A Nonlinear Optimization Method Applied to the Hydraulic Conductivity Identification in Unconfined Aquifers
| Autor: | Aya Mourad, Carole Rosier |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
geography
021103 operations research Control and Optimization Optimization problem geography.geographical_feature_category Applied Mathematics Numerical analysis 0211 other engineering and technologies Aquifer 010103 numerical & computational mathematics 02 engineering and technology Management Science and Operations Research Inverse problem 01 natural sciences Nonlinear programming Parameter identification problem Hydraulic conductivity Applied mathematics Saltwater intrusion 0101 mathematics Mathematics |
| Zdroj: | Journal of Optimization Theory and Applications. 183:705-730 |
| ISSN: | 1573-2878 0022-3239 |
| Popis: | This article is concerned with the identification, from observations or field measurements, of the hydraulic conductivity for the saltwater intrusion problem in an unconfined aquifer. The involved model consists in a cross-diffusion system describing the evolutions of two interfaces: one between freshwater and saltwater and the other one between the saturated and unsaturated zones of the aquifer. The inverse problem is formulated as an optimization problem, where the cost function is a least square functional measuring the discrepancy between experimental interfaces depths and those provided by the model. Considering the exact problem as a constraint for the optimization problem and introducing the Lagrangian associated with the cost function, we prove that the optimality system has at least one solution. Moreover, we establish the first-order necessary optimality conditions. A numerical method is implemented to solve this identification problem. Some numerical results are presented to illustrate the ability of the method to determine the unknown parameters. |
| Databáze: | OpenAIRE |
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