CHARLEMAGNE DISTINGUISHED LECTURE SERIES - Patera Seminar
Prof. Anthony Patera, Ph.D. - Parametrized Partial Differential Equations: Mathematical Models, Computational Methods, and Applications
SSD - Stein Seminar
Prof. Dr. Oliver Stein - On Pessimistic Bilevel Optimization
Institute for Operations Research, Karlsruhe Institute of Technology
Pessimistic bilevel optimization problems, as optimistic ones, possess a structure involving three interrelated optimization problems. Moreover, their finite infima are only attained under strong conditions. We address these difficulties within a framework of moderate assumptions and a perturbation approach which allow us to approximate such finite infima arbitrarily well by minimal values of a sequence of solvable single-level problems.
To this end, we introduce the standard version of the pessimistic bilevel problem. For its algorithmic treatment, we reformulate it as a standard optimistic bilevel program with a two follower Nash game in the lower level. The latter lower level game, in turn, is replaced by its Karush-Kuhn-Tucker conditions, resulting in a single-level mathematical program with complementarity constraints.
The perturbed pessimistic bilevel problem, its standard version, the two follower game as well as the mathematical program with complementarity constraints are equivalent with respect to their global minimal points, while the connections between their local minimal points are more intricate. As an illustration, we numerically solve a regulator problem from economics for different values of the perturbation parameters.
SSD - Peric Seminar
Prof. Djordje Peric, Ph.D. - On Computational Strategies for Fluid-Structure Interaction: Concepts, Algorithms and Applications
College of Engineering, Swansea University, United Kingdom
This talk is concerned with algorithmic developments underpinning computational modelling of the interaction of incompressible fluid flow with rigid bodies and flexible structures.
Fluid-structure interaction (FSI) represents a complex multiphysics problem, characterised by a coupling between the fluid and solid domains along moving and often highly deformable interfaces. Spatial and temporal discretisations of the FSI problem result in a coupled set of nonlinear algebraic equations, which is solved by a variety of different computational strategies. The talk discusses different options available to the developers, ranging from weakly coupled partitioned schemes to strongly coupled monolithic solvers. Simple model problems are employed to illustrate the algorithmic properties of different methodologies, including a detailed convergence and accuracy analysis.
FSI problems often experience topological changes, typically associated with evolving contact conditions between solid components. In such circumstances, a careful assessment of the discretisation strategy is required in order to accurately and efficiently accommodate evolving topology of computational domain. In this context different strategies are discussed focussing on recently developed embedded interface methods and finite element formulations. The methodology relies on Cartesian b-spline grid discretization allowing for straightforward h- and p-refinement and employs Nitsche’s method to impose interface and boundary conditions. In order to ensure stability for a wide range of flow conditions a stabilized finite element formulation is employed.
Numerical examples are presented throughout the talk in order to illustrate the scope and benefits of the developed strategies. The examples are characterised by complex interaction between both external and internal flows with rigid bodies and flexible structures relevant for different areas of engineering including civil, mechanical and bio-engineering.
SSD - Pettermann Seminar
Prof. Dr. Heinz Pettermann - Modeling and Simulation of Composite Materials and Components
Institute of Lightweight Design and Structural Biomechanics,Vienna University of Technology, Vienna
Computational predictions of the mechanical behavior of composite materials and components made thereof are presented. For the simulation of components up to peak load and beyond, appropriate nonlinear constitutive material laws and efficient modeling strategies are required, which will be illustrated by two examples.
On the one hand, a constitutive law for unidirectional fiber reinforced polymers is shown. The nonlinearities are attributed to damage as well as plasticity which are treated by a direction dependent formulation. On the other hand, impact simulations on fabric laminates are presented based on a numerical efficient modeling strategy which allows for simulations of large composite structures and components.
SSD - Helzel Seminar
Prof. Dr.Christiane Helzel - A Third Order Accurate Wave Propagation Algorithm for Hyperbolic Partial Differential Equations
Institute of Mathematics, Heinrich-Heine-Universität Düsseldorf