Departement Mathematik

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Zurich colloquium in applied and computational mathematics

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Frühjahrssemester 2015

Datum / Zeit Referent:in Titel Ort
4. Februar 2015
16:15-17:15 		Prof. Dr. Martin Schanz
TU Graz
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Zurich Colloquium in Applied and Computational Mathematics

Titel Multi field problems in poroelasticity: Governing equations and boundary element solution
Referent:in, Affiliation Prof. Dr. Martin Schanz, TU Graz
Datum, Zeit 4. Februar 2015, 16:15-17:15
Ort HG E 1.2
Abstract Many engineering problems are coupled field problems. These couplings are not only interface couplings but also volumetric coupled problems. An example for the latter is poroelasticity, where the displacement field is strongly coupled to the pore pressure field. Such kind of coupling result in a coupled set of differential equations to be solved. In the presentation, the three field model for partial saturated poroelasticity is presented. The equations may be used to model the dynamic behavior of soil. As well the saturated case will be shown and its analogy to thermoelasticity. Finally, a collocation boundary element formulation for partial saturated poroelasticity is presented with a numerical realization.
Multi field problems in poroelasticity: Governing equations and boundary element solutionread_more
HG E 1.2
18. Februar 2015
16:15-17:15 		Prof. Dr. Claude Bardos
Laboratoire Jacques Louis Lions Paris and University of Paris 7, France
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Zurich Colloquium in Applied and Computational Mathematics

Titel Appearance of turbulence in the Euler limit with Boundary effects
Referent:in, Affiliation Prof. Dr. Claude Bardos, Laboratoire Jacques Louis Lions Paris and University of Paris 7, France
Datum, Zeit 18. Februar 2015, 16:15-17:15
Ort HG E 1.2
Abstract It seems that it is in presence of boundary effects that the classical issues of turbulence ie loss of regularity, the appearance of a non trivial Reynolds stress tensor and anomalous energy dissipation are the more visible. Up to know the only general result is a theorem of Kato which connect these different effect. I intend to give some observation on these issues using first the notion of wild solution of De Lellis and Sz\'{e}kelyhidi . Then to show the robustness of these problem to compare zero viscosity limit of the Navier Stokes in presence of boundary effects with macroscopic limit of the Boltzmann equation in the incompressible limit. Most of the material of this talk is contained in a joint paper with Francois Golse and Lionel Paillard.
Appearance of turbulence in the Euler limit with Boundary effectsread_more
HG E 1.2
10. März 2015
17:15-18:30 		Prof. Dr. Holger Rauhut
RWTH Aachen
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Zurich Colloquium in Applied and Computational Mathematics

Titel Solving high-dimensional parametric operator equations via compressive sensing
Referent:in, Affiliation Prof. Dr. Holger Rauhut, RWTH Aachen
Datum, Zeit 10. März 2015, 17:15-18:30
Ort HG D 1.2
Abstract Compressive sensing enables accurate recovery of approximately sparse vectors from incomplete information. We apply this principle to the numerical solution of parametric operator equations where the parameter domain is high-dimensional. In fact, one can show that the solution of certain parametric operator equations (parametric PDEs) is analytic in the parameters which can be exploited to show convergence rates for nonlinear (sparse) approximation. Building on this fact, we show that methods from compressive sensing can be used to compute approximations from samples (snapshots) of the parametric operator equation for randomly chosen parameters. In order to make our scheme work, we require a weighted version of standard compressive sensing, for which theory and algorithms have been developed recently. Based on the snapshots obtained by Petrov-Galerkin approximation, coefficients of a polynomial chaos expansion of the parametric solution in terms of tensorized Chebyshev polynomials are computed via weighted l1-minimization. We provide theoretical approximation rates for this scheme. Based on joint works with Christoph Schwab and Rachel Ward.
Solving high-dimensional parametric operator equations via compressive sensingread_more
HG D 1.2
11. März 2015
16:15-17:15 		Prof. Dr. Philippe Ciarlet
City University of Hong Kong
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Zurich Colloquium in Applied and Computational Mathematics

Titel Direct Computation Of The Stresses In Elasticity
Referent:in, Affiliation Prof. Dr. Philippe Ciarlet, City University of Hong Kong
Datum, Zeit 11. März 2015, 16:15-17:15
Ort HG E 1.2
Abstract We describe and analyze an ?intrinsic approach? to the pure Neumann problem of two-dimensional or three-dimensional linearized elasticity, whose novelty consists in considering the strain tensor field as the sole unknown, instead of the displacement vector field as is customary. This approach leads to a well-posed minimization problem of a new type, constrained by a weak form of the classical Saint Venant compatibility conditions. We then describe a natural finite element subspace for approximating this minimization problem in dimension two, which possesses the remarkable feature that the Saint-Venant compatibility conditions can be exactly satisfied by the approximate strains obtained over such a subspace. This discretization of the intrinsic approach thus provides a direct finite element approximation of the strain tensor field, or equivalently, by means of the constitutive equation, a direct finite element approximation of the stress tensor field.
Direct Computation Of The Stresses In Elasticityread_more
HG E 1.2
17. März 2015
16:15-17:15 		Karoline Köhler
Humboldt-Universität Berlin
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Zurich Colloquium in Applied and Computational Mathematics

Titel Non-conforming FEM for the obstacle problem
Referent:in, Affiliation Karoline Köhler, Humboldt-Universität Berlin
Datum, Zeit 17. März 2015, 16:15-17:15
Ort Y27 H28
Abstract This talk studies the obstacle problem for the Laplace operator and its discretisation with non-conforming Crouzeix-Raviart finite element methods. It focuses on a posteriori error analysis. This analysis relies on the discrete Lagrange multiplier, which is not unique and allows for various choices. The resulting a posteriori error estimator is studied with respect to its reliability and efficiency and the analysis focuses on the terms which involve the discrete Lagrange multiplier. Numerical experiments hightlight these results and present an outlook on adaptive mesh-refinement.
Non-conforming FEM for the obstacle problemread_more
Y27 H28
22. April 2015
16:15-17:15 		Dr. Ricardo Ruiz-Baier
University of Lausanne
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Zurich Colloquium in Applied and Computational Mathematics

Titel Modelling, numerics, and analysis of cardiac electromechanics
Referent:in, Affiliation Dr. Ricardo Ruiz-Baier, University of Lausanne
Datum, Zeit 22. April 2015, 16:15-17:15
Ort HG E 1.2
Abstract We present an overview of the numerical simulation of the interaction between cardiac electrophysiology, sub-cellular activation mechanisms, and macroscopic tissue contraction; that together comprise the essential elements of the electromechanical function of the human heart. We discuss the development of some mathematical models tailored for the simulation of the cardiac excitation-contraction mechanisms, which are primarily based on nonlinear elasticity theory and phenomenological descriptions of the mechano-electrical feedback. Here the link between contraction and the biochemical reactions at microscales is described by an active strain decomposition model. Then we turn to the mathematical analysis of a simplified version of the model problem consisting in a reaction-diffusion system governing the dynamics of ionic quantities, intra and extra-cellular potentials, and the elastodynamics equations describing the motion of an incompressible material. Under the assumption of linearized elastic behavior and a truncation of the updated nonlinear diffusivities, we are able to prove existence of weak solutions to the underlying coupled system and uniqueness of regular solutions. A finite element formulation is also introduced, for which we establish existence of discrete solutions and show convergence to a weak solution of the original problem. We close with some numerical examples illustrating the convergence of the method and some features of the model.
Modelling, numerics, and analysis of cardiac electromechanicsread_more
HG E 1.2
29. April 2015
16:15-17:15 		Prof. Dr. Zdzislaw Brzezniak
University of York
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Zurich Colloquium in Applied and Computational Mathematics

Titel Finite element based discretisations of the incompressible Navier-Stokes equations with multiplicative random forcing
Referent:in, Affiliation Prof. Dr. Zdzislaw Brzezniak, University of York
Datum, Zeit 29. April 2015, 16:15-17:15
Ort HG E 1.2
Abstract I will discuss finite element based space-time discretisations of the incompressible Navier-Stokes equations with noise. For the 3-d case, our sequence of numerical solutions converges, for vanishing discretisation parameters, to a weak martingale solution. For the 2-d case, our sequence of numerical solutions converges, to the unique strong solution. We will also discuss rates of convergence. This is based on a joint work with Erich Carelli and Andreas Prohl. At the end I will also mention about a result (joint with H Bessaih and A Millet) about a time splitting method for 2-d Stochastic NSEs.
Finite element based discretisations of the incompressible Navier-Stokes equations with multiplicative random forcingread_more
HG E 1.2
6. Mai 2015
16:15-17:15 		Ivan Oseledets
INM RAS and SkolTech, Moscow, Russia
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Zurich Colloquium in Applied and Computational Mathematics

Titel Tensor networks: applications and algorithms
Referent:in, Affiliation Ivan Oseledets, INM RAS and SkolTech, Moscow, Russia
Datum, Zeit 6. Mai 2015, 16:15-17:15
Ort HG E 1.2
Abstract Low-rank factorizations of matrices and tensors attract a lot of attention in recent years in numerical analysis and linear algebra. They help to reduce dimensionality of the problem and in many cases even break the "curse of dimensionality" in the solution of multiparametric and stochastic problems, modelling of biochemical networks, solution of high-dimensional PDEs and many others. However, the more we look into the application areas, the more we find similar concepts in absolutely different areas. To name only few: Sum-of-product networks in machine learning, probabilistic context-free grammars in natural language processing, weighted finite automata, graphical models in machine learning and statistical physics, tensor networks and quantum information theory and solid state physics. Many of the approaches used in these areas are similar, however many of them are different. In this talk, I will present a brief introduction to these new areas (and point out the results that may be interesting for the numerical analysis) and also present several new results about low-rank approximation of matrices and tensors.
Tensor networks: applications and algorithmsread_more
HG E 1.2
13. Mai 2015
16:15-17:15 		Prof. Dr. Steffen Börm
Ch.-Albrechts-Universität Kiel, Germany
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Zurich Colloquium in Applied and Computational Mathematics

Titel Tensor multigrid
Referent:in, Affiliation Prof. Dr. Steffen Börm, Ch.-Albrechts-Universität Kiel, Germany
Datum, Zeit 13. Mai 2015, 16:15-17:15
Ort HG E 1.2
Abstract We consider multigrid solvers for elliptic partial differential equations with axially-aligned singular perturbations, e.g., the equation \begin{displaymath} -\operatorname{div} \begin{pmatrix} r & \\ & 1/r \end{pmatrix} \operatorname{grad} u(r,\psi) = r f(r,\psi) \end{displaymath} arising when expressing Poisson's equation in polar coordinates. Standard multigrid methods do not show mesh-independent convergence for this kind of problem. A well-known approach is to replace the standard isotropically refined mesh hierarchy by a \emph{semi-coarsened} mesh and to replace standard Gauss-Seidel or Jacobi smoothers by \emph{block smoothers} that treat entire rows of indices simultaneously. In this talk, we present an elegant proof for a mesh-independent bound for the resulting convergence rate. This bound is even robust with respect to varying coefficients. The fundamental idea of the proof is to consider an auxiliary eigenvalue problem that gives rise to a decomposition of the trial space into invariant subspaces. In each of these subspaces, the bilinear form is closely related to a simple one-dimensional problem that can be analyzed to obtain robust bounds.
Tensor multigridread_more
HG E 1.2
20. Mai 2015
16:15-17:15 		Prof. Dr. Manuel Castro Diaz
University of Malaga, Spain
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Zurich Colloquium in Applied and Computational Mathematics

Titel Bedload sediment transport in shallow flows: models and numerics
Referent:in, Affiliation Prof. Dr. Manuel Castro Diaz, University of Malaga, Spain
Datum, Zeit 20. Mai 2015, 16:15-17:15
Ort HG E 1.2
Abstract In this talk, we focus on models for sedimentation transport consisting of a shallow water system coupled with a so called Exner equation that described the evolution of the topography. We present different parametrizations of the bedload transport rate and we discuss the hiperbolicity of the proposed models. We also present the discretization of the system in the framework of path-conservative schemes and an efficient implementation on GPUs using non-structured meshes. Finally, some numerical results will be presented.
Bedload sediment transport in shallow flows: models and numericsread_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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