Zurich colloquium in applied and computational mathematics

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Spring Semester 2018

Date / Time

Speaker

Title

Location

21 February 2018
16:15-17:15

Prof. Dr. Jun Zou
Chinese University of Hong Kong

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Precondioners and analyses for Maxwell systems
Speaker, Affiliation	Prof. Dr. Jun Zou, Chinese University of Hong Kong
Date, Time	21 February 2018, 16:15-17:15
Location	Y27 H25
Abstract	In this talk we discuss several preconditioners for the large-scale discrete systems arising from finite element discretizations of various Maxwell systems, including the time-harmonic Maxwell system and Maxwell scattering systems.

Precondioners and analyses for Maxwell systemsread_more

Y27 H25

28 February 2018
16:15-17:15

Prof. Dr. Christophe Chalons
Université Versailles Saint Quentin

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Title T.B.A.
Speaker, Affiliation	Prof. Dr. Christophe Chalons, Université Versailles Saint Quentin
Date, Time	28 February 2018, 16:15-17:15
Location	Y27 H25

Title T.B.A.

Y27 H25

7 March 2018
16:15-17:15

Prof. Dr. Olivier Faugeras
INRIA

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Neural networks do not become asynchronous in the large size limit: there is no propagation of chaos
Speaker, Affiliation	Prof. Dr. Olivier Faugeras, INRIA
Date, Time	7 March 2018, 16:15-17:15
Location	Y27 H25
Abstract	We have developed a new method for establishing the thermodynamic limit of a network of fully connected rate neurons with correlated, Gaussian distributed, synaptic weights, and random inputs. The method is based on the formulation of a large deviation principle (LDP) for the probability distribution of the neuronal activity of a sequence of networks of increasing sizes. The motivation for using random connections comes from the fact that connections in neural networks are complex, poorly known and heterogeneous. The motivation for introducing correlation is the emphasis in computational modelling of neuroscience that neural networks are modular, and the correlations in the connection distribution reproduce this modularity, unlike in previous work. The limiting probability law is Gaussian and its mean and covariance functions are computed using a very quickly converging fixed point algorithm. Our outstanding new result is that in the thermodynamic limit the network does not become asynchronous, there is no propagation of chaos: neurons remain correlated and the amount of correlation can be described precisely from the correlation between the synaptic weights.

Neural networks do not become asynchronous in the large size limit: there is no propagation of chaosread_more

Y27 H25

14 March 2018
16:15-17:15

Prof. Dr. Peter Kritzer
Johann Radon Institute for Comp. and Appl. Mathematics

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Modified component-by-component constructions of (polynomial) lattice points
Speaker, Affiliation	Prof. Dr. Peter Kritzer, Johann Radon Institute for Comp. and Appl. Mathematics
Date, Time	14 March 2018, 16:15-17:15
Location	Y27 H 25
Abstract	The (fast) component-by-component construction of lattice point sets and polynomial lattice point sets is a powerful method to obtain quadrature rules for approximating integrals over the d-dimensional unit cube. In this talk, we present modifications of the component-by-component algorithm and of the more recent successive coordinate search algorithm, which yield savings of the construction cost for lattice rules and polynomial lattice rules in weighted function spaces. The idea is to reduce the size of the search space for coordinates which are associated with small weights and are therefore of less importance to the overall error compared to coordinates associated with large weights. We analyze tractability conditions of the resulting quasi-Monte Carlo rules, and show some numerical results. The talk is based on joint work with J. Dick (UNSW Sydney), A. Ebert (KU Leuven), G. Leobacher (KFU Graz), and F. Pillichshammer (JKU Linz).

Modified component-by-component constructions of (polynomial) lattice pointsread_more

Y27 H 25

21 March 2018
16:15-17:15

Prof. Dr. Yalchin Efendiev
Texas A&M University

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Generalized multiscale methods for porous media flows and their applications
Speaker, Affiliation	Prof. Dr. Yalchin Efendiev, Texas A&M University
Date, Time	21 March 2018, 16:15-17:15
Location	Y27 H 25
Abstract	Subsurface formations often display high degrees of variability over multiple length scales. This permeability's spatial variations and complex connectivity impact flow and transport. For this reason, these effects must be included in simulations of flows. Upscaling techniques are introduced to coarsen these geological models for flow calculations. The main idea of upscaling techniques is to formulate macroscopic equations on a coarse grid and ways to compute macroscopic parameters. It is important that these coarsened flow models replicate the fine scale characterizations. Recently, multiscale methods are introduced to perform coarse-grid simulations. In this talk, I will give an overview of some multiscale methods and discuss their relation to flow-based upscaling. I will mostly focus on single-phase flow and show how to derive upscaled models and compute effective properties using multiscale methods and flow-based upscaling. I will describe subgrid errors in these methods and show a relation between multiscale methods and flow-based upscaling methods. Then, I will describe a general multiscale framework and show how one can achieve an accurate coarse-grid models using multi-continuum and non-local upscaling. I will describe some applications of multiscale methods to Bayesian approaches and inverse problems.

Generalized multiscale methods for porous media flows and their applicationsread_more

Y27 H 25

11 April 2018
16:15-17:15

Dr. Irene Waldspurger
CEREMADE

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Convergence Rate of the Douglas-Rachford Method for Finding Best Approximating Pairs
Speaker, Affiliation	Dr. Irene Waldspurger, CEREMADE
Date, Time	11 April 2018, 16:15-17:15
Location	Y27 H 25
Abstract	The problem of finding best approximating pairs consists, given two closed sets in a metric space, in finding two points, one in each set, such that the distance between the points is minimal. We will discuss the case where the sets are convex polyhedrons in R^n. In this situation, several algorithms are known. The simplest one is alternating projections, and its convergence speed is relatively well understood. However, in practice, another algorithm, Douglas-Rachford, often seems to perform on par or better than alternating projections. We will discuss the convergence speed of this second algorithm, globally as well as locally. This is a joint work with Stefanie Jegelka.

Convergence Rate of the Douglas-Rachford Method for Finding Best Approximating Pairsread_more

Y27 H 25

25 April 2018
16:15-17:15

Prof. Dr. Sergey Repin
V.A. Steklov Institute of Mathematics

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Estimates of the distance to the set of divergence free fields and applications to analysis of incompressible viscous flow problems
Speaker, Affiliation	Prof. Dr. Sergey Repin, V.A. Steklov Institute of Mathematics
Date, Time	25 April 2018, 16:15-17:15
Location	Y27 H 25
Abstract	We discuss mathematical questions that play a fundamental role in quantitative analysis of incompressible viscous fluids and other incompressible media. Reliable verification of the quality of approximate solutions requires explicit and computable estimates of the distance to the corresponding generalized solution. In the context of this problem, one of the most essential questions is how to estimate the distance (measured in terms of the gradient norm) to the set of divergence free fields. It is closely related to the so-called inf-sup (LBB) condition or stability lemma for the Stokes problem and requires estimates of the LBB constant. We discuss methods of getting computable bounds of the constant and respective estimates of the distance to exact solutions of the Stokes, generalized Oseen, and Navier-Stokes problems.

Estimates of the distance to the set of divergence free fields and applications to analysis of incompressible viscous flow problems read_more

Y27 H 25

2 May 2018
16:15-17:15

Prof. Dr. Francesco Andriulli
Politecnico di Torino

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Handling Magnetic Field Integral Operators at Extremely Low Frequency
Speaker, Affiliation	Prof. Dr. Francesco Andriulli, Politecnico di Torino
Date, Time	2 May 2018, 16:15-17:15
Location	Y27 H 25
Abstract	When solving electromagnetic scattering problems with the boundary element method, the Electric Field and the Magnetic Field Integral Operators are the building blocks for a large number of formulations in literature. When modelling increasingly low frequency scenarios, however, the electric operator is known to give rise, upon discretization, to increasingly ill-conditioned problems whose iterative solution converges very slowly (a problem traditionally handled by leveraging on Helmholtz-Hodge decompositions). The magnetic operator, instead, gives rise to uniformly well-conditioned matrices (on simply connected geometries) independently of the frequency. At low-frequency, when the magnetic operator associated problems are solved via an iterative procedure, they converge rapidly but, lamentably, this rapid convergence is towards a severely incomplete solution since numerical cancellations occur in finite precision. We will discuss several aspects of this issue in detail delineating effective strategies to handle it and to obtain electromagnetic full-wave solvers providing stable solutions from high to arbitrarily low frequency.

Handling Magnetic Field Integral Operators at Extremely Low Frequencyread_more

Y27 H 25

23 May 2018
16:15-17:15

Prof. Dr. Markus Bachmayr
Institut für Numerische Simulation, Universität Bonn

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Stability of Low-Rank Tensor Representations and Structured Multilevel Preconditioning for Elliptic PDEs
Speaker, Affiliation	Prof. Dr. Markus Bachmayr, Institut für Numerische Simulation, Universität Bonn
Date, Time	23 May 2018, 16:15-17:15
Location	Y27 H 25
Abstract	Folding grid value vectors into high-order tensors, combined with low-rank representation in the tensor train format, has been shown to lead to highly efficient approximations for various classes of functions. These include solutions of elliptic PDEs on nonsmooth domains or with oscillatory data. This tensor-structured approach is attractive because it leads to highly compressed, adaptive approximations based on simple discretizations. Straightforward choices of the underlying basis, such as piecewise multilinear finite elements on uniform tensor product grids, lead to the well-known basis ill-conditioning of discretized operators. We demonstrate that for low-rank representations, the use of tensor structure additionally leads to representation ill-conditioning, a new effect specific to computations in tensor networks. We construct an explicit tensor-structured representation of a BPX preconditioner with ranks independent of the number of discretization levels, which combined with a carefully chosen representation of its product with the stiffness matrix turns out to remove both basis and representation ill-conditioning. Numerical tests, including problems with highly oscillatory coefficients, show that one arrives at reliable and efficient solvers which remain numerically stable for mesh sizes near machine precision.

Stability of Low-Rank Tensor Representations and Structured Multilevel Preconditioning for Elliptic PDEsread_more

Y27 H 25

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