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Zurich colloquium in applied and computational mathematics

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Autumn Semester 2013

Date / Time Speaker Title Location
21 August 2013
16:15-17:15 		Dr. Dmitry Savostyanov
University of Southampton, UK
Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title Quasioptimality of maximum-volume cross interpolation of tensors
Speaker, Affiliation Dr. Dmitry Savostyanov, University of Southampton, UK
Date, Time 21 August 2013, 16:15-17:15
Location HG E 1.2
Abstract We consider a cross interpolation of high-dimensional arrays in the tensor train format. We prove that the maximum-volume choice of the interpolation sets provides the quasioptimal interpolation accuracy, that differs from the best possible accuracy by the factor which does not grow exponentially with dimension. For nested interpolation sets we prove the interpolation property and propose greedy cross interpolation algorithms. We justify the theoretical results and test the speed and accuracy of the proposed algorithm with convincing numerical experiments.
Quasioptimality of maximum-volume cross interpolation of tensorsread_more
HG E 1.2
25 September 2013
16:15-17:15 		Dr. Martin Eigel
Weierstrass Institut Berlin, Germany
Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title On tensor approximations with ASGFEM
Speaker, Affiliation Dr. Martin Eigel, Weierstrass Institut Berlin, Germany
Date, Time 25 September 2013, 16:15-17:15
Location HG E 1.2
Abstract We present some preliminary results concerning iterative solvers for tensor approximations of PDE with stochastic coefficients. A recent Adaptive Stochastic Galerkin FEM (ASGFEM) is employed to control the approximation of some model problem. The natural tensor structure of the discretisation leads to memory efficient representations. These require iterative solvers with subsequent tensor truncations for iterates to retain efficiency. Based on joint work with Claude Gittelson, Christoph Schwab and Elmar Zander.
On tensor approximations with ASGFEMread_more
HG E 1.2
2 October 2013
16:15-17:15 		Dr. Staffan Ronnas
University of Heidelberg, Germany
Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title HiFlow3 - a multi-purpose library for high-performance FEM simulations
Speaker, Affiliation Dr. Staffan Ronnas, University of Heidelberg, Germany
Date, Time 2 October 2013, 16:15-17:15
Location HG E 1.2
Abstract The topic of this presentation is the use of hp-version discontinuous Galerkin finite element methods for solving linear second-order elliptic problems in polyhedral domains. In order to achieve exponential error convergence in the presence of corner-, edge-, and corner-edge singularities, we apply a highly specialized a priori adaptation strategy, which involves local anisotropic mesh refinement with varying refinement ratios and shape functions with anisotropic polynomial degrees. We shall discuss some of the technical details that went into creating an implementation of this strategy using the FEM library HiFlow3, and present numerical results from a set of test scenarios.
HiFlow3 - a multi-purpose library for high-performance FEM simulationsread_more
HG E 1.2
9 October 2013
16:15-17:15 		Dr. Josef Dick
University of New South Wales, Sydney, Australia
Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title Markov chain Monte Carlo on continuous state spaces using deterministic driver sequences
Speaker, Affiliation Dr. Josef Dick, University of New South Wales, Sydney, Australia
Date, Time 9 October 2013, 16:15-17:15
Location HG E 1.2
Abstract The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0, 1) random variables. Some numerical experiments by Tribble show substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. In this talk we discuss results for deterministic driver sequences for some MCMC algorithms for continuous stationary distributions. The main motivation is the search for quasi-Monte Carlo versions of MCMC.
Markov chain Monte Carlo on continuous state spaces using deterministic driver sequencesread_more
HG E 1.2
13 November 2013
16:15-17:15 		Jean-Marie Mirebeau
Université Paris-Dauphine, France
Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title Adaptive, Anisotropic and Hierarchical Cones of Convex functions
Speaker, Affiliation Jean-Marie Mirebeau, Université Paris-Dauphine, France
Date, Time 13 November 2013, 16:15-17:15
Location HG E 1.2
Abstract We address the discretization of variational problems posed on the cone of convex functions. Such problems include optimal transport with quadratic cost, as well as various long lasting geometric conjectures such as Newton's problem of the convex body of least resistance. Our main motivation is the principal agent problem in economics, which models the impact of monopoly on product quality. Consider a two dimensional domain, sampled on a grid of N points. We show that the cone of restrictions to the grid of convex functions is in general characterized by N^2 linear inequalities; a direct computational use of this description thus has a prohibitive complexity. We thus introduce a hierarchy of sub-cones of discrete convex functions, associated to stencils which can be adaptively, locally, and anisotropically refined. The trace on the grid of a convex function on is always contained (in an average sense over grid orientations) in a such a sub-cone defined by N ln^3 N linear constraints. Applications take advantage of these results through iterative, a-posteriori stencil refinement strategies, similar in spirit with adaptive mesh refinement methods for elliptic PDEs.
Adaptive, Anisotropic and Hierarchical Cones of Convex functionsread_more
HG E 1.2
4 December 2013
16:15-17:15 		Prof. Dr. Wesley Petersen
Seminar for Applied Mathematics, ETH Zurich
Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title A stable finite difference method for growth and diffusion equations on a terrestial map
Speaker, Affiliation Prof. Dr. Wesley Petersen, Seminar for Applied Mathematics, ETH Zurich
Date, Time 4 December 2013, 16:15-17:15
Location HG E 1.2
Abstract Growth and diffusion equations are common models in biology. In this talk, we will discuss a two dimensional version of the Fisher/Kolmogorov-Petrovsky-Piskunov equation applied to human migration on a terrestial map. An out-of-Africa simulation which uses a space/time varying carrying capacity will be the principal example. The method is semi-implicit, dimensionally split (Godunov), and uses a data compression suitable for Mercator projection maps.
A stable finite difference method for growth and diffusion equations on a terrestial mapread_more
HG E 1.2
18 December 2013
16:15-17:15 		Prof. Dr. Raul Rojas
FU Berlin
Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title The architecture of Zuse's Z1
Speaker, Affiliation Prof. Dr. Raul Rojas, FU Berlin
Date, Time 18 December 2013, 16:15-17:15
Location HG E 1.2
Abstract We have been studying the papers and documents donated by Konrad Zuse's family to Deutsches Museum. The collection is being documented in the "Konrad Zuse Internet Archive". Recently, we finished analyzing 1400 blueprints drawn for the reconstruction of the Z1 housed at Technikmuseum Berlin. The original of the Z1 (1936-38) was destroyed during WWII. The reconstructed machine was finished in 1989. A virtual visit is available under: http://zuse-z1.zib.de/zuse-z1-pano/intermediate-view/ Only the memory of the Z1 was described in 1989. Now we have documented the structure of the complete processor, of the microcontroller, and of the I/O. A complete functional description of the Z1 is available now, for the first time, in written form. The Z1 was a mechanical device, used floating-point, and could compute the four basic arithmetic operations. The program was contained on a punched tape. In the talk I will describe the micro-architecture of the processor and I will discuss its novelty relative to scientific computing.
The architecture of Zuse's Z1read_more
HG E 1.2

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Organizers: Philipp Grohs, Ralf Hiptmair, Arnulf Jentzen, Siddhartha Mishra, Christoph Schwab

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09

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