Zurich Colloquium in Applied and Computational Mathematics

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Archive 2012

Date / Time

Speaker

Title

Location

7 March 2012
16:15-17:15

Dr. Matthias Messner
INRIA, France

Event Details

Speaker invited by

R. Hiptmair

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 equation

HG E 1.2

12 March 2012
16:15-17:15

Dr. Wang-Q Lim
TU Berlin

Event Details

Speaker invited by

Ph. Grohs

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 representation

HG D 3.2

14 March 2012
16:15-17:15

Prof. Dr. Markus Reiher
Theoretical Chemistry, ETH Zürich

Event Details

Speaker invited by	V. Gradinaru

New electron correlation theories for quantum mechanical studies of molecules

HG E 1.2

21 March 2012
16:15-17:15

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

Event Details

Speaker invited by

C. Schwab

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 applications

HG E 1.2

30 March 2012
10:00-12:00

Sonya Cox
TU Delft, The Netherlands

Event Details

Speaker invited by

C. Schwab

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 spaces

HG G 19.2

30 March 2012
14:00-16:00

Raphael Kruse
University of Bielefeld, Germany

Event Details

Speaker invited by

C. Schwab

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 equation

HG G 19.2

5 April 2012

Event Details

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