Zurich colloquium in applied and computational mathematics

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Spring Semester 2012

Date / Time

Speaker

Title

Location

7 March 2012
16:15-17:15

Dr. Matthias Messner
INRIA, France

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	A directional fast multipole boundary element method for the Helmholtz equation
Speaker, Affiliation	Dr. Matthias Messner, INRIA, France
Date, Time	7 March 2012, 16:15-17:15
Location	HG E 1.2
Abstract	First, a fast multipole method (FMM) for n-body problems of oscillatory nature is presented. The approach is based on the approximation of the kernel function by means of the Chebyshev interpolation scheme and on a directional partitioning of the far-field. Then, the presented FMM is used to speedup a collocation boundary element method (BEM) for the Helmholtz equation. The talk ends with convergence studies and the simulation of acoustic problems.

A directional fast multipole boundary element method for the Helmholtz equationread_more

HG E 1.2

12 March 2012
16:15-17:15

Dr. Wang-Q Lim
TU Berlin

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Shearlets - optimally sparse geometric representation
Speaker, Affiliation	Dr. Wang-Q Lim, TU Berlin
Date, Time	12 March 2012, 16:15-17:15
Location	HG D 3.2
Abstract	Many important problem classes are governed by anisotropic features such as singularities concentrated on lower dimensional embedded manifolds. Therefore, analyzing the intrinsic geometrical features of the underlying object is essential in many applications. Recently, shearlets were introduced as means to sparsely encode anisotropic singularities of multivariate data while allowing compactly supported analyzing elements. In this talk, we will overview recent developments in the theory and applications of shearlets. Finally, we will present some numerical results on the applications of shearlets in imaging sciences and PDEs.

Shearlets - optimally sparse geometric representationread_more

HG D 3.2

14 March 2012
16:15-17:15

Prof. Dr. Markus Reiher
Theoretical Chemistry, ETH Zürich

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	New electron correlation theories for quantum mechanical studies of molecules
Speaker, Affiliation	Prof. Dr. Markus Reiher, Theoretical Chemistry, ETH Zürich
Date, Time	14 March 2012, 16:15-17:15
Location	HG E 1.2
Assets	Abstractfile_download

New electron correlation theories for quantum mechanical studies of moleculesread_more

HG E 1.2

21 March 2012
16:15-17:15

Prof. Dr. Ivan Oseledets
Russian Academy of Sciences, Moscow

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Computational tensor methods and their applications
Speaker, Affiliation	Prof. Dr. Ivan Oseledets, Russian Academy of Sciences, Moscow
Date, Time	21 March 2012, 16:15-17:15
Location	HG E 1.2
Abstract	The computational tensor methods are a new promising research field, which tries to adapt well-known algebraic results from the matrix analysis to solve high-dimensional problems. In this talk I will discuss several high-dimensional applications, and describe the basic algebraic problems that arise. The main focus will be on the so-called Tensor Train (TT) representation of high-dimensional tensors. In two words, it is a robust algebraic technique for separation of variables. I will discuss, its advantages and disadvantages, what problems we can solve with the help of the novel tensor problems and what we can not (yet). It was recently discovered, that several seemingly unrelated fields of science, like quantum information theory, solid state physics, computational molecular chemistry are using similar tools to solve similar algebraic problems. There is a direct connection between the so-called QTT-format and the wavelet decomposition which is very promising for the creating of specialized FEM/BEM solvers. There are other connections that still need to be established: the main problem is that the numerical tools are far ahead of the available theoretical results.

Computational tensor methods and their applicationsread_more

HG E 1.2

* 30 March 2012
10:00-12:00

Sonya Cox
TU Delft, The Netherlands

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Pathwise estimates for the implicit Euler scheme for SDEs in Banach spaces
Speaker, Affiliation	Sonya Cox, TU Delft, The Netherlands
Date, Time	30 March 2012, 10:00-12:00
Location	HG G 19.2
Abstract	In the first part of my talk I will explain what is meant by pathwise estimates for an approximation scheme of a stochastic differential equation (SDE), and why such estimates are of importance. In recent work by Jan van Neerven and myself, we obtained pathwise estimates for the implicit Euler scheme for SDEs in Banach spaces. In the second half of the talk I will sketch how we obtained these results and indicate what challenges arise when working in Banach spaces.

Pathwise estimates for the implicit Euler scheme for SDEs in Banach spacesread_more

HG G 19.2

* 30 March 2012
14:00-16:00

Raphael Kruse
University of Bielefeld, Germany

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Weak Galerkin approximation of a linear stochastic evolution equation
Speaker, Affiliation	Raphael Kruse, University of Bielefeld, Germany
Date, Time	30 March 2012, 14:00-16:00
Location	HG G 19.2
Abstract	In this talk we analyze the weak error of convergence for Galerkin finite element methods applied to a linear stochastic evolution equation. We present a useful error representation and show that the order of weak convergence is almost twice the corresponding order of strong convergence. The main novelty in this work is that in the proof we avoid using the Kolmogorov equation associated with the stochastic differential equation. Instead we apply results from Malliavin Calculus.

Weak Galerkin approximation of a linear stochastic evolution equationread_more

HG G 19.2

5 April 2012

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Osterferien bis 15. April
Speaker, Affiliation
Date, Time	5 April 2012,
Location

Osterferien bis 15. April

25 April 2012
16:15-17:15

Prof. Dr. Johannes Wallner
TU Graz

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Self-supporting surfaces
Speaker, Affiliation	Prof. Dr. Johannes Wallner, TU Graz
Date, Time	25 April 2012, 16:15-17:15
Location	HG E 1.2
Abstract	Self-supporting masonry is one of the most ancient and elegant techniques for building curved shapes. Because of the geometric nature of their failure, analyzing and modeling such strutures is more a geometry processing problem than one of continuum mechanics. We use the thrust network method of analysis (developed by P. Block of ETH Zurich) for efficiently approximating freeform shapes by self-supporting ones via iterative nonlinear optimization. There are close connections to discrete differential geometry, such as a discrete Airy stress potential, perfect graph Laplacians, and computing admissible loads via curvatures of polyhedral surfaces.

Self-supporting surfacesread_more

HG E 1.2

16 May 2012
16:15-16:55

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Tag vor Auffahrt. Schliessung ETH Gebäude um 17.00 Uhr!
Speaker, Affiliation
Date, Time	16 May 2012, 16:15-16:55
Location

Tag vor Auffahrt. Schliessung ETH Gebäude um 17.00 Uhr!

23 May 2012
16:15-17:15

Prof. Dr. Victor Nistor
Penn State University, USA

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Boundary value problems on polyhedral domains and applications to quasi-optimal rates for the Finite Element Method
Speaker, Affiliation	Prof. Dr. Victor Nistor, Penn State University, USA
Date, Time	23 May 2012, 16:15-17:15
Location	HG E 1.2
Abstract	I will first review some of the issues and earlier results on boundary value problems on polyhedral domains. The main lesson is that there is a 'loss of regularity' for boundary value problems on singular domains if the usual Sobolev spaces are used. This is inconvenient however in practical applications such as the Finite Element Method. An alternative approach is to use 'weighted Sobolev' spaces. Then one can then restore full regularity for elliptic problems on such domains under the additional condition of that there are no 'Newmann-Newmann' corners or edges (joint result with Bacuta, Mazzucato, and Zikatanov). The case of 'Newmann-Newmann' corners requires some additional ideas. I will then present some results in this case in two dimensions and how they can be used to construct sequences of Finite Element Spaces that provide quasi-optimal approximation rates for transmission and pure Neumann problems (joint work with Mazzucato and Li). This method is then generalized to three dimensions.

Boundary value problems on polyhedral domains and applications to quasi-optimal rates for the Finite Element Methodread_more

HG E 1.2

30 May 2012
16:15-17:15

Prof. Dr. Helmut Bölcskei
Institut für Kommunikationstechnik, ETH Zürich

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Compressive identification of linear operators
Speaker, Affiliation	Prof. Dr. Helmut Bölcskei, Institut für Kommunikationstechnik, ETH Zürich
Date, Time	30 May 2012, 16:15-17:15
Location	HG E 1.2
Abstract	We consider the problem of identifying a linear deterministic operator from an input-output measurement. For the large class of continuous (and hence bounded) operators, under additional mild restrictions, we show that stable identifiability is possible if the total support area of the operator's spreading function satisfies Δ ≤ ½. This result holds for arbitrary (possibly fragmented) support regions of the spreading function, does not impose limitations on the total extent of the support region, and, most importantly, does not require the support region of the spreading function to be known prior to identification. Furthermore, we prove that asking for identifiability of only almost all operators, stable identifiability is possible if Δ ≤ 1. This result is surprising as it says that there is no penalty for not knowing the support region of the spreading function prior to identification.

Compressive identification of linear operatorsread_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