Fréchet Sensitivity Analysis and Parameter Estimation in Groundwater Flow Models

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dc.contributor.authorLeite Dos Santos Nunes, Vitor Manuelen
dc.contributor.committeechairBorggaard, Jeffrey T.en
dc.contributor.committeememberZietsman, Lizetteen
dc.contributor.committeememberBurns, John A.en
dc.contributor.committeememberAdjerid, Slimaneen
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-11-01T06:00:12Zen
dc.date.available2014-11-01T06:00:12Zen
dc.date.issued2013-05-09en
dc.description.abstractIn this work we develop and analyze algorithms motivated by the parameter estimation problem corresponding to a multilayer aquifer/interbed groundwater flow model. The parameter estimation problem is formulated as an optimization problem, then addressed with algorithms based on adjoint equations, quasi-Newton schemes, and multilevel optimization. In addition to the parameter estimation problem, we consider properties of the parameter to solution map. This includes invertibility (known as identifiability) and differentiability properties of the map. For differentiability, we expand existing results on Fréchet sensitivity analysis to convection diffusion equations and groundwater flow equations. This is achieved by proving that the Fréchet  derivative of the solution operator is Hilbert-Schmidt, under smoothness assumptions for the parameter space. In addition, we approximate this operator by time dependent matrices, where their singular values and singular vectors converge to their infinite dimension peers. This decomposition proves to be very useful as it provides vital information as to which perturbations in the distributed parameters lead to the most significant changes in the solutions, as well as applications to uncertainty quantification. Numerical results complement our theoretical findings.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:724en
dc.identifier.urihttp://hdl.handle.net/10919/50653en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectFréchet derivative operatorsen
dc.subjectgroundwater  flow modelsen
dc.subjectparameter estimationen
dc.subjectparameter zonationen
dc.subjectsensitivity analysisen
dc.titleFréchet Sensitivity Analysis and Parameter Estimation in Groundwater Flow Modelsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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