SQLSTATE[42000]: Syntax error or access violation: 1064 You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near ')' at line 1 DFG SPP 1962 - Projects from Phase 1

Phase 1 of the SPP1962 ran from October 2016 to October 2019 and has been superseded by the current phase.

List of projects in Phase 1

  • Approximation of Monge-Kantorovich Problems
  • Coupling Hyperbolic PDEs with Switched DAEs: Analysis, Numerics and Application to Blood Flow Models
  • Numerical Methods for Diagnosis and Therapy Design of Cerebral Palsy by Bilevel Optimal Control of Constrained Biomechanical Multi-Body Systems
  • Parameter Identification in Models With Sharp Phase Transitions
  • Multiobjective Optimal Control of Partial Differential Equations Using Reduced-Order Modeling
  • Analysis and Solution Methods for Bilevel Optimal Control Problems
  • Identification of Energies from Observations of Evolutions
  • A Calculus for Non-Smooth Shape Optimization with Applications to Geometric Inverse Problems
  • Optimal Control of Dissipative Solids: Viscosity Limits and Non-Smooth Algorithms
  • Generalized Nash Equilibrium Problems with Partial Differential Operators: Theory, Algorithms, and Risk Aversion
  • Optimal Control of Elliptic and Parabolic Quasi-Variational Inequalities
  • Coordination Funds
  • Simulation and Control of a Nonsmooth Cahn-Hilliard Navier–Stokes System with Variable Fluid Densities
  • Algorithms for Quasi-Variational Inequalities in Infinite-Dimensional Spaces
  • Non-smooth Methods for Complementarity Formulations of Switched Advection-Diffusion Processes
  • Optimal Control of Variational Inequalities of the Second Kind with Application to Yield Stress Fluids
  • Optimizing Fracture Propagation Using a Phase-Field Approach
  • Optimal Control of Static Contact in Finite Strain Elasticity
  • Shape Optimization for Maxwell's Equations Including Hysteresis Effects in the Material Laws
  • Optimizing Variational Inequalities on Shape Manifolds
  • Multi-Leader-Follower Games in Function Space
  • Stress-Based Methods for Variational Inequalities in Solid Mechanics: Finite Element Discretization and Solution by Hierarchical Optimization
  • Optimization methods for mathematical programs with equilibrium constraints in function spaces based on adaptive error control and reduced order or low rank tensor approximations
  • Optimization of Non-smooth Hyperbolic Maxwell's Equations in Type-II Superconductivity Based on the Bean Critical State Model

Communicating Research Areas

  • Modeling, problem analysis, algorithm design and convergence analysis

    The focus of this area is on the development and analysis of genuinely non-smooth models in the sciences in order to properly capture real-world effects and to avoid comprising smoothing approaches. In simulation and optimization this requires to advance set-valued analysis and the design of robust algorithms for non-smooth problems.

  • Realization of algorithms, adaptive discretization and model reduction

    As the target applications of this SPP involve non-smooth structures and partial differential operators, the discretization of the associated problems and robust error estimation are important issues to be address, and proper model-reduction techniques need to be developed.

  • Incorporation of parameter dependencies and robustness

    In many applications the robustness of solutions with respect to a given parameter range (uncertainty set) is highly relevant. Correspondingly, in this research area of the SPP, bi- or multilevel optimization approaches will be studied in order to robustify problem solutions against uncertain parameters.