EU Regional School - Püschel Seminar
Prof. Dr. Markus Püschel - Optimal Performance Numerical Code: Challenges and Solutions
Department of Computer Science, ETH Zürich, Switzerland
The complexity of modern computing platforms has made it extremely difficult to write numerical code that achieves the best possible performance. Straightforward implementations in C based on algorithms that minimize the operations count often fall short in performance by at least one order of magnitude. The reason are the inherent limitations of compilers to optimize for deep memory hierarchies, vector instruction sets, and multiple cores. The goal of this short course is to explain the problem and techniques for performance optimization using matrix multiplication and the fast Fourier transform as examples. Finally, I will discuss program generators as a way to reduce the implementation and optimization effort.
Click here for his slides.
I³MS - Voigt Seminar
Prof. Dr. Axel Voigt - Thin Films of Liquid Crystals: Modeling and Numerics
Institute of Scientific Computing, Technical University Dresden
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
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
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