Events

CHARLEMAGNE DISTINGUISHED LECTURE SERIES - Patera Seminar

Location: Heizkraftwerk (Toaster), Hörsaal 1132|603 - HKW5, from 3 pm - 4 pm

Prof. Anthony Patera, Ph.D. - Parametrized Partial Differential Equations: Mathematical Models, Computational Methods, and Applications

Ford Professor of Engineering and Professor of Mechanical Engineering
Department of Mechanical Engineering, Massachusetts Institute of Technology, USA
 

Abstract

Parametrized partial differential equations (pPDEs) play an important role in many physical disciplines and a wide variety of engineering applications. We first discuss the interplay between mathematical model and subsequent numerical treatment. We next describe two mathematical features of pPDEs which inform associated computational methods: low-dimensionality, as suggested by the parametric manifold; parameter spatial localization, as suggested by evanescence. We then consider several computational perspectives: user interfaces and apps; model reduction, in particular the reduced basis method
and the reduced basis component method; data assimilation and classification. Finally, we present applications from a range of disciplines: acoustics — mufflers and woodwinds; structures — from microtrusses to infrastructure digital twins; fluid mechanics and heat transfer — culinary natural convection. We also take advantage of pPDEs to illustrate the remarkable advances in algorithms, architectures, and processing power over the past four decades.

SSD - Stein Seminar

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Prof. Dr. Oliver Stein - On Pessimistic Bilevel Optimization

Institute for Operations Research, Karlsruhe Institute of Technology

Abstract

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

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Prof. Djordje Peric, Ph.D. - On Computational Strategies for Fluid-Structure Interaction: Concepts, Algorithms and Applications

College of Engineering, Swansea University, United Kingdom 

Abstract

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

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Prof. Dr. Heinz Pettermann - Modeling and Simulation of Composite Materials and Components

Institute of Lightweight Design and Structural Biomechanics,Vienna University of Technology, Vienna

Abstract

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

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Prof. Dr.Christiane Helzel - A Third Order Accurate Wave Propagation Algorithm for Hyperbolic Partial Differential Equations

Institute of Mathematics, Heinrich-Heine-Universität Düsseldorf

Abstract

The wave propagation algorithm of LeVeque and its implementation in the software package Clawpack are widely used for the approximation of hyperbolic problems. The method belongs to the class of truly multidimensional, high-resolution finite volume methods. Furthermore, it can be characterised as a one-step Lax-Wendroff type method, i.e. the PDE is solved simultaneously in space and time. Approximations obtained with this method are second order accurate for smooth solutions and avoid unphysical oscillations near discontinuities or steep gradients. 
 
Second order accurate methods are often a good choice in terms of balance between computational cost and desired resolution, especially for solutions dominated by shock waves or contact discontinuities and relatively simple structures between these discontinuities. However, for problems containing complicated smooth solution structures, where the accurate resolution of small scales is require, schemes with a higher order of accuracy are more efficient and computationally affordable.
 
I will present my recent work towards the construction of a third order accurate wave propagation algorithm for hyperbolic pdes. The resulting method shares main properties with the original method, i.e. it is based on a wave decomposition at grid cell interfaces, it can be used to approximate hyperbolic problems in divergence form as well as in quasilinear form and limiting is introduced in the form of
a wave limiter. Furthermore, I will compare this new method with other recently proposed third order accurate finite volume methods.