SPP 1253:  Optimisation with Partial Differential Equations

• Subject Area: Mathematics
• Term: from 2006 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 20252111

Solving optimisation problems subject to constraints involving distributed parameter systems (DPS) is one of the most challenging problems in the context of industrial, medical and economical applications. In particular, in the design of aircraft, "moving bed" processes in chemical engineering, crystal growth etc. the forward simulation followed by the variation of the optimisation variables has proved to be inefficient. Instead, the optimisation of design and topology of structures and the control of processes involving partial differential equations (PDEs), interpreted as DPS, has to be treated simultaneously such that modern mathematical methods for optimisation with PDEs are interlinked with adaptive goal-oriented simulation tools. After proper structure respecting discretisation, the number of optimisation variables varies typically in the range of up to several millions. It is only very recently that the enormous advances in computing power have made it possible to attack problems of this size. However, in order to accomplish this task it is crucial to utilise and further explore the specific mathematical structure of prototype applications and to develop new mathematical approaches concerning structure exploiting algorithms, model reduction, parallelisability, adaptivity of numerical schemes for the corresponding optimality systems based on a posteriori error estimates and the optimisation with PDEs involving control and state constraints. Methods of automatic differentiation (AD) will turn out to be very important in handling the massive data involved in problems of optimal design, shape and topology as well as in time-dependent problems.
The aim of this Priority Programme is thus to combine numerical analysis of PDEs and optimisation governed by prototype applications so that the most recent activities in the fields are merged and further explored, and new analytic and algorithmic paradigms will be developed, implemented, and, ultimately, validated in the context of real-world applications.

• DFG Programme: Priority Programmes
• International Connection: Austria, Switzerland

Projects

• Adaptive multilevel SQP-methods for PDAE-constrained optimization with restrictions on control and state. Theory and Applications (Applicants Lang, Jens ;  Ulbrich, Stefan )
• Adaptive Trust Region POD Algorithms (Applicant Sachs, Ekkehard )
• Advanced numerical methods for PDE constrained optimization with application to optimal design and control of a racing yacht in the America`s Cup (Applicants Heuveline, Vincent ;  Ulbrich, Stefan ;  Ulbrich, Michael )
• Analysis and Numerical Techniques for Optimal Control Problems Involving Variational Inequalities Arising in Elastoplasticity (Applicants Herzog, Roland ;  Meyer, Christian )
• Automated extension of fixed point PDE solvers for optimal design with bounded retardation (Applicants Gauger, Nicolas R. ;  Griewank, Andreas ;  Slawig, Thomas )
• Automatic Differentiation for large scale flow control with application to non-Newtonian flows (Applicants Heuveline, Vincent ;  Walther, Andrea )
• consistent finite elements for otimal control problems in computational fluid dynamics (Applicants Braack, Malte ;  Prohl, Andreas )
• Control of nanostructures through electric fields (Applicant Voigt, Axel )
• Control of System Dynamics in Gas and Water Networks (Applicants Gugat, Martin ;  Herty, Michael )
• Design and Analysis of Adaptive Finite element Discretizations for Optimal Control Problems (Applicant Siebert, Kunibert G. )
• Elliptic Mathematical Programs with Equilibrium Constraints (MPECs) in function space: optimality conditions and numerical realization (Applicant Hintermüller, Michael )
• Estimation of parameters in three dimensional volume models for signal processing in neurons by optimization multigrid (Applicants Queisser, Gillian ;  Wittum, Gabriel )
• Hierarchical solution concepts for flow control problems (Applicants Hinze, Michael ;  Turek, Stefan )
• Koordinatorprojekt (Applicant Leugering, Günter )
• Model reduction by adaptive discretization in optimal control (Applicant Rannacher, Rolf )
• Multi-Scale Shape Optimization under Uncertainty (Applicants Conti, Sergio ;  Rumpf, Martin ;  Schultz, Rüdiger )
• Multilevel parameterizations and fast multigrid methods for aerodynamic shape optimization (Applicants Gauger, Nicolas R. ;  Schulz, Volker )
• Numerical analysis and discretization strategies for optimal control problems with singularities (Applicants Apel, Thomas ;  Rösch, Arnd ;  Vexler, Boris )
• Numerical analysis of state-constrained optimal control problems for PDEs (Applicant Tröltzsch, Fredi )
• Optimal control and inverse problems in radiative heat transfer (Applicant Pinnau, René )
• Optimal control-based feedback stabilization in multi-field flow problems (Applicants Benner, Peter ;  Bänsch, Eberhard )
• Optimal control in cryopreservation of cells and tissues (Applicant Hoffmann, Karl-Heinz )
• Optimal Control of Periodic Adsorption Processes (Applicants Bock, Hans Georg ;  Engell, Sebastian )
• Optimal control of self-consistent classical and quantum particle systems (Applicants Burger, Martin ;  Pinnau, René )
• Optimal control of switched networks for nonlinear hyperbolic conservation laws (Applicant Ulbrich, Stefan )
• Optimal Nodal Control Of Networked Systems Of Conservation Laws (Applicants Klar, Axel ;  Leugering, Günter )
• Optimal Treatment Planning in Radiotherapy based on Boltzmann Transport Equations (Applicants Frank, Martin ;  Herty, Michael )
• Optimization and optimal control of therapy parameters for radio-frequency-ablation (Applicants Büskens, Christof ;  Preusser, Tobias )
• Optimization of electro-mechanical smart structures (Applicants Bänsch, Eberhard ;  Kaltenbacher, Ph.D., Manfred ;  Leugering, Günter )
• Optimization of particle synthesis (Applicants Leugering, Günter ;  Peukert, Wolfgang )
• Optimization problems governed by Allen-Cahn and Cahn-Hilliard variational inequalities (Applicants Blank, Luise ;  Garcke, Harald )
• PDE Constrained Optimization Based on Adaptive Model Reduction with Applications to Shape Optimization of Microfluidic Biochips and to Blood Flow in Microchannels (Applicants Franke, Thomas ;  Hoppe, Ronald H.W. )
• Robust Shape Optimization for Artifical Blood Pumps: Hematological Design, Large-scale Transient Simulations, and Influence of Constitutive Models, Sensitivity Analysis (Applicants Behr, Ph.D., Marek ;  Bischof, Christian )
• Shape calculus for the efficient solution of shape optimization problems with elliptic and parabolic state equation (Applicants Eppler, Karsten ;  Harbrecht, Helmut )
• Structure exploiting Galerkin schemes for optimization problems with pde constraints (Applicants Deckelnick, Klaus ;  Hinze, Michael )
• Towards Optimum Experimental Design for Partial Differential Equations (Applicant Kostina, Ekaterina )

• Spokesperson: Professor Dr. Günter Leugering