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dc.contributor.advisor Sorensen, Danny C.
dc.creatorChaturantabut, Saifon
dc.date.accessioned 2013-03-08T00:33:05Z
dc.date.available 2013-03-08T00:33:05Z
dc.date.issued 2012
dc.identifier.urihttps://hdl.handle.net/1911/70218
dc.description.abstract This 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.extent 165 p.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectApplied sciences
Nonlinear model reduction
Empirical interpolation
Nonlinear differential equations
Proper orthogonal decomposition
Mechanics
dc.title Nonlinear model reduction via discrete empirical interpolation
dc.identifier.digital ChaturantabutS
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Computational and Applied Mathematics
thesis.degree.discipline Engineering
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy
dc.identifier.citation Chaturantabut, Saifon. "Nonlinear model reduction via discrete empirical interpolation." (2012) Diss., Rice University. https://hdl.handle.net/1911/70218.


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