Departement Mathematik

Zurich colloquium in applied and computational mathematics

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Herbstsemester 2014

Datum / Zeit Referent:in Titel Ort
4. September 2014
11:00-11:45 		Prof. Dr. Wolf-Jürgen Beyn
Universität Bielefeld, Germany
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Zurich Colloquium in Applied and Computational Mathematics

Titel Stability and computation of interacting nonlinear waves
Referent:in, Affiliation Prof. Dr. Wolf-Jürgen Beyn, Universität Bielefeld, Germany
Datum, Zeit 4. September 2014, 11:00-11:45
Ort Y27 H 28
Abstract We consider the numerical solution of semilinear time-dependent partial differential equations that support the propagation of nonlinear waves such as traveling, rotating or spiral waves. Depending on initial data, the solutions of such systems often show multiple patterns which are composed of several waves that either travel towards each other and collide (strong interaction) or miss each other and depart (weak interaction). Such multiple patterns look like linear superpositions of single waves which, however, cannot be true in a strict sense due the nonlinear character of the system.
We suggest a numerical method that allows to handle several coordinate frames in which the single patterns can stabilize while still keeping their full nonlinear interaction.The procedure is adaptive in the sense that the position of the single frames is not prescribed a-priori but determined during computation. Several numerical experiments illustrate the method for multi-fronts in one space dimension and for multiple spinning solitons in two space dimensions. The approach extends an earlier method (called the freezing method), which allows to stabilize dynamic patterns in a single co-moving frame. For the case of weak interaction in one space dimension, we present a theoretical result which shows stability with asymptotic phase for the decomposition system.
Stability and computation of interacting nonlinear wavesread_more
Y27 H 28
16. September 2014
10:15-11:15 		Prof. Dr. Gitta Kutyniok
TU Berlin
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Zurich Colloquium in Applied and Computational Mathematics

Titel Compactly Supported Shearlets: Theory and Applications
Referent:in, Affiliation Prof. Dr. Gitta Kutyniok, TU Berlin
Datum, Zeit 16. September 2014, 10:15-11:15
Ort HG D 16.2
Abstract Many important problem classes are governed by anisotropic features such as singularities concentrated on lower dimensional embedded manifolds, for instance, edges in images or shear layers in solutions of transport dominated equations. While the ability to reliably capture and sparsely represent anisotropic structures is obviously the more important the higher the number of spatial variables is, principal difficulties arise already in two spatial dimensions. Since it was shown that the well-known (isotropic) wavelet systems are not capable of efficiently approximating such anisotropic features, the need arose to introduce appropriate anisotropic representation systems. Among various suggestions, shearlets are the most widely used today. Main reasons for this are their optimal sparse approximation properties within a model situation in combination with their unified treatment of the continuum and digital realm, leading to faithful implementations. An additional advantage is the availability of stable compactly supported systems for high spatial localization. In this talk, we will provide an introduction to the anisotropic representation system of shearlets, in particular, compactly supported shearlets, present the main theoretical results, and discuss applications to imaging science and adaptive numerical solution of partial differential equations.
Compactly Supported Shearlets: Theory and Applicationsread_more
HG D 16.2
16. September 2014
13:15-14:15 		Prof. Dr. Philipp Grohs
SAM ETH Zurich
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Zurich Colloquium in Applied and Computational Mathematics

Titel Geometric Data Representations
Referent:in, Affiliation Prof. Dr. Philipp Grohs, SAM ETH Zurich
Datum, Zeit 16. September 2014, 13:15-14:15
Ort HG D 16.2
Geometric Data Representations
HG D 16.2
17. September 2014
16:15-17:15 		Prof. Dr. Jan Nordström
Linköping University
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Zurich Colloquium in Applied and Computational Mathematics

Titel New Developments for Initial Boundary Value Problems at Linköping University
Referent:in, Affiliation Prof. Dr. Jan Nordström, Linköping University
Datum, Zeit 17. September 2014, 16:15-17:15
Ort Y27 H 25
Abstract During the last decade, stable high order finite difference methods and finite volume methods applied to initial-boundary-value-problems have been developed. The stability is due to the use of so-called summation-by-parts operators, penalty techniques for implementing boundary and interface conditions, and the energy method for proving stability. In this talk we discuss new aspects of this technique including the relation to the initial-boundary-value-problem. By reusing the main ideas behind the development, new time-integration procedures, boundary conditions, boundary procedures, multi-physics couplings and uncertainty quantification, have been derived. We will present the theory by analyzing simple examples and apply to very complex problems.
New Developments for Initial Boundary Value Problems at Linköping Universityread_more
Y27 H 25
1. Oktober 2014
16:15-17:15 		Dr. Alexander Veit
University of Chicago
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Zurich Colloquium in Applied and Computational Mathematics

Titel Efficient computation of highly oscillatory integrals by using QTT tensor approximation
Referent:in, Affiliation Dr. Alexander Veit, University of Chicago
Datum, Zeit 1. Oktober 2014, 16:15-17:15
Ort Y27 H 25
Abstract We propose a new method for the efficient approximation of a class of highly oscillatory weighted integrals where the oscillatory function depends on the frequency parameter $\omega \geq 0$, typically varying in a large interval. Our approach is based, for fixed but arbitrary oscillator, on the precomputation and low-parametric approximation of certain $\omega$-dependent prototype functions whose evaluation leads in a straightforward way to an approximation of the target integral. The difficulty that arises is that these prototype functions consist of oscillatory integrals and are itself oscillatory which makes them both difficult to evaluate and to approximate.
Here we use the quantized-tensor train (QTT) approximation method for functional $m$-vectors of logarithmic complexity in $m$ in combination with a cross-approximation scheme for TT tensors. This allows the accurate approximation and efficient storage of these functions for a wide range of grid and frequency parameters.
We will present theoretical results and numerical experiments that illustrate the efficiency of the QTT-based numerical integration scheme in one and several spatial dimensions.
Efficient computation of highly oscillatory integrals by using QTT tensor approximationread_more
Y27 H 25
2. Oktober 2014
10:15-11:15 		Prof. Dr. Habib Ammari
Ecole Normale Supérieure, Paris
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Zurich Colloquium in Applied and Computational Mathematics

Titel Bio-inspired imaging for medical applications
Referent:in, Affiliation Prof. Dr. Habib Ammari, Ecole Normale Supérieure, Paris
Datum, Zeit 2. Oktober 2014, 10:15-11:15
Ort HG D 16.2
Abstract In this talk, we will suggest schemes for electrical sensing of objects by weakly electrical fish and for echolocation by bats. We will present recent results for shape identification and classification in electro-sensing using pulse form and waveform signals. We will also introduce an efficient and novel approach based on frequency-dependent shape descriptors for shape perception and classification in echolocation. Finally, we will apply the developed bio-inspired approaches in biomedical imaging in order to enhance the resolution, the robustness, and the specificity of tissue property imaging modalities.
Bio-inspired imaging for medical applicationsread_more
HG D 16.2
15. Oktober 2014
16:15-17:15 		Prof. Dr. Reinhold Schneider
TU Berlin
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Zurich Colloquium in Applied and Computational Mathematics

Titel Hierarchical tensor approximation of tensor network states by convex optimization
Referent:in, Affiliation Prof. Dr. Reinhold Schneider, TU Berlin
Datum, Zeit 15. Oktober 2014, 16:15-17:15
Ort Y27 H 25
Abstract Hierarchical Tucker tensor format (Hackbusch) and a particular case Tensor Trains (TT) (Tyrtyshnikov) have been introduced for high dimensional problems. The parametrization has been known in quantum physics as tensor network states. There are several ways to cast an approximate numerical solution into a variational framework. The Ritz Galerkin ansatz leads to an optimization problem on Riemannian manifolds. With this techniques, or in simplyfied form with a one-site DMRG one can be easily trapped into local minima. Although this problem can be avoided in combination with greedy techniques, we pursue a variational framework allowing concepts of compressive sensing. We obtain a soft shrinkage iteration scheme with in a Hierarchical SVD (HSVD) (or Vidal decomposition). We show that the iterates converge to the unique minimum of a convex optimization problem, even if the problem is ill-conditioned. We show a quasi-optimal error rate for the solution. The talk presents ongoing joint work with M. Bachmayr (RWTH Aachen).
Hierarchical tensor approximation of tensor network states by convex optimizationread_more
Y27 H 25
22. Oktober 2014
16:15-17:15 		Prof. Dr. Boris Vexler
TU München
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Zurich Colloquium in Applied and Computational Mathematics

Titel Sparse Optimal Control Problems in Measure Spaces
Referent:in, Affiliation Prof. Dr. Boris Vexler, TU München
Datum, Zeit 22. Oktober 2014, 16:15-17:15
Ort Y27 H 25
Abstract tba
Sparse Optimal Control Problems in Measure Spacesread_more
Y27 H 25
29. Oktober 2014
16:15-17:15 		Gerhard Kitzler
TU Wien
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Zurich Colloquium in Applied and Computational Mathematics

Titel Spectral polynomial discontinuous Galerkin method for the Boltzmann equation
Referent:in, Affiliation Gerhard Kitzler, TU Wien
Datum, Zeit 29. Oktober 2014, 16:15-17:15
Ort Y27 H 25
Abstract We present a Discontinuous Galerkin method for the Boltzmann equation \[\frac{\partial f}{\partial t} + {\rm div}_x vf = Q(f)\] with the nonlinear Boltzmann collision operator Q(f). The distribution function f is approximated by a shifted Maxwellian in momentum times a polynomial in space and momentum. The test functions are chosen as polynomials in space and momentum. The first property leads to a good approximation close to equilibrium, while the second property ensures natural conservation of the physical quantities mass, momentum and energy. The focus of the talk is on an efficient algorithm for the collision operator. Therefore the solution is transformed between nodal, hierarchical and polar polynomial bases to reduce the inner integral operator to diagonal form.
Spectral polynomial discontinuous Galerkin method for the Boltzmann equationread_more
Y27 H 25
5. November 2014
16:15-17:15 		Dr. Roman Andreev
RICAM Linz
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Zurich Colloquium in Applied and Computational Mathematics

Titel Variational source conditions in inverse problems
Referent:in, Affiliation Dr. Roman Andreev, RICAM Linz
Datum, Zeit 5. November 2014, 16:15-17:15
Ort Y27 H 25
Abstract Tikhonov regularization is a popular device for the stable approximate resolution of linear ill-posed problems. The quality of the approximate solution depends on the regularization parameter and the uncertainty in the data. Under the optimal choice of the regularization parameter, the approximate solution converges to the exact one as the uncertainty is reduced; in order to obtain a convergence rate, however, additional assumptions on the exact solution are necessary. Such assumptions are called source conditions. In this talk we discuss variational source conditions that characterize the convergence rate in the low order regime.
Variational source conditions in inverse problemsread_more
Y27 H 25
12. November 2014
16:15-16:45 		Jackie Ma
Technische Universität Berlin
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Zurich Colloquium in Applied and Computational Mathematics

Titel Reconstruction from Fourier Data by using Compactly Supported Multiscale Systems
Referent:in, Affiliation Jackie Ma, Technische Universität Berlin
Datum, Zeit 12. November 2014, 16:15-16:45
Ort Y27 H 25
Abstract The acquisition of Fourier data appears in many real world problems, such as magnetic resonance imaging, X-ray computed tomography, etc. The collected data, can be viewed as a collection of point samples of the Fourier transform of some object of interest, e.g. the human brain. Having these measurements, we are then left with the task to find an approximation of the original object. In this talk we discuss how this sampling and reconstruction task can be modeled using the so-called generalized sampling reconstruction method. In particular, we will present some benchmark results regarding the number of measurements that are needed in order to guarantee stable reconstructions. The results are presented for some compactly supported multiscale systems, such as wavelets and shearlets.
Reconstruction from Fourier Data by using Compactly Supported Multiscale Systemsread_more
Y27 H 25
12. November 2014
16:45-17:15 		Philipp Petersen
Technische Universität Berlin
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Zurich Colloquium in Applied and Computational Mathematics

Titel Regularization and Numerical Solution of the Inverse Scattering Problem Using Shearlet Frames
Referent:in, Affiliation Philipp Petersen, Technische Universität Berlin
Datum, Zeit 12. November 2014, 16:45-17:15
Ort Y27 H 25
Abstract In this talk we discuss regularization techniques for the numerical solution of inverse scattering problems in two space dimensions. Assuming that the boundary of a scatterer is its most prominent feature, we exploit as model the class of cartoonlike functions. Since functions in this class are asymptotically optimally sparsely approximated by shearlet frames, we consider shearlets as a means for the regularization in a Tikhonov method. We examine both directly the nonlinear problem and a linearized problem obtained by the Born approximation technique. As problem classes we study the acoustic inverse scattering problem and the electromagnetic inverse scattering problem. Our approach introduces a sparse regularization for the nonlinear setting and we present a result describing the behavior of the local regularity of a scatterer under linearization, which shows that the linearization does not affect the sparsity of the problem. The analytical results are illustrated by numerical examples for the acoustic inverse scattering problem that highlight the effectiveness of this approach.
Regularization and Numerical Solution of the Inverse Scattering Problem Using Shearlet Framesread_more
Y27 H 25
18. November 2014
17:00-18:00 		Mary Aprahamian
Manchester University
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Zurich Colloquium in Applied and Computational Mathematics

Titel The Matrix Unwinding Function
Referent:in, Affiliation Mary Aprahamian, Manchester University
Datum, Zeit 18. November 2014, 17:00-18:00
Ort HG G 43
Abstract In this talk we introduce the matrix unwinding function, which describes the discrepancy between a matrix and the principal logarithm of its exponential. We show that the unwinding function is instrumental in the derivation of correct identities involving logarithms and facilitates the understanding of other complex multivalued matrix functions, including inverse trigonometric functions. We also use it to study the matrix sign function. We give a numerical scheme for computing the matrix unwinding function and show how it can be used in conjunction with the scaling and squaring algorithm to compute the matrix exponential using the idea of argument reduction. (Joint work with Nick Higham)
The Matrix Unwinding Functionread_more
HG G 43
19. November 2014
16:15-17:15 		Prof. Dr. Kristof Cools
University of Nottingham
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Zurich Colloquium in Applied and Computational Mathematics

Titel Calderon Preconditioning in Computational Electromagnetics
Referent:in, Affiliation Prof. Dr. Kristof Cools, University of Nottingham
Datum, Zeit 19. November 2014, 16:15-17:15
Ort Y27 H 25
Calderon Preconditioning in Computational Electromagnetics
Y27 H 25
26. November 2014
16:15-17:15 		Prof. Dr. Eric Cances
Ecole des Ponts and INRIA, Paris
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Zurich Colloquium in Applied and Computational Mathematics

Titel Numerical methods for electronic structure calculation
Referent:in, Affiliation Prof. Dr. Eric Cances, Ecole des Ponts and INRIA, Paris
Datum, Zeit 26. November 2014, 16:15-17:15
Ort Y27 H 25
Abstract Electronic structure calculation has become an essential tool in chemistry, condensed matter physics, molecular biology, materials science, and nanosciences. It is also an inexhaustible source of exciting mathematical and numerical problems. In this talk, I will focus on Density Functional Theory and the Kohn-Sham model, which is to date the most widely used approach in electronic structure calculation, as it provides the best compromise between accuracy and computational efficiency. The Kohn-Sham model is a constrained optimization problem, whose Euler-Lagrange equations have the form of a coupled system of nonlinear elliptic eigenvalue problems. I will present some recent progress made in the numerical analysis of this model, which paves the road to high-fidelity numerical simulations (with a posteriori error bounds) of the electronic structure of large molecular systems. I will then discuss the difficult issue of coupling the Kohn-Sham model with coarser models in view of simulating even larger molecular systems, such as drug-protein complexes in solution.
Numerical methods for electronic structure calculationread_more
Y27 H 25
3. Dezember 2014
16:15-17:15 		Prof. Dr. John Maddocks
EPF Lausanne
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Zurich Colloquium in Applied and Computational Mathematics

Titel Some Mathematical and Computational Techniques arising in the Multi-Scale Modelling of DNA mechanics
Referent:in, Affiliation Prof. Dr. John Maddocks, EPF Lausanne
Datum, Zeit 3. Dezember 2014, 16:15-17:15
Ort Y27 H 25
Abstract It is now widely accepted that in addition to coding for proteins there is a second, mechanical, code in the sequence of DNA which controls biological function in various ways. Starting from large scale Molecular Dynamics simulation data I will discuss how to construct and parametrize coarse grain models of DNA at various scales. The models capture variations in shape and stiffness as a function of sequence in ways that can be tested against experiment. Mathematical techniques that arise include maximum parameter estimation, and symmetry breaking using Poincare-Melnikov functions in Hamiltonian ODE two-point boundary value problems.
Some Mathematical and Computational Techniques arising in the Multi-Scale Modelling of DNA mechanicsread_more
Y27 H 25
4. Dezember 2014
12:15-13:15 		Prof. Dr. Athanasios Tzavaras
KAUST, Saudi Arabia
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Zurich Colloquium in Applied and Computational Mathematics

Titel On problems with discontinuous motions in solid mechanics: shear bands and cavitation
Referent:in, Affiliation Prof. Dr. Athanasios Tzavaras, KAUST, Saudi Arabia
Datum, Zeit 4. Dezember 2014, 12:15-13:15
Ort HG G 19.2
Abstract Various problems in solid mechanics concern phenomena where discontinuous motions emerge. Such phenomena lie outside the traditional premiss of continuum modeling and their study raises questions at the interface of discrete and continuum modeling and poses challenges to the mathematical theory. In this talk we will review recent work on two specific examples: In the first part we will present results on nonuniqueness on the system of radial elasticity and the notion of singular induced from continuum solutions, which is a strengthening of the notion of weak solutions attempting to account for the surface energy required to open a cavity. The second part will consider the onset of localization and the formation of shear bands in high strain-rate plasticity of metals. Shear strain localization is tyically associated with ill-posedness of an underlying initial value problem, what has coined the term Hadamard-instability for its description in the mechanics literature. It should however be noted that while Hadamard instability indicates the catastrophic growth of oscillations around a mean state, it does not by itself explain the formation of coherent structures typically observed in localization. For a simple model capturing the essence of the mechanism of localization in metals we will construct self-similar solutions that describe the self-organization into a localized solution starting from well prepared data.
On problems with discontinuous motions in solid mechanics: shear bands and cavitationread_more
HG G 19.2
10. Dezember 2014
16:15-17:15 		Prof. Dr. David Ryckelynck
MINES Paristech, Evry, France
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Zurich Colloquium in Applied and Computational Mathematics

Titel Hyper-reduction in nonlinear mechanics of solid materials
Referent:in, Affiliation Prof. Dr. David Ryckelynck, MINES Paristech, Evry, France
Datum, Zeit 10. Dezember 2014, 16:15-17:15
Ort Y27 H 25
Abstract Reduced-order models reveal common features between solutions of parametric partial differential equations (PDE). They aim to save computational time when modelling complex mechanical phenomena, as setting-up convenient nonlinear constitutive equations or boundary conditions for instance. The Garlerkin weak form of nonlinear reduced equations do not provide sufficient speed-up, mainly because the computation of the reduced-residual can’t be performed offline. Hence, this computation remains affected by the complexity of the original model. Hyper-reduction methods aim to generate reduced-order model whose complexity does not depend on the complexity of the original model by introducing a reduced integration domain (RID). This domain contains only few elements of the original mesh. We propose both an explicit hyper-reduced scheme and implicit hyper-reduced schemes applied to nonlinear mechanics of solid materials. The explicit approach aims to interpolate missing boundary conditions on the boundary of the RID. The implicit approach predicts the reduced coordinate of the displacement field by using balance conditions restricted to the RID. The RID is generated offline by aggregating the magic points of various reduced bases, depending on the physics involved in the original model. These magic points depend on the shape of the empirical modes by following the empirical interpolation method. The reduced-bases are obtained by using either: an a posteriori approach such as the snapshot POD method and the derivative extended POD method; or an a priori approach such as the APHR (A priori Hyper Reduction) method. In case of standard materials, an a posteriori error estimation is proposed by following the constitutive-relation-error method. We also develop a snapshotless approach to adapt the hyper-reduced approximation, without additional FE solution of the DPE.
Hyper-reduction in nonlinear mechanics of solid materialsread_more
Y27 H 25
12. Dezember 2014
13:00-14:00 		Prof. Dr. Carsten Carstensen
Humboldt-Universität Berlin
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Zurich Colloquium in Applied and Computational Mathematics

Titel The Axioms of Adaptivity
Referent:in, Affiliation Prof. Dr. Carsten Carstensen, Humboldt-Universität Berlin
Datum, Zeit 12. Dezember 2014, 13:00-14:00
Ort Y27 H 25
The Axioms of Adaptivity
Y27 H 25

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

Archiv: 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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