Fréchet Sensitivity Analysis and Parameter Estimation in Groundwater Flow Models

In 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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2013

Author dc:creator

• Leite Dos Santos Nunes, Vitor Manuel

Chair dc:contributor.committeechair

• Borggaard, Jeffrey T.

Committee members dc:contributor.committeemember

• Zietsman, Lizette
• Burns, John A.
• Adjerid, Slimane

• Fréchet derivative operators
• groundwater flow models
• parameter estimation
• parameter zonation
• sensitivity analysis

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:724

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/50653