Workshop on Applied Problems with Partial Differential Equations
The purpose of the workshop is to bring together experts from the
mathematical, computational, physical, and engineering communities
from Vienna, who work with Partial Differential Equations, and to
provide a platform for the exchange of new ideas. The meeting aims at
identifying scientific contact points and stimulating joint research
between the different communities, for instance in the framework of
joint projects or joint bachelor, master, and PhD theses. The workshop
welcomes both junior as well as senior participants.
Time: December 15, 2015, 9:00h - 17:30h
Location: TUtheSky, 11th floor, Getreidemarkt 9, 1060 Wien
Organizers: Anton Arnold (Vienna), Ansgar Jüngel (Vienna)
- Lukas Jadachowski (Automation and Control, TU Wien)
Backstepping observers for some classes of parabolic PDEs
This talk is mainly concerned with the state estimation problem for some classes
of parabolic PDEs with boundary sensing. For this, a Luenberger-type state
observer is introduced with observer corrections entering both the PDE and the
boundary conditions. The backstepping method for PDEs is employed and suitably
extended to systematically determine the output injection gains, which ensures
the exponential decay of the observer error dynamics. Additionally, an efficient
approach for the solution of the arising kernel-PDE of the backstepping
transformation is proposed. Finally, some extensions of the backstepping-based
observer design for hyperbolic PIDEs are presented.
- Georg Kresse (Computational materials Physics, Uni Wien)
Schrödinger equation for many electrons: an unsolved or unsolvable problem
The solution of the many particle Schrödinger equation scales
combinatorial with the basis set size (M) and the number
of electrons N, specifically the scaling is (M over N).
This makes an exact solution of the many particle Schrödinger
equation practically impossible for all but the simplest few electron systems.
Finding approximate solutions to the Schrödinger equation has
been an active field of research for almost 50 years in physics
and chemistry, but progress has been slow and at best incremental.
This talk summarises successful approaches to the
solution of the Schrödinger equation. Usually the approaches rely on
second quantization (a compact algebra for Fermions),
and either Monte-Carlo procedures or an exponential ansatz for the many body wave
function. Whereas the Monte-Carlo procedures retains exponential scaling
with the particle number, the exponential ansatz yields
algebraic scaling with respect to the basis set size,
which is quite remarkable considering that the original problem is
generally considered to be NP-hard. Alternative approaches, such as
tensor networks will be also briefly mentioned.
- Dirk Praetorius (Analysis and Scientific Computing, TU Wien)
Numerical integration of the Landau-Lifshitz-Gilbert equation
The nonlinear Landau-Lifshitz-Gilbert equation (LLG) describes time-dependent
micromagnetic phenomena in terms of a magnetization field m which solves LLG.
Numerical challenges arise from an inherent non-convex constraint |m| = 1 and a
possibly nonlinear coupling with other partial differential equations to describe, e.g.
magnetostrictive effects or the interaction of m with spin-polarized currents. In our
talk, we will discuss numerical integrators which are proved to be unconditionally
convergent in the sense that any CFL-type coupling of the space discretization and
the time stepping is avoided. A particular focus will be on IMEX-type integrators
which also decouple the time stepping of LLG and the coupled second PDE.
- Stefan Rotter (Theoretical Physics, TU Wien)
I will discuss our recent work on non-Hermitian systems with gain or loss in which
so-called "exceptional points" appear.
These are non-Hermitian degeneracies at which
two eigenvalues coalesce in both their real and imaginary parts. As we could recently
demonstrate in collaboration with several experimental groups, such exceptional
points are a veritable source of non-trivial phenomena. I will discuss our recent
insights on this matter as well as open questions and possible future directions.
Non-Hermitian physics close to exceptional points
- Karl Rupp (Microelectronics, TU Wien)
Massively parallel numerical solution of PDEs: challenges and opportunities
The efficient numerical solution of PDEs on current supercomputers equipped with
thousands of cores requires algorithms exposing fine-grained parallelism. Also,
all-to-all communication between processors becomes increasingly expensive, hence
novel algorithms employ so-called pipelining techniques and avoid communication
whenever possible. This talk provides an overview of the current status of research
and outlines promising directions for scaling the numerical solution of PDEs to even
- Christian Schmeiser (Mathematics, Uni Wien)
Cell membrane interaction with membrane proteins and with the cytoskeleton
Biological cells and intracellular compartments are enclosed by
the cell membrane, a lipid bilayer, which resists bending and has the
tangential behavior of a two-dimensional incompressible fluid. It strongly
interacts with other cellular compartments and it is important for the
regulation of various cellular processes. A model for the interaction of
the cell membrane with the cytokeleton in lamellipodia will be presented,
and various modeling and computational issues will be discussed. These are
results of cooperations with experimental biologists at IMBA and at IST.
- Jörg Schmiedmayer (Vienna Center for Quantum Science and Technology,
Bose-Einstein condensates described by the Gross-Pitaevskii equation -
numerics helps experiment
In our experiments we study the equilibrium and out of equilibrium properties of
ultra-cold one-dimensional degenerate quantum fluids. To a good approximation our
experiments are described by the Gross-Pitaevskii equation (GPE), and simulating
the finite temperature states and their dynamics guides the experiments. I will
give a few examples ranging from relaxation in 1d systems, to dynamics and optimal
control. Finally I will discuss physical situations when the stochastic GPE is
not sufficient enough and one needs to apply multi-configurational methods like
MCTDHB to describe the many body dynamics.
- Herbert Steinrück (Fluid Mechanics and Heat Transfer, TU Wien)
Marginal separation, the Fisher equation and blow-ups
In flows around an airfoil, small separation bubbles may occur near
the leading edge. The structure of the flow near these bubbles can be analyzed
using an asymptotic expansion with respect to large Reynolds numbers
and small deviations of the angle of attack from a critical value.
An integro-differential equation can be obtained as a solvability condition
which describes the local flow behavior. For two-dimensional, stationary flows
this equation has two, one or no solution depending on the scaled angle of
attack. Near the bifurcation point a further analysis for weakly three-dimensional,
slowly time-varying flows is possible yielding the so-called
Fisher-Kolmogoroff-Petrovsky-Piscounoff (FKPP) equation.
The FKPP-equation has solutions with a finite time blow-up.
From a physical point of view, these blow-ups have an interpretation as
bubble bursts when fluid is rapidly ejected from the boundary in a very
short event. After that, the boundary-layer flow calms down again.
Thus, the question arises if there is a meaningful mathematical concept to
continue the solution after the (local) blow-ups and how to handle the
|09:00 - 09:45
|09:50 - 10:20
|10:20 - 11:05
|11:10 - 11:55
|12:00 - 13:30
|13:30 - 14:15
|14:20 - 15:05
|15:10 - 15:40
|15:40 - 16:10
|16:15 - 16:45
|16:50 - 17:20