# Events

# I³MS - Voigt Seminar

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

Institute of Scientific Computing, Technical University Dresden

### Abstract

# EU Regional School - Hennig Seminar

## 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

## 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

## 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

# I³MS - Kirchhart Seminar

## 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.