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Tuesday, 20.02.2018, 15:00 (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. P. Dvurechensky, WIAS Berlin:
Faster algorithms for (regularized) optimal transport
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
We propose an alternative to ubiquitous Sinkhorn algorithm for solving regularized optimal transport problem. Our approach is based on accelerated gradient descent applied to the dual problem and allows to solve not only entropy-regularized optimal transport problem, but also squared-2-norm-regularized OT problem, which produces sparser optimal transport plan approximation. We prove that, our algorithm, allows to solve non-regularized optimal transport problem with support size $p$ up to accuracy $epsilon$ in $Oleft(minleftfracp^9/4epsilon, fracp^2epsilon^2 rightright)$ arithmetic operations, which is better than state-of-the-art result $Oleft(fracp^2epsilon^3right)$.

Host
WIAS Berlin
Wednesday, 21.02.2018, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar) & Seminar Materialmodellierung
Dr. M. Morandotti, TU München:
Dimension reduction in the context of structured deformations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The theory of structured deformations shows good potential to deal with mechanical problems where multiple scales and fractures are present. Math- ematically, it amounts to relaxing a given energy functional and to show also the relaxed one has an integral representation. In this seminar, I will focus on a problem for thin objects: the derivation of a 2D relaxed energy via dimension reduction from a 3D energy, incorporat- ing structured deformations in the relaxation procedure. I will discuss the two-step relaxation (first dimension reduction, then structured deformations and vice versa) and I will compare it with another result in which the two relaxation procedures are carried out simultaneously. An explicit example for purely interfacial initial energies will complete the presentation. These results have been obtained in collaboration with G. Carita, J. Matias, and D.R. Owen.

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Thursday, 01.03.2018, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. F. Dassi, Politecnico di Milano, Italien:
Recent advancements of the Virtual Element Method in 3D
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The Virtual Element Method is a novel way to discretize a partial differential equation. It avoids the explicit integration of shape functions and introduces an innovative construction of the stiffness matrix so that it acquires very interesting properties and advantages. One among them is the possibility to apply the VEM to general polygonal/polyhedral domain decomposition, also characterized by non-conforming and non-convex elements.
In this talk we focus on the definition/construction of the Virtual Element functional spaces in three dimensions and how apply this new strategy to set a standard Laplacian problem in 3D.
Finally we test the method to show its robustness with respect to element distortion and the polynomial approximation degree $k$. Then, we move to more involved cases: convection-diffusion-reaction problems with variable coefficients and magnetostatic Maxwell equations.

Host
WIAS Berlin
Thursday, 03.05.2018, 14:00 (WIAS-ESH)
Seminar Numerische Mathematik
Dr. H. Stephan, WIAS Berlin:
One million perrin pseudo primes including a few giants
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin