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Wednesday, 19.12.2018, 11:00 (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. O. Huber, Humboldt-Universität zu Berlin:
Using reformulations in nonsmooth mathematical programming: the examples of friction contact problems and optimal value functions
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk we illustrate how reformulations can be used to deal with nonsmoothness. In particular, we look at two specific structures arising from applications: the first one concerns finite dimensional variational inequalities with a nonsmooth functional. This is motivated by the study of contact problems with Coulomb friction. The second example involves optimization models with Optimal Value Functions (OVF) in the problem data. The OVF concept subsumes regularizers from fitting problems and coherent risk measures from Stochastic Optimization. Each reformulation scheme rely on tools from convex and variational analysis. In both instances, we obtain equivalent problems that are solvable by off-the-shelf solvers. Finally, numerical results are presented and discussed: in the OVF case, the example is a risk-averse equilibrium problem from the electricity market.

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Joint Research Seminar on Mathematical Optimization / Non-smooth Variational Problems and Operator Equations

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Wednesday, 19.12.2018, 11:30 (WIAS-406)
Seminar Interacting Random Systems
C. Betken, Universität Osnabrück:
Dynamic random graphs: Sedentary random waypoint and preferential attachment models
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Further Informations
Seminar Interacting Random Systems

Host
WIAS Berlin
Thursday, 10.01.2019, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. N. Ahmed, Lahore University of Management Sciences, Pakistan:
Numerical comparisons of finite element stabilized methods for a 2D vortex dynamics simulation at high Reynolds number
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk, I will present an up-to-date and classical Finite Element (FE) stabiliz ed methods for time-dependent incompressible flows. All studied methods belong to the Variational MultiScale (VMS) framework. So, different realizations of stabilized FE-VMS methods are compared in a high Reynolds number vortex dynamics simulation. In particular, a fully Residual-Based (RB)-VMS method is compared with the classical Streamline-Upwind Petrov--Galerkin (SUPG) method together with grad-div stabilization, a standard one-level Local Projection Stabilization (LPS) method, and a recently proposed LPS method by interpolation. These procedures do not make use of the statistical theory of equilibrium turbulence, and no ad-hoc eddy viscosity modeling is required for all methods. Applications to the simulation of a high Reynolds numbers flow with vortical structures on relatively coarse grids are showcased, by focusing on a two-dimensional plane mixing-layer flow. Both Inf-Sup Stable (ISS) and Equal Order (EO) (H^1)-conforming FE pairs are explored, using a second-order semi-implicit Backward Differentiation Formula (BDF2) in time. Based on the numerical studies, it is concluded that the SUPG method using EO FE pairs performs best among all methods. Furthermore, there seems to be no reason to extend the SUPG method by the higher order terms of the RB-VMS method.

Host
WIAS Berlin
Wednesday, 23.01.2019, 11:30 (WIAS-406)
Seminar Interacting Random Systems
P. Houdebert, Aix-Marseille Université, Frankreich:
Sharp phase transition for the Widom-Rowlinson model
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
The Widom-Rowlinson model is formally defined as two homogeneous Poisson point processes forbidding the points of different type to be too close. For this Gibbs model the question of uniqueness/ non-uniqueness depending on the two intensities is relevant. This model is famous because it was the first continuum Gibbs model for which phase transition was proven, in the symmetric case of equal intensities large enough. But nothing was known in the non-symmetric case, where it is conjectured that uniqueness would hold. In a recent work with D. Dereudre (Lille), we partially solved this conjecture, proving that for large enough activities the phase transition is only possible in the symmetric case of equal intensities. The proof uses percolation and stochastic domination arguments.

Further Informations
Seminar Interacting Random Systems

Host
WIAS Berlin
Wednesday, 23.01.2019, 15:00 (WIAS-ESH)
Seminar Numerische Mathematik
Prof. V. A. Garanzha, Russian Academy of Sciences:
Moving adaptive meshes based on the hyperelastic stress deformation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We suggest an algorithm for the time-dependent mesh deformation based on the minimization of hyperelastic quasi-isometric functional without introducing time derivatives. The source of deformation is a time-dependent metric tensor in Eulerian coordinates. Due to the nonlinearity of the Euler-Lagrange equations we can not assume that the norm of its residual is reduced to zero at each time step. Thus, time continuity of the moving mesh is not guaranteed since iterative minimization may result in considerable displacements even for infinitely small time steps. To solve this problem, we introduce a special variant of factorized representation of Lagrangian metric tensor and nonlinear interpolation procedure for factors of this metric tensor. Continuation problem with respect to interpolation parameters is similar to the hypoelastic deformation with a controlled stress relaxation. At each time step we start with a Lagrangian metric tensor which completely eliminates internal elastic stresses and makes current mesh an exact solution of the Euler-Lagrange equations. The continuation procedure gradually introduces internal stresses back while forcing the deformation to follow the prescribed Eulerian metric tensor. At each step of the continuation procedure the functional is approximately minimized using a few steps of the parallel preconditioned gradient search algorithm. We derive an auxiliary discrete evolution equation for target shape matrices (factors of Lagrangian metric tensor) which resembles stress relaxation equations in hypoelasticity. We present 2d and 3d examples of moving deforming meshes which serve to represent moving bodies for parallel immersed boundary flow solver.

Host
WIAS Berlin