Events

I³MS - Voigt Seminar

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Prof. Dr. Axel Voigt - Thin Films of Liquid Crystals: Modeling and Numerics

Institute of Scientific Computing, Technical University Dresden

Abstract

We consider a thin film limit of a Frank-Oseen and a Landau-de Gennes model. In the limiting process we observe a continuous transition where the normal and tangential parts of the director field and the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. Main properties of the thin film model, like uniaxiality and parameter phase space, are preserved in the limiting process. For the derived surface Frank-Oseen and surface Landau-de Gennes model, we consider an $L^2$-gradient flow. The resulting vector- and tensor-valued surface partial differential equations are numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties and the topology of the surface. We will explain the 
numerical approaches in detail and discuss various model extensions. 

EU Regional School - Hennig Seminar

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Prof. Philipp Hennig, Ph.D - Probabilistic Numerics — Uncertainty in Computation

Department of Probabilistic Numerics, Max Planck Institute for Intelligent Systems, Tübingen

Abstract

Data Analysis and Machine learning are prominent topics of contemporary computer science. Their computational complexity is dominated by the solution of non-analytic numerical problems (large-scale linear algebra, optimization, integration, the solution of differential equations). But a converse of sorts is also true: numerical algorithms for these tasks are learning machines! They estimate intractable quantities from observable (computable) quantities. Because they also decide which numbers to compute, these methods can be interpreted as autonomous inference agents. This observation lies at the heart of the emerging area of probabilistic numerical computation, which applies the concepts of probabilistic inference to the design of algorithms, assigning a notion of uncertainty to the result of even deterministic computations. I will outline how this viewpoint is connected to that of classic numerical analysis, then show some concrete examples of algorithms that use the probabilistic formalism to address contemporary algorithmic challenges in large-scale machine learning.

I³MS - Lindgren Seminar

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Dr. Eric Lindgren - Modelling of Electrostatic Self-Assembly in Many-Body Dielectric Systems

AICES Graduate School, RWTH Aachen University

Abstract

A numerical method based on a Galerkin approximation of an integral equation formulation to compute electrostatic interactions between many dielectric particles will be introduced. The method is sufficiently general, as it is able to treat systems embedded in a homogeneous dielectric medium, containing an arbitrary number of spherical particles of arbitrary size, charge, dielectric constant and position in the three-dimensional space. Simple numerical examples will be presented to illustrate the capabilities of the model, and special focus will be given to the influence of non-additive mutual polarization between particles in an electrostatic interaction. Calculations that successfully reproduce many of the observed patterns of behaviour of two experimental studies relating to electrostatic self-assembly will also be presented. The first study relates to experiments on the assembly of polymer particles that have been subjected to tribocharging, and the second study explores events observed following collisions between single particles and small clusters composed of charged particles derived from a metal oxide composite. Finally, current developments relating to the continuum treatment of ionic species in the medium will be briefly addressed.

I³MS - Rozza Seminar

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Prof. Gianluigi Rozza, Ph.D - Reduced Order Methods: State of the Art and Perspectives with a Special Focus on Computational Fluid Dynamics

SISSA, International School for Advanced Studies, Mathematics Area, mathLab, Trieste, Italy

Abstract

In this talk, we provide the state of the art of Reduced Order Methods (ROM) for parametric Partial Differential Equations (PDEs), and we focus on some perspectives in their current trends and developments, with a special interest in parametric problems arising in offline-online Computational Fluid Dynamics (CFD). Systems modelled by PDEs are depending by several complex parameters in need of being reduced, even before the computational phase in a pre-processing step, in order to reduce parameter space.
Efficient parametrizations (random inputs, geometry, physics) are very important to be able to properly address an offline-online decoupling of the computational procedures and to allow competitive computational performances. Current ROM developments in CFD include: a better use of stable high fidelity methods, considering also spectral element method, to enhance the quality of the reduced model too; more efficient sampling techniques to reduce the number of the basis functions, retained as snapshots, as well as the dimension of online systems; the improvements of the certification of accuracy based on residual based error bounds and of the stability factors, as well as the the guarantee of the stability of the approximation with proper space enrichments. For nonlinear systems, also the investigation on bifurcations of parametric solutions are crucial and they may be obtained thanks to a reduced eigenvalue analysis of the linearised operator. All the previous aspects are very important in CFD problems to be able to focus in real time on complex parametric industrial and biomedical flow problems, or even in a control flow setting, and to couple viscous flows -velocity, pressure, as well as thermal field - with a structural field or a porous medium, thus requiring also an efficient reduced parametric treatment of interfaces between different physics.

I³MS - Kirchhart Seminar

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Dr. Matthias Kirchhart - Vortex Methods for Incompressible Flows

AICES Graduate School, RWTH Aachen University

Abstract

Vortex methods are numerical schemes for solving the incompressible
Navier–Stokes equations. These equations accurately describe the motion
of both gases and liquids as we encounter them in everyday life, i.e.,
at velocities far below the speed of sound and not subject to extreme
temperatures or pressures. It is hard to overestimate their importance
in engineering applications, where they can for example be used to
minimise air-resistance and thereby fuel consumption of cars. However,
current numerical schemes for these equations face severe problems when
applied to turbulent flows: stringent time-step constraints,
instabilities, or the introduction of significant amounts of artificial,
spurious viscosity make their application infeasible or render the
results unusable.

Vortex methods, on the other hand, are particle methods that are based
on the vorticity formulation of the Navier–Stokes equations. This
formulation comes with two main benefits: the pressure variable is
eliminated and the system consists of separate dynamic and kinematic
parts, which can be treated independently with semi-analytical schemes.
The dynamic part is discretised using particles, which are then
convected with the flow. This natural treatment of convection renders
the method virtually free of artificial viscosity. The kinematic part of
the equations is solved using a solver based on the Biot–Savart law,
which guarantees incompressibility in the strong, point-wise sense. In
addition, in the two-dimensional case, the resulting schemes can be
shown to also conserve circulation, linear momentum, angular momentum,
and energy. These properties make vortex methods an interesting
alternative to current, mesh-based alternatives.

In this talk we will first describe a simple vortex method in the
unbounded, two-dimensional setting to illustrate the intuition of
vortex methods. We then present basic results from their analysis,
before moving on to discuss some of the problems vortex methods are
facing in three-dimensional bounded domains. We present recent research
results on one of these problems and conclude with an outlook to further
research opportunities.

References
[1] G.-H. Cottet and P. D. Koumoutsakos. Vortex Methods. Theory and
Practice. Cambridge University Press, 2000. ISBN: 0521621860.

[2] A. J. Majda and A. L. Bertozzi. Vorticity and Incompressible Flow.
Cambridge University Press, Nov. 2001. ISBN: 0521630576.

[3] M. Kirchhart and S. Obi. ‘A Smooth Partition of Unity Finite Element
Method for Vortex Particle Regularization’. In: SIAM Journal on
Scientific Computing 39.5 (Oct. 2017), pp. A2345–A2364. ISSN: 1064–8275.
DOI: 10.1137/17M1116258.