Zurich Colloquium in Applied and Computational Mathematics

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Archive 2011

Date / Time

Speaker

Title

Location

23 February 2011
16:15-17:15

Prof. Dr. Olivier Le Maitre
LIMSI, Paris, France

Event Details

Speaker invited by

C. Schwab

Abstract

We present a Galerkin method for the propagation of parametric uncertainties in systems of conservation laws. The method is based on a probabilistic treatment of the uncertainties, yielding a stochastic system of equations assumed hyperbolic almost surely. For the resolution of this system, we use a Galerkin technique with a stochastic discretization involving the expansion of the solution on a basis of orthonormal (uncorrelated) stochastic functionals. The Galerkin projection of the stochastic problem results in a large system of deterministic equations for the expansion coefficients of the solution, with a structure similar to conservation laws. We first study the properties of the Galerkin system and show, in particular, conditions ensuring its hyperbolic character.

A Galerkin method for parametric uncertainty propagation in hyperbolic systems

HG E 1.2

2 March 2011
16:15-17:15

Prof. Dr. Thorsten Hohage
University of Göttingen, Germany

Event Details

Speaker invited by

R. Hiptmair

Abstract

If partial differential equations on infinite domains are solved by finite elements, the infinite domain is split into a bounded computational domain in which standard finite elements are used, and unbounded exterior domain which requires special methods. In this talk we discuss so-called Hardy space infinite elements for the solution of time-harmonic electromagnetic scattering and resonance problems. They are based on the pole condition as radiation condition which requires the Laplace transform of the solution in radial direction to have a holomorphic extension to the lower part of the complex plane for each point on the (star-shaped) coupling boundary. It turns out that the restrictions of these holomorphically extended Laplace transforms belong to the corresponding L^2 based Hardy space. The pole condition is equivalent to the standard Silver Mueller radiation condition (or Sommerfeld in the scalar case). After the Laplace transform, incoming and outgoing solutions belong to orthogonal subspaces, and the radiation condition can be imposed by a Galerkin ansatz in a transformed variational formulation of the problem. More precisely, we discuss the construction of an exact sequence of Hardy space infinite element spaces using tensor products of chain complexes on the coupling boundary and in radial direction. Hardy space infinite element methods fit naturally into the finite element framework and exhibit super-algebraic convergence with the number of degress of freedom in the Hardy space. Moreover, they are particularly well suited for the solution of resonance problems since they preserve the eigenvalue structure of these problems.

Hardy space infinite elements for Maxwell's equations

HG E 1.2

9 March 2011
16:15-17:15

Prof. Dr. Per Christian Hansen
Technical University of Denmark, Lyngby, Denmark

Event Details

Speaker invited by

D. Kressner

Abstract

We present a MATLAB package AIR Tools with implementations of several Algebraic Iterative Reconstruction methods for discretizations of inverse problems. Two classes of methods are implemented: Simultaneous Iterative Reconstruction Techniques (SIRT) and Algebraic Reconstruction Techniques (ART). In addition we provide a few simplified test problems from medical and seismic tomography. For each iterative method, a number of strategies are available for choosing the relaxation parameter and the stopping rule. The relaxation parameter can be fixed, or chosen adaptively in each iteration; in the former case we provide the possibility for choosing the parameter by means of "training," i.e., finding the optimal parameter for a given test problem. The stopping rules provided are the discrepancy principle, the monotone error rule, and the NCP criterion; for the first two methods ``training'' can be used to find the optimal discrepancy parameter. In addition to giving an overview of the package, we will present some of the underlying theory related to the semi-convergence, the parameter-choice methods, and the stopping criteria.

AIR tools -- A MATLAB package of algebraic iterative reconstruction methods

HG E 1.2

16 March 2011
16:15-17:15

Prof. Dr. Ronald Hoppe
University of Augsburg, Germany, and University of Houston, USA

Event Details

Speaker invited by

D. Kressner

Abstract

We are concerned with optimal matching of dynamically deformable curves and surfaces R3 with applications in biomedical imaging. In particular, we will focus on diffeomorphic matching which amounts to the solution of an optimization problem featuring a regularized disparity cost functional subject to a dynamical system in terms of a time-dependent family of diffeomorphisms in R3 describing the temporal deformation of the curve or surface under consideration. As an application in biomedical imaging, we will consider the optimal matching of snapshots from the mitral valve apparatus of the human heart extracted from echocardiographical data. The presented results are based on joint work with R. Azencott, R. Glowinski, J. He, A. Ja joo, Y. Li, A. Martynenko (all UofH), and S. Ben Zekry, MD, S.A. Little, MD, W.A. Zoghbi, MD (all The Methodist Hospital Research Institute, Houston).

Optimal diffeomorphic matching with applications in biomedical imaging

HG E 1.2

30 March 2011
16:15-17:15

Dr. Manuel Castro
University of Malaga, Spain

Event Details

Speaker invited by	S. Mishra

Simulating shallow flows on GPUs: Numerical schemes, implementation and applications

HG E 1.2

27 April 2011
16:15-17:15

Dr. Dave Hewett
University of Reading, England

Event Details

Speaker invited by

R. Hiptmair

Abstract

Traditional numerical methods for time-harmonic acoustic scattering problems become prohibitively expensive in the high-frequency regime where the scatterer is large compared to the wavelength of the incident wave. By enriching the approximation space with oscillatory basis functions, chosen to efficiently capture the high-frequency asymptotic behaviour of the solution, it is sometimes possible to dramatically reduce the number of degrees of freedom required, thereby making tractable problems which are currently beyond the capability of traditional methods. In this talk we focus in particular on the problem of scattering by polygons in two dimensions. We propose and analyse, with rigorous error bounds, a hybrid boundary element method (BEM) for a class of non-convex polygonal scatterers, which requires only O(log f) degrees of freedom to maintain a fixed accuracy as the frequency f tends to infinity. This appears to be the first effective hybrid BEM for a class of non-convex obstacles. We also discuss possible extensions to transmission problems and three dimensional scattering problems.

Novel boundary element methods for high frequency scattering problems

HG E 1.2

4 May 2011
16:15-17:15

Dr. Annalisa Buffa
University of Pavia, Italy

Event Details

Speaker invited by	R. Hiptmair

Advances in Isogeometric analysis: the blessing of regularity

HG E 1.2

5 May 2011
00:00-17:00

Event Details

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