Veranstaltungen

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Donnerstag, 12.12.2019, 14:00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Nancy Hitschfeld Kahler, Universdad de Chile, Santiago:
GPU computing and meshing
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
GPUs are an efficient and low cost alternative to CPU clusters for solving problems that are data-parallel or close to data parallel, but there are some restrictions in the current GPU hardware that must be taken into account in order to get efficient solutions. In this talk, fundamental concepts of GPU computing will be first introduced along with relevant techniques to make optimal use of GPU hardware, such as thread branching, coalesced memory, effective use of shared memory, thread mappings onto a triangular mesh, dynamic memory allocation, thread-safe exclusion mechanisms for neighboring triangles, and indeterminate decisions and traversals over the discrete graph structure of unstructured meshes. Then, an algorithm to transform any triangulation into a Delaunay triangulation and an implementation of a particle tracking algorithm that uses previous algorithm will be discussed. Finally, other relevant aspects to take into account such as gpu-mapping techniques and the ongoing work will be mentioned.

Veranstalter
WIAS Berlin
Donnerstag, 12.12.2019, 16:00 Uhr (WIAS-ESH)
Seminar Laserdynamik
Denis S. Goldobin, Perm State University, Russia:
Dynamics of oscillator populations beyond the Ott--Antonsen ansatz
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
WIAS Berlin
Montag, 16.12.2019, 14:00 Uhr (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
André Uschmajew, MPI Leipzig:
Optimization on low-rank manifolds
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Low-rank matrix and tensor models are important in many applications for representing and embedding high-dimensional data or functions. They typically lead to non-convex optimization problems on sets of matrices or tensors of given rank. In this talk, we give a basic introduction to the geometry of such sets and how it can be used to derive and study optimization algorithms. Compared to direct optimization of the factors in the model, the geometric approach is more intrinsic and can lead to improved methods. For a class of quadratic cost functions on matrices we also discuss how the geometric viewpoint is useful for studying the non-convex optimization landscape under low-rank constraints.

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

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Mittwoch, 18.12.2019, 11:30 Uhr (WIAS-406)
Seminar Interacting Random Systems
Siragan Gailus, Hausdorff Institute for Mathematics/Boston University:
Homogenization of multiscale diffusion processes with small noise
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
Dynamical systems exhibiting multiple characteristic scales in space or time arise naturally as models in a great variety of applied fields. It is moreover common to incorporate random perturbations into these models in order to account for imperfect information or to capture random phenomena. We will discuss homogenization and fluctuations limit theorems for a model of diffusion type. Results on statistical inference will be introduced if time permits.

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Seminar Interacting Random Systems

Veranstalter
WIAS Berlin
Mittwoch, 18.12.2019, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Jürgen Sprekels, WIAS Berlin, Humboldt-Universität zu Berlin:
Optimal control of a Cahn--Hilliard--Darcy system with mass source modeling tumor growth
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

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Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen”

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Donnerstag, 19.12.2019, 14:00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Lia Strenge, Technische Universität Berlin:
A multilayer, multi-timescale model approach for economic and frequency control in power grids using Julia
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Power systems are subject to fundamental changes due to the increasing infeed of decentralized renewable energy sources and storage. The decentral nature of the new actors in the system requires new concepts for structuring the power grid, and achieving a wide range of control tasks ranging from seconds to days. Here we introduce a multilayer dynamical network model covering a wide range of control time scales. Crucially we combine a decentralized, self-organized low-level control and a smart grid layer of devices that can aggregate information from remote sources. The stability critical task of frequency control is performed by the former, the economic objective of demand matching dispatch by the latter. Having both aspects present in the same model allows us to study the interaction between the layers. Remarkably we find that adding communication in the form of aggregation does not improve the performance in the cases considered. Instead the self-organised state of the system already contains the information required to learn the demand structure in the entire power grid. The model introduced here is highly flexible, and can accommodate a wide range of scenarios relevant to future power grids. We expect that it will be especially useful in the context of low-energy microgrids with distributed generation. All simulations and numerical experiments for control design and analysis with sampling-based methods are performed in Julia 1.1.0. The overall model is implemented as stiff nonlinear ordinary differential equation (ODE) with periodic callbacks for the control actions. The ODE has dimension 4 N, where N is the number of edges of the graph representing the power grid (i.e., N feed-in/load connections). It is planned to use automatic differentiation to learn more about the overall nonlinear model.

Veranstalter
WIAS Berlin
Mittwoch, 08.01.2020, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Michiel Renger, WIAS Berlin:
Fast reaction limits via Γ-convergence of the flux rate functional
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We consider a system of linear ODEs on a finite graph with multiple time scales, and revisit the classical problem of deriving effective equations for the evolution. If solutions of the ODEs minimise an action functional, one can study Γ-convergence of that functional, and find the effective equations as the minimiser of the limit functional. In this work we use a natural action functional that is related to the large deviations of a random particle system; the value at each vertex can then be interpreted as a particle density. Our central idea is to study densities as well as particle fluxes through each edge. This additional information allows a full decomposition of the graph into separate components, which simplifies the Γ-convergence considerably.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Donnerstag, 06.02.2020, 14:00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Holger Stephan, WIAS Berlin:
A general concept of majorization and a corresponding Robin Hood method
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
The Robin Hood method is a numerical method for constructing a double-stochastic matrix that maps a given vector to another vector that is also given. This is possible if the preimage majorizes the image. The majorization of vectors is a special order sometimes called the Lorentz order. A double-stochastic matrix is a special case of a Markov (or stochastic) matrix. In the case of a general Markov matrix, it is not yet clear when such a construction is possible, what kind of condition similar to the majorization must be fulfilled by the given vectors, nor is a numerical method for determining the matrix known (regardless some heuristic iterative versions of the Robin-Hood method).
In the talk, we give a complete solution to all these problems, including a general direct Robin Hood method. It turns out that the construction of a Markov matrix from two given pairs of two vectors is possible if and only if the pairs satisfy a certain order condition. If one interprets the vectors as states of a physical system, then this order is exactly the order known as the natural time order or the second law of thermodynamics.

Veranstalter
WIAS Berlin
Donnerstag, 27.02.2020, 14:00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Anton Stephan, Institut für Physik der Atmosphäre:
Modeling Navier--Stokes equations for high Reynolds number flows and complex geometries in aerodynamic applications
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
WIAS Berlin