Forschungsgruppe ''Numerische Mathematik und Wissenschaftliches Rechnen''
2011 2010 2009 2008 2007 2006 2005 2004 2003 2002
Seminar Numerische Mathematik / Numerical mathematics seminars
aktuelles Programm / current program
Donnerstag, 16. 02. 2012, 14:00 Uhr (ESH)
Dr. S. V. Sobolev (GFZ Potsdam)
Major challenges in computational geodynamicsAbstract:
Geological-scale processes in solid Earth are dominated by plate tectonics (PT). PT is a non-trivial (not existing at Venus or Mars) surface manifestation of the solid-state thermo-chemical convection in the Earth mantle. A key feature of the deformation processes in PT is extreme strain localization. The major challenge of computational geodynamics is to replicate main features of PT and its relation with mantle convection. I’ll show examples of how that is done now and which computational problems arise.
Donnerstag, 09. 02. 2012, 14:00 Uhr (ESH)
Dr. R. Schneider (Technische Universität Dresden)
With edge based refinement towards anisotropic adaptive refinement in FEMAbstract:
We propose a new paradigm for adaptive mesh refinement. Instead of considering local mesh diameters and their adaption to solution features, we propose to evaluate the benefit of possible refinements in a direct fashion, and to select the most profitable refinements. We demonstrate that based on this approach a directional refinement of triangular elements can be achieved, allowing arbitrarily high aspect ratios. However, only with the help of edge swapping and/or node removal (directional un-refinement) near optimal performance can be achieved for strongly anisotropic solution features. With these ingredients even re-alignment of the mesh with arbitrary error directions is achieved. Numerical experiments demonstrate the utility of the proposed anisotropic refinement strategy.
Donnerstag, 26. 01. 2012, 14:00 Uhr (ESH)
Dr. H. Stephan (WIAS Berlin)
Ein abstrakter Zugang zu klassischen linearen TransportproblemenAbstract:
Lineare Transportphänomene wie Drift, Diffusion oder lineare Reaktionen (Teilchenumwandlungen) lassen sich für einfache Situationen (Zustandsraum ist beschränktes Gebiet, Gleichung ist streng elliptisch) recht gut beschreiben. Unter anderem läßt sich das asymptotische Verhalten durch die Existenz von Lyapunovfunktionen abschätzen. In komplizierteren Situationen (Heterostrukturen, wechselnde Dimensionen) ist manchmal nicht einmal klar, wie der Zustandsraum zu wählen ist, was ein Wahrscheinlichkeitsmaß ist und welche Größe als Konzentration zu verstehen ist. Im Vortrag wird ein abstrakter Zugang für allgemeine Transportprobleme vorgestellt. Damit ist es - neben der Klärung der obigen Fragen - unter anderem möglich, optimale Funktionenräume für die Lösungen zu finden und manche numerischen Verfahren als Reduktion des physikalischen Problems auf ein endliches zu verstehen.
Donnerstag, 19. 1. 2012, 14:00 Uhr (ESH)
Prof. M. Bause (Helmut Schmidt Universität, Universität der Bundeswehr Hamburg)
Efficient and reliable numerical approximation of transport equations with small diffusionAbstract:
hier
Donnerstag, 12. 1. 2012, 14:00 Uhr (ESH)
G. Bauer (Technische Universität München, Lehrstuhl für Numerische Mechanik )
A variational multiscale finite element method for the numerical simulation of electrochemical systemsAbstract:
The consideration of ion-transport due to convection, diffusion and (electro-)migration plays a fundamental role for the mathematical modeling of many electrochemical systems. For example, electrodeposition of metals is an important industrial application. In typical electro-plating baths rather complex, often turbulent flow conditions arise, directly influencing the plating process. Hence, the apparent coupling to (turbulent) flow needs to be taken into account in the computational model. In this presentation, first the governing equations for incompressible flow, multi-ion transport, electric field and electrochemical reactions at electrode surfaces will be summarized, and the respective computational challenges are highlighted. Afterwards, our novel variational multiscale finite element method for solving the coupled nonlinear problem in complex cell geometries will be presented, and results from various three-dimensional numerical examples will be shown, demonstrating that the proposed method is robust and provides accurate results. Finally, our recent progress towards the simulation of ionic mass transport under turbulent flow conditions will be addressed.