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12. Januar14:00  15:30
Ort: 48210Graduate SchoolSuchde, Pratik: Conservation and Accuracy in Meshfree Generalized Finite Difference Methods
Kategorie: Disputationen, Graduate School 
16. Januar17:15  18:30
Ort: Raum 48210Fachbereich MathematikProf. Dr. Andreas Neuenkirch, Universität Mannheim, "Recent Developments in Numerical Methods for SDEs"
Kategorie: FelixKleinKolloquienStochastic differential equations (SDEs) are an important modeling tool in many areas of science. Since explicit solutions are unknown, one has to rely on numerical methods for the simulation of such SDEs. The traditional convergence analysis for numerical methods relies on the global Lipschitz assumption for the coefficients of the SDEs. However, this is rarely met in practice.
The last ten years have seen a rapid growth in the numerical analysis of SDEs without the global Lipschitz condition. Examples include superlinear or square root coefficients, which appear e.g. in biology and mathematical finance.
After an introduction into SDEs and classical numerical results I will give a review of these developments. Moreover, I will present recent findings in the case of discontinuous coefficients. This final part is based on a joint work with M. Szölgyenyi (ETH Zürich) and L. Szpruch (U Edinburgh).

18. Januar11:30  13:00
Ort: 32349Dr. Görtz, DLR: Surrogate and ReducedOrder Models for Use in Aerodynamic Applications, MDO and Robust Design
Kategorie: AG TechnomathematikReduced Order Models (ROMs) have found widespread application in fluid dynamics and aerodynamics. In their direct application to Computational Fluid Dynamics (CFD) ROMs seek to reduce the computational complexity of a problem by reducing the number of degrees of freedom rather than simplifying the physical model. Here, parametric nonlinear ROMs based on highfidelity CFD are used to provide approximate flow solutions, but at lower evaluation time and storage than the original CFD model. ROMs for both steady and unsteady aerodynamic applications are presented. We consider ROMs combining proper orthogonal decomposition (POD) and Isomap, which is a manifold learning method, with surrogatebased interpolation methods as well as physicsbased ROMs, where an approximate solution is found in the PODsubspace by minimizing the corresponding steady or unsteady flowsolver residual. The issue of how to best “train” the ROM with highfidelity CFD data is also addressed. The goal is to train ROMs that yield a large domain of validity across all parameters and flow conditions at the expense of a relatively small number of CFD solutions. The different ROM methods are demonstrated on a widebody transport aircraft configuration at transonic flow conditions.
In the second part of this talk we present a robust design optimization framework for aircraft design and show results for robust aerodynamic design. As a first step, we focus on quantifying uncertainties in the drag coefficient using nonintrusive methods. To reduce the computational effort required to compute the output uncertainties we make use of a Sobol sequencebased quasi Monte Carlo method (QMC) and a gradientenhanced Kriging (GEK) surrogate model. A small number of samples is computed with the fullorder CFD code TAU and its adjoint version to construct the GEK model. The statistics are computed by interrogating the surrogate model with a QMC method using a sufficiently large number of samples. In terms of the input uncertainties, we are interested both in operational and geometrical uncertainties. Our strategy to model the inherently large number of geometrical uncertainties is by using a truncated KarhunenLoève expansion (tKLE), which introduces some elements of model uncertainty. Then, a Subplex algorithm is used to optimize different robustness measures. The test case used here to demonstrate the framework is a transonic RAE2822 airfoil.
Finally, current work aiming to extend our framework for uncertainty quantification and management (UQ&M) based on highfidelity CFD to the loads process, especially at extremes of the flight envelope. 
18. Januar17:00  18:00
Ort: 48436AG Algebra, Geometrie und Computer AlgebraFlorian Eisele, University of London: A counterexample to the first Zassenhaus conjecture
Kategorie: AG Algebra, Geometrie und ComputeralgebraThere are many interesting problems surrounding the unit group U(RG) of the ring RG, where R is a commutative ring and G is a finite group. Of particular interest are the finite subgroups of U(RG). In the seventies, Zassenhaus conjectured that any u in U(ZG) is conjugate, in the group U(QG), to an element of the form +/g, where g is an element of the group G. This came to be known as the "Zassenhaus conjecture". In recent joint work with L. Margolis, we were able to construct a counterexample to this conjecture. In this talk I will give an introduction to the various conjectures surrounding finite subgroups of U(RG), and how they can be reinterpreted as questions on the (non)existence of certain R(GxH)modules, where H is another finite group. This establishes a link with the representation theory of finite groups, and I will explain how, plocally, our example is made up of certain ppermutation modules.

19. Januar13:45  15:15
Ort: 48210Graduate SchoolLo, Pak Hang: An Iterative Plugin Algorithm for Optimal Bandwidth Selection in Kernel Intensity Estimation for Spatial Data
Kategorie: Disputationen, Graduate School 
25. Januar17:00  18:00
Ort: 48436AG Algebra, Geometrie und Computer AlgebraPetra Schwer, KIT Karlsruhe: Reflection length in affine Coxeter groups
Kategorie: AG Algebra, Geometrie und ComputeralgebraAffine Coxeter groups have a natural presentation as reflection groups on some affine space. Hence the set R of all its reflections, that is all conjugates of its standard generators, is a natural (infinite) set of generators. Computing the reflection length of an element in an affine Coxeter group means that one wants to determine the length of a minimal presentation of this element with respect to R. In joint work with Joel Brewster Lewis, Jon McCammond and T. Kyle Petersen we were able to provide a simple formula that computes the reflection length of any element in any affine Coxeter group. In this talk I would like to explain this formula, give its simple uniform proof and allude to the geometric intuition behind it.