Nonlinear model reduction via discrete empirical interpolation

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dc.contributor.advisorSorensen, Danny C.
dc.creatorChaturantabut, Saifon
dc.date.accessioned2013-03-08T00:33:05Z
dc.date.available2013-03-08T00:33:05Z
dc.date.issued2012
dc.description.abstractThis thesis proposes a model reduction technique for nonlinear dynamical systems based upon combining Proper Orthogonal Decomposition (POD) and a new method, called the Discrete Empirical Interpolation Method (DEIM). The popular method of Galerkin projection with POD basis reduces dimension in the sense that far fewer variables are present, but the complexity of evaluating the nonlinear term generally remains that of the original problem. DEIM, a discrete variant of the approach from [11], is introduced and shown to effectively overcome this complexity issue. State space error estimates for POD-DEIM reduced systems are also derived. These [Special characters omitted.] error estimates reflect the POD approximation property through the decay of certain singular values and explain how the DEIM approximation error involving the nonlinear term comes into play. An application to the simulation of nonlinear miscible flow in a 2-D porous medium shows that the dynamics of a complex full-order system of dimension 15000 can be captured accurately by the POD-DEIM reduced system of dimension 40 with a factor of [Special characters omitted.] (1000) reduction in computational time.
dc.format.extent165 p.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.callnoTHESIS MATH.SCI. 2012 CHATURANTABUT
dc.identifier.citationChaturantabut, Saifon. "Nonlinear model reduction via discrete empirical interpolation." (2012) Diss., Rice University. <a href="https://hdl.handle.net/1911/70218">https://hdl.handle.net/1911/70218</a>.
dc.identifier.digitalChaturantabutSen_US
dc.identifier.urihttps://hdl.handle.net/1911/70218
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.subjectApplied sciences
dc.subjectNonlinear model reduction
dc.subjectEmpirical interpolation
dc.subjectNonlinear differential equations
dc.subjectProper orthogonal decomposition
dc.subjectMechanics
dc.titleNonlinear model reduction via discrete empirical interpolation
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematical Sciences
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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