Zurich colloquium in applied and computational mathematics

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Autumn Semester 2015

Date / Time

Speaker

Title

Location

16 September 2015
16:15-17:15

Prof. Dr. Ivan Graham
University of Bath

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	On domain decomposition preconditioners for finite element approximations of the Helmholtz equation using absorption
Speaker, Affiliation	Prof. Dr. Ivan Graham, University of Bath
Date, Time	16 September 2015, 16:15-17:15
Location	Y27 H 25

On domain decomposition preconditioners for finite element approximations of the Helmholtz equation using absorption

Y27 H 25

23 September 2015
16:15-17:15

Prof. Dr. Eugene Tyrtyshnikov
Russian Academy of Sciences

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Advances in low-rank approximation of tensors and matrices
Speaker, Affiliation	Prof. Dr. Eugene Tyrtyshnikov, Russian Academy of Sciences
Date, Time	23 September 2015, 16:15-17:15
Location	HG E 1.2
Abstract	We consider special decompositions for multi-dimensional matrices (tensors) that are intrinsically based on low-rank decompositions of some associated matrices and chiefly focus on the ``cross methods'' that construct these decompositions using only very small portion of the entries of those matrices. We consider possible extensions of the maximal volume concept and relation with the following classical problem: given a system of n vectors of size m, find a subsystem consisting of k vectors so that the expansion of any other vector over this subsystem has the coefficients sufficiently small in modulus. The maximal volume principle allows one to find a subsystem of k=m vectors with a guarantee that all expansions have the coefficients in modulus bounded by 1. If we increase k, then smaller coefficients could be obtained. We present different settings of the problem and some new results and discuss applications to the problem of construction of low-rank approximations to matrices and tensors.

Advances in low-rank approximation of tensors and matricesread_more

HG E 1.2

14 October 2015
16:15-17:15

Prof. Dr. Jean-Claude Latché
CEA-IRNS

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Staggered schemes for all Mach flows
Speaker, Affiliation	Prof. Dr. Jean-Claude Latché, CEA-IRNS
Date, Time	14 October 2015, 16:15-17:15
Location	Y27 H 25
Abstract	Finite volume schemes using a staggered arrangement of the unknowns are widely used for the computation of incompressible flows. This talk will present extensions of theses algorithms to compressible flows. Space discretization is based either on the classical Marker And Cell (MAC) scheme or on the low-order finite elements of Rannacher&Turek or Crouzeix&Raviart. Time discretization may be implicit or realized by a fractional step algorithm inspired from pressure-correction techniques. The barotropic Euler equations will first be addressed : the schemes will be described, and the asymptotic preserving property for vanishing Mach numbers will be proved ; more precisely speaking, we will show that, for a given mesh and when the Mach number tends to zero, the discrete density converges to a constant, and the pressure and velocity fields converge to a solution of a standard (inf-sup stable) scheme for incompressible flows. Then the approach will be extended to cope with full (i.e. non-barotropic) Euler equations.

Staggered schemes for all Mach flowsread_more

Y27 H 25

28 October 2015
16:15-17:15

Prof. Dr. Thomas Wihler
Uni Bern

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Fully Adaptive Newton-Galerkin Methods for Semilinear Problems
Speaker, Affiliation	Prof. Dr. Thomas Wihler, Uni Bern
Date, Time	28 October 2015, 16:15-17:15
Location	Y27 H 25
Abstract	In this talk we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples. An outlook to time-dependent problems will be given also.

Fully Adaptive Newton-Galerkin Methods for Semilinear Problemsread_more

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4 November 2015
16:15-17:15

Volker Mehrmann
TU Berlin

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Model reduction vs reduced order modeling in optimal feedback control of flow problems
Speaker, Affiliation	Volker Mehrmann, TU Berlin
Date, Time	4 November 2015, 16:15-17:15
Location	Y27 H 25
Abstract	In optimal control of physical problems governed by non-stationary partial differential-equations, a typical procedure is to first discretize the forward problem, then to carry out a model order reduction and to perform the optimization on the reduced order model. Although this works very well for many parabolic problems, it quickly gets to its limits (in particular for transport dominated problems) due to the high cost of the model reduction process and the difficulty to capture the important phenomena. In classical control engineering, instead one uses a small surrogate model that is produced from measured or simulated input/output data via a realization and applies the optimal control in a local feedback loop. This approach is very successful in almost all areas of science and technology but also reaches its limits when it is difficult to capture highly nonlinear behavior. In this talk we present a concept that uses a direct Galerkin/Petrov Galerkin discretization of the input/output map that can be adapted to the behavior of the transfer operator as well as the state behavior to obtain reduced order models and to use in optimal control of flow problems. We present some analytic results that show that in this way the error between space, time and transfer operator discretization can be balanced. We also present several numerical examples of successful applications of this technique.

Model reduction vs reduced order modeling in optimal feedback control of flow problemsread_more

Y27 H 25

11 November 2015
17:30-18:30

Prof. Dr. Christof Schuette
FU Berlin

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Computational Science Distinguished Colloquium: Computational Molecular Design - From Mathematical Theory via High Performance Computing to In Vivo Experiments
Speaker, Affiliation	Prof. Dr. Christof Schuette, FU Berlin
Date, Time	11 November 2015, 17:30-18:30
Location	ML E 12
Abstract	Molecular dynamics and related computational methods enable the description of biological systems with all-atom detail. However, these approaches are limited regarding simulation times and system sizes. A systematic way to bridge the micro-macro scale range between molecular dynamics and experiments is to apply coarse-graining (CG) techniques. We will discuss Markov State Modelling, a CG technique that has attracted a lot of attention in physical chemistry, biophysics, and computational biology in recent years. First, the key ideas of the mathematical theory and its algorithmic realization behind Markov State Modelling will be explained, next we will discuss the question of how to apply it to understanding molecular function, and last we will ask whether this may help in designing molecules with prescribed function. All of this will be illustrated by telling the story of the design process of a pain relief drug without concealing the potential pitfalls and obstacles.

Computational Science Distinguished Colloquium: Computational Molecular Design - From Mathematical Theory via High Performance Computing to In Vivo Experiments read_more

ML E 12

18 November 2015
16:15-17:15

Prof. Dr. Sonja Cox
University of Amsterdam

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Weak convergence of numerical approximations to stochastic (partial) differential equations
Speaker, Affiliation	Prof. Dr. Sonja Cox, University of Amsterdam
Date, Time	18 November 2015, 16:15-17:15
Location	Y27 H 25
Abstract	Suppose one wishes to evaluate some (deterministic!) statistical quantity derived from the solution of a stochastic differential equation (SDE). Examples of such quantities are: the expected energy of the solution at a certain point in time, the expected maximum, etc. If exact simulations of the solution are not available, the desired statistical quantity can be approximated based on numerically schemes for the SDE. Weak convergence rates for the numerical schemes indicate how good the approximation is. A general rule of thumb is that the optimal weak convergence rates of numerical schemes are generally twice as large as the optimal strong convergence rates, but significantly more difficult to establish -- especially for stochastic differential equations in infinite dimensions, i.e., stochastic partial differential equations. In my talk I will give an overview of the known results on weak convergence rates, explain some proof techniques, and explain what results we believe to obtain by new methods.

Weak convergence of numerical approximations to stochastic (partial) differential equationsread_more

Y27 H 25

2 December 2015
16:15-17:15

Prof. Dr. Guido Kanschat
University Heidelberg, Germany

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Asymptotically Correct Discontinuous Galerkin Methods for Radiation Transport
Speaker, Affiliation	Prof. Dr. Guido Kanschat, University Heidelberg, Germany
Date, Time	2 December 2015, 16:15-17:15
Location	Y27 H 25
Abstract	While discontinuous Galerkin (DG) methods had been developed and analyzed in the 1970s and 80s with applications in radiative transfer and neutron transport in mind, it was pointed out later in the nuclear engineering community, that the upwind DG discretization by Reed and Hill may fail to produce physically relevant approximations, if the scattering mean free path length is smaller than the mesh size. Mathematical analysis reveals, that in this case, convergence is only achieved in a continuous subspace of the finite element space. Furthermore, if boundary conditions are not chosen isotropically, convergence can only be expected in relatively weak topology. While the latter result is a property of the transport model, asymptotic analysis reveals, that the forcing into a continuous subspace can be avoided. By choosing a weighted upwinding, the conditions on the diffusion limit can be weakened. It has been known for long time, that the so called diffusion limit of radiative transfer is the solution to a diffusion equation; it turns out, that by choosing the stabilization carefully, the DG method can yield either the LDG method or the method by Ern and Guermond in its diffusion limit. Finally, we will discuss an efficient and robust multigrid method for the resulting discrete problems.

Asymptotically Correct Discontinuous Galerkin Methods for Radiation Transportread_more

Y27 H 25

9 December 2015
16:15-17:15

Dr. Larisa Yaroslavtseva
University of Passau

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	On very hard approximation problems for stochastic differential equations
Speaker, Affiliation	Dr. Larisa Yaroslavtseva, University of Passau
Date, Time	9 December 2015, 16:15-17:15
Location	Y27 H 25
Abstract	In this talk we consider two classical approximation problems for stochastic differential equations (SDEs) – the pathwise approximation of the solution at the final time and the corresponding quadrature problem, i.e. approximation of the expected value of a function of the solution at the final time. While the majority of results for these problems deals with equations that have globally Lipschitz continuous coefficients, such assumptions are typically not met for real world applications. In recent years a range of positive results for these problems has been established under substantially weaker assumptions on the coefficients such as global monotonicity conditions: new types of algorithms have been constructed that are easy to implement and still achieve a polynomial rate of convergence under these weaker assumptions. In our talk we present negative results. First, we show that there exist SDEs with smooth and bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion solves the pathwise approximation problem with a polynomial rate. Second, we present classes of SDEs with smooth and bounded coefficients such that no algorithm based on finitely many evaluations of the coefficients and all their derivatives solves the quadrature problem with a polynomial rate in the worst case sense with respect to the equations. Our results generalize recent results of M.Hairer, M.Hutzenthaler, A.Jentzen, Loss of regularity for Kolmogorov equations, Ann. Probab. 2015, where a non-polynomial rate has been established for the Euler scheme in the case of the pathwise approximation problem and the Euler Monte Carlo method in the case of the quadrature problem.

On very hard approximation problems for stochastic differential equationsread_more

Y27 H 25

16 December 2015
16:15-17:15

Prof. Dr. Josselin Garnier
Université Paris-Diderot

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	The random paraxial wave equation and application to correlation-based imaging
Speaker, Affiliation	Prof. Dr. Josselin Garnier, Université Paris-Diderot
Date, Time	16 December 2015, 16:15-17:15
Location	Y27 H 25
Abstract	We analyze wave propagation in random media in the so-called paraxial regime, which is a special high-frequency regime in which the wave propagates along a privileged axis. We show by multiscale analysis how to reduce the problem to the Ito-Schrodinger stochastic partial differential equation. We also show how to close and solve the moment equations for the random wave field. Based on these results we propose to use correlation-based methods for imaging in complex media and consider two examples: virtual source imaging in seismology and ghost imaging in optics.

The random paraxial wave equation and application to correlation-based imagingread_more

Y27 H 25

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