.isoengen_US
dc.titleDimension Reduction for Unsteady Nonlinear Partial Differential Equations via Empirical Interpolation Methodsen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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