Departement Mathematik

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Zurich colloquium in applied and computational mathematics

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Frühjahrssemester 2011

Datum / Zeit Referent:in Titel Ort
23. Februar 2011
16:15-17:15 		Prof. Dr. Olivier Le Maitre
LIMSI, Paris, France
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Zurich Colloquium in Applied and Computational Mathematics

Titel A Galerkin method for parametric uncertainty propagation in hyperbolic systems
Referent:in, Affiliation Prof. Dr. Olivier Le Maitre, LIMSI, Paris, France
Datum, Zeit 23. Februar 2011, 16:15-17:15
Ort HG E 1.2
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 systemsread_more
HG E 1.2
2. März 2011
16:15-17:15 		Prof. Dr. Thorsten Hohage
University of Göttingen, Germany
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Zurich Colloquium in Applied and Computational Mathematics

Titel Hardy space infinite elements for Maxwell's equations
Referent:in, Affiliation Prof. Dr. Thorsten Hohage, University of Göttingen, Germany
Datum, Zeit 2. März 2011, 16:15-17:15
Ort HG E 1.2
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 equationsread_more
HG E 1.2
9. März 2011
16:15-17:15 		Prof. Dr. Per Christian Hansen
Technical University of Denmark, Lyngby, Denmark
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Zurich Colloquium in Applied and Computational Mathematics

Titel AIR tools -- A MATLAB package of algebraic iterative reconstruction methods
Referent:in, Affiliation Prof. Dr. Per Christian Hansen, Technical University of Denmark, Lyngby, Denmark
Datum, Zeit 9. März 2011, 16:15-17:15
Ort HG E 1.2
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 methodsread_more
HG E 1.2
16. März 2011
16:15-17:15 		Prof. Dr. Ronald Hoppe
University of Augsburg, Germany, and University of Houston, USA
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Zurich Colloquium in Applied and Computational Mathematics

Titel Optimal diffeomorphic matching with applications in biomedical imaging
Referent:in, Affiliation Prof. Dr. Ronald Hoppe, University of Augsburg, Germany, and University of Houston, USA
Datum, Zeit 16. März 2011, 16:15-17:15
Ort HG E 1.2
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 imagingread_more
HG E 1.2
30. März 2011
16:15-17:15 		Dr. Manuel Castro
University of Malaga, Spain
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Zurich Colloquium in Applied and Computational Mathematics

Titel Simulating shallow flows on GPUs: Numerical schemes, implementation and applications
Referent:in, Affiliation Dr. Manuel Castro, University of Malaga, Spain
Datum, Zeit 30. März 2011, 16:15-17:15
Ort HG E 1.2
Unterlagen https://math.ethz.ch/ndb/00017/01289/abstract_castro.pdffile_download
Simulating shallow flows on GPUs: Numerical schemes, implementation and applicationsread_more
HG E 1.2
27. April 2011
16:15-17:15 		Dr. Dave Hewett
University of Reading, England
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Zurich Colloquium in Applied and Computational Mathematics

Titel Novel boundary element methods for high frequency scattering problems
Referent:in, Affiliation Dr. Dave Hewett, University of Reading, England
Datum, Zeit 27. April 2011, 16:15-17:15
Ort HG E 1.2
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 problemsread_more
HG E 1.2
4. Mai 2011
16:15-17:15 		Dr. Annalisa Buffa
University of Pavia, Italy
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Zurich Colloquium in Applied and Computational Mathematics

Titel Advances in Isogeometric analysis: the blessing of regularity
Referent:in, Affiliation Dr. Annalisa Buffa, University of Pavia, Italy
Datum, Zeit 4. Mai 2011, 16:15-17:15
Ort HG E 1.2
Unterlagen https://math.ethz.ch/ndb/00017/01278/buffa_eth.pdffile_download
Advances in Isogeometric analysis: the blessing of regularityread_more
HG E 1.2
5. Mai 2011
00:00-17:00
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Zurich Colloquium in Applied and Computational Mathematics

Titel Osterferien bis 15. April
Referent:in, Affiliation
Datum, Zeit 5. Mai 2011, 00:00-17:00
Ort
Osterferien bis 15. April
9. Mai 2011
08:15-09:00 		Dr. Philippe Grohs
ETH Zurich
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Zurich Colloquium in Applied and Computational Mathematics

Titel Multiscale analysis beyond wavelets
Referent:in, Affiliation Dr. Philippe Grohs, ETH Zurich
Datum, Zeit 9. Mai 2011, 08:15-09:00
Ort HG F 33.1
Abstract Since the wavelet-boom in the 1980's, researchers have come a long way in exploiting the capabilities of multiscale methods with impressive results in both pure and applied mathematics. However, by now also the inherent limitations of wavelets are quite well-understood. Examples include the incapability to deal with data taking values in nonlinear manifolds, the incapability to deal with high dimensional data with singularities along subsurfaces (think of edges in images), or the incapability to discretize hyperbolic PDEs in a stable fashion. Of these three topics I will focus on the problem of processing manifold-valued data. Such data arises in several modern applications such as stress/strain measurements and diffusion tensor MRI in medical imaging (where the data points are elements of the symmetric space of symmetric positive definite matrices) or kinematics (where the data points are elements of the Lie group of Euclidean motions). Due to the inherent nonlinearity, for these data types conventional methods of signal processing break down. I will describe new strategies capable of processing manifold valued data, and I will also talk about the analysis of such nonlinear multiscale methods.
Multiscale analysis beyond waveletsread_more
HG F 33.1
9. Mai 2011
10:15-11:00 		Dr. Armin Lechleiter
Ecole Polytechnique, Palaiseau, France
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Zurich Colloquium in Applied and Computational Mathematics

Titel Time and frequency domain wave imaging
Referent:in, Affiliation Dr. Armin Lechleiter, Ecole Polytechnique, Palaiseau, France
Datum, Zeit 9. Mai 2011, 10:15-11:00
Ort HG F 33.1
Abstract A wave hitting an object creates a scattered wave. The shape of the scattering object can be mathematically characterized and numerically computed from (partial) measurements of scattered waves using so-called sampling methods. These methods compute an indicator function of the object's support on a grid of sampling points to produce an image of the scatterer. In contrast to, e.g., non-linear optimization techniques, sampling methods do not need to solve direct scattering problems to obtain information on the scattering object. Sampling methods for inverse scattering problems have been introduced in recent years in the frequency domain, that is, for time-harmonic waves. In practice (e.g., in ultrasound applications) one often measures time-domain signals. Working with Fourier- transformed data at a single frequency means to potentially throw away information, and it introduces the new problem to choose that single frequency. Multi-frequency approaches usually introduce the need to synthesize several single frequency reconstructions. In this talk, we consider time-domain sampling methods that naturally incorporate multiple frequencies, and that share many of the good features of their frequency domain counterparts.  
Time and frequency domain wave imagingread_more
HG F 33.1
9. Mai 2011
13:30-14:15 		Dr. Ludwig Gauckler
University of Tübingen, Germany
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Zurich Colloquium in Applied and Computational Mathematics

Titel Long-time analysis of Hamiltonian partial differential equations and their discretizations
Referent:in, Affiliation Dr. Ludwig Gauckler, University of Tübingen, Germany
Datum, Zeit 9. Mai 2011, 13:30-14:15
Ort HG F 33.1
Abstract The long-time behaviour of numerical methods for ODEs is in many aspects well understood. For example the energy, a conserved quantity of a Hamiltonian differential equation, is nearly conserved along a symplectic discretization of a Hamiltonian ODE. The situation is much less clear in the case of PDEs. In this talk we discuss long-time near-conservation properties of numerical discretizations of Hamiltonian PDEs, for example nonlinear Schroedinger equations, in a weakly nonlinear regime. The considered numerical methods are based on a splitting integrator in time and a spectral method in space. It is shown that energy and also actions are nearly conserved over long times along such a numerical solution, uniformly in the discretization parameters. This result is obtained by analysing a modulated Fourier expansion of the numerical solution, that will be introduced in the talk. As a preparatory work for such a numerical analysis, but also as an interesting problem in its own right, we study the influence of a nonlinear perturbation on the exact solution of a Hamiltonian PDE using modulated Fourier expansions as well.
Long-time analysis of Hamiltonian partial differential equations and their discretizationsread_more
HG F 33.1
9. Mai 2011
15:30-16:15 		Dr. Arnulf Jentzen
Princeton University, USA
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Zurich Colloquium in Applied and Computational Mathematics

Titel On the global Lipschitz assumption in computational stochastics
Referent:in, Affiliation Dr. Arnulf Jentzen, Princeton University, USA
Datum, Zeit 9. Mai 2011, 15:30-16:15
Ort HG F 33.1
Abstract Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. The important case of superlinearly growing coefficients, however, remained an open question for a long time now. The main difficulty is that numerically weak convergence fails to hold in many cases of superlinearly growing coefficients. In this talk we overcome this difficulty and establish convergence of the Monte Carlo Euler method for a large class of stochastic differential equations whose drift functions have at most polynomial growth.
On the global Lipschitz assumption in computational stochasticsread_more
HG F 33.1
11. Mai 2011
16:15-17:15 		Katharina Kormann
University of Uppsala, Sweden
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Zurich Colloquium in Applied and Computational Mathematics

Titel An adaptive Magnus-Lanczos-spectral element solver for the time-dependent Schrödinger equation
Referent:in, Affiliation Katharina Kormann, University of Uppsala, Sweden
Datum, Zeit 11. Mai 2011, 16:15-17:15
Ort HG E 1.2
Abstract In this talk, we present a discretization of the time-dependent Schrödinger equation based on a Magnus-Lanczos time integrator and high-order Gauss-Lobatto elements in space. A truncated Galerkin orthogonality is used to obtain duality-based a posteriori error estimates that treat the temporal and the spatial error separately. Based on this theory, an adaptive solver for the Schrödinger equation is devised. Since high-order elements are used, the memory consumption of a sparse matrix implementation of the spatial operator is prohibitive. Instead, we present an implementation based on cell-based stencils. In this way, we can also exploit the structure of the tensor-product operator to reduce the number of computations per matrix-vector product. We demonstrate the performance of the algorithm for the example of matter-field interaction.
An adaptive Magnus-Lanczos-spectral element solver for the time-dependent Schrödinger equationread_more
HG E 1.2
18. Mai 2011
16:15-17:15 		Dr. Jinzhi Li
Seminar for Applied Mathematics, ETH Zurich
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Zurich Colloquium in Applied and Computational Mathematics

Titel Shape calculus in differential forms : Ideas and applications
Referent:in, Affiliation Dr. Jinzhi Li, Seminar for Applied Mathematics, ETH Zurich
Datum, Zeit 18. Mai 2011, 16:15-17:15
Ort HG E 1.2
Abstract We treat Zolesio's velocity method of shape calculus using the formalism of differential forms, in particular, the notion of Lie derivative. This provides a unified and elegant approach to computing even higher order shape derivatives of domain and boundary integrals and skirts the tedious manipulations entailed by classical vector calculus. Hitherto unknown expressions for shape Hessians can be derived with little effort. The perspective of differential forms perfectly fits second-order boundary value problems. We illustrate its power by deriving the shape derivatives of solutions to second-order elliptic boundary value problems with Dirichlet, Neumann and Robin boundary conditions. A new dual mixed variational approach is employed in the case of Dirichlet boundary conditions. Moreover, applications to acoustic and Maxwell scattering problems will also be addressed.
Shape calculus in differential forms : Ideas and applicationsread_more
HG E 1.2
25. Mai 2011
16:15-17:15 		Prof. Dr. Holger Rauhut
University of Bonn, Germany
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Zurich Colloquium in Applied and Computational Mathematics

Titel Sparse and low rank recovery
Referent:in, Affiliation Prof. Dr. Holger Rauhut, University of Bonn, Germany
Datum, Zeit 25. Mai 2011, 16:15-17:15
Ort HG E 1.2
Abstract Compressive Sensing (sparse recovery) predicts that sparse vectors can be recovered from what was previously believed to be highly incomplete linear measurements. Efficient algorithms such as convex relaxations and greedy algorithms can be used to perform the reconstruction. Remarkably, all good measurement matrices known so far in this context are based on randomness. Recently, it was observed that similar findings also hold for the recovery of low rank matrices from incomplete information, and for the matrix completion problem in particular. Again, convex relaxations and random are crucial ingredients. The talk gives an introduction and overview on sparse and low rank recovery with emphasis on results due to the speaker.
Sparse and low rank recoveryread_more
HG E 1.2
1. Juni 2011
16:15-17:15 		Prof. Dr. Carlos Pares
University of Malaga, Spain
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Zurich Colloquium in Applied and Computational Mathematics

Titel Well-balanced High order methods based on reconstruction of states
Referent:in, Affiliation Prof. Dr. Carlos Pares, University of Malaga, Spain
Datum, Zeit 1. Juni 2011, 16:15-17:15
Ort HG E 1.2
Abstract This talk focuses on the numerical approximation of 1d hyperbolic systems involving source terms. A number of simplified flow models have this form. The goal is to present a general framework for designing high-order well-balanced shock-capturing numerical methods. The emphasis will be put on the well-balanced property: the numerical schemes are required to solve exactly the stationary solutions of the system or at least a certain family among them. The idea is to extend to high order a first-order path-conservative method by using a reconstruction operator. The main difficulty comes from the fact that, in order to have a well-balanced numerical scheme, this operator has also to preserve the stationary solutions of the system. A strategy to overcome this difficulty will be presented and some examples will be shown.
Well-balanced High order methods based on reconstruction of statesread_more
HG E 1.2

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

Archiv: FS 25 HS 24 FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 FS 21 HS 20 FS 20 HS 19 FS 19 HS 18 FS 18 HS 17 FS 17 HS 16 FS 16 HS 15 FS 15 HS 14 FS 14 HS 13 FS 13 HS 12 FS 12 HS 11 FS 11 HS 10 FS 10 HS 09

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