German Title: Numerische Methoden für Optimierungsprobleme in Wasser- und Stofftransportprozessen von Xenobiotika in Böden

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Translation of abstract (English)

Inverse modeling is increasingly used in the modeling of water flow and reactive solute transport in the unsaturated zone to determine unknown parameters, e.g. degradation rates. In this thesis new contributions are made to the following fields: 1. Modeling of parameter estimation problems and optimal experimental design problems: Mathematical modeling of water and solute transport processes in the unsaturated zone leads to instationary partial differential equations (PDEs) coupled with nonlinear ordinary differential equations (ODEs). 2. ECOFIT: An efficient method for parameter estimation of xenobiotics in soils: The parameter estimation problem constrained by PDEs and ODEs is transformed by discretization into a large scale nonlinear constrained least-squares problem. Finite differences are employed for spatial discretization. Discretization in time is done by multiple shooting. A reduced Generalized Gauss-Newton method is presented that exploits that the systems have only few degrees of freedom. Using directional derivatives for setting up the linearized problems, we end up with essentially the same computational effort as for the single shooting method while maintaining the advantages of multiple shooting. For the computation of derivatives in discretized PDE-systems highly efficient strategies are derived exploiting structures on several levels. 3. ECOPLAN: An approach for optimizing experimental conditions and sampling schemes: Embedding the optimal experimental design problem in the framework of optimal control theory results in an intricate, nonlinear, state-constrained optimization problem that is solved by a structured SQP-method. 4. Application of ECOFIT and ECOPLAN to column, lysimeter and field studies: Numerous types of examples are worked out to demonstrate the power and the possibilities of ECOFIT and ECOPLAN, some of them using hypothetical data, some of them building on data provided by experiments.