Departement Mathematik

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Zurich colloquium in applied and computational mathematics

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Herbstsemester 2010

Datum / Zeit Referent:in Titel Ort
15. September 2010
16:15-17:15 		Prof. Dr. Alexey Chernov
Hausdorff Institute, Bonn, Germany
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Zurich Colloquium in Applied and Computational Mathematics

Titel Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex in R^d, d > 1
Referent:in, Affiliation Prof. Dr. Alexey Chernov, Hausdorff Institute, Bonn, Germany
Datum, Zeit 15. September 2010, 16:15-17:15
Ort HG E 5
Abstract In this talk we consider the L2-projection operator onto the space of polynomials up to degree p on a simplex S in R^d and study its approximation properties in L2 on the boundary of S. Optimal error estimates are established in the case of the finite Sobolev regularity for arbitrary spatial dimension d > 1, and illustrated on several numerical examples. The convergence proof is based on the collapsed coordinate transform and expansions into various polynomial bases involving Jacobi polynomials and their antiderivatives. Our convergence analysis generalizes corresponding estimates for cubes in R^d from the paper [P.Houston, Ch.Schwab, E.Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133–2163].
Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex in R^d, d > 1read_more
HG E 5
22. September 2010
16:15-17:15 		Prof. Dr. Endre Süli
Oxford University, England
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Zurich Colloquium in Applied and Computational Mathematics

Titel Navier-Stokes-Fokker-Planck systems in kinetic models of dilute polymers: existence and equilibration of global weak solutions
Referent:in, Affiliation Prof. Dr. Endre Süli, Oxford University, England
Datum, Zeit 22. September 2010, 16:15-17:15
Ort HG E 1.2
Abstract We show the existence of global in-time weak solutions to a general class of coupled bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker-Planck equation; in particular, the drag term need not be corotational. With a square-integrable and divergence-free initial velocity datum for the Navier Stokes equation and a nonnegative initial probability density function for the Fokker-Planck equation, which has finite relative entropy with respect to the Maxwellian of the model, we prove the existence of a global in-time weak solution to the coupled Navier-Stokes-Fokker Planck system. It is also shown that in the absence of a body force, the weak solution decays exponentially in time to the equilibrium solution, at a rate that is independent of the choice of the initial datum and of the centre-of-mass diffusion coefficient. The lecture is based on joint work with John W. Barrett [Imperial College London].
Navier-Stokes-Fokker-Planck systems in kinetic models of dilute polymers: existence and equilibration of global weak solutionsread_more
HG E 1.2
29. September 2010
16:15-17:15 		Dr. Carlos Jerez
Seminar for Applied Mathematics, ETH Zürich
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Zurich Colloquium in Applied and Computational Mathematics

Titel Variational forms for the inverses of integral logarithmic operators over an interval
Referent:in, Affiliation Dr. Carlos Jerez , Seminar for Applied Mathematics, ETH Zürich
Datum, Zeit 29. September 2010, 16:15-17:15
Ort HG E 1.2
Abstract We present explicit and exact variational formulations for the weakly singular and hypersingular operators over an open interval as well as for their corresponding inverses. Contrary to the case of a closed curve, these operators no longer map fractional Sobolev spaces in a dual fashion but degenerate into different subspaces depending on their extensibility by zero. We show that a symmetric and antisymmetric decomposition leads to precise coercivity results in fractional Sobolev spaces and characterize the mismatch occurring between associated functional spaces in this limiting case. Moreover, we naturally define Calderon-type identities in each case with potential use as preconditioners.
Variational forms for the inverses of integral logarithmic operators over an intervalread_more
HG E 1.2
6. Oktober 2010
16:15-17:15 		Prof. Dr. Eitan Tadmor
University of Maryland, USA
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Zurich Colloquium in Applied and Computational Mathematics

Titel Linear PDEs in critical regularity spaces: Hierarchical construction of their nonlinear solutions
Referent:in, Affiliation Prof. Dr. Eitan Tadmor, University of Maryland, USA
Datum, Zeit 6. Oktober 2010, 16:15-17:15
Ort HG E 1.2
Abstract We construct uniformly bounded solutions of the equations div(U)=f and curl(U)=f, for general f's in the critical regularity spaces L^d(R^d) and, respectively, L^3(R^3). The study of these equations was motivated by recent results of Bourgain & Brezis. The equations are linear but construction of their solutions is not. Our constructions are, in fact, special cases of a rather general framework for solving linear equations, L(U)=f, covered by the closed range theorem. The solutions are realized in terms of nonlinear hierarchical representations, U=\sum(u_j), which we introduced earlier in the context of image processing. The u_j's are constructed recursively as proper minimizers, yielding a multi-scale decomposition of the solutions U.
Linear PDEs in critical regularity spaces: Hierarchical construction of their nonlinear solutionsread_more
HG E 1.2
13. Oktober 2010
16:15-17:15 		Prof. Dr. Zdenek Strakos
Charles University, Prague, Czech Republic
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Zurich Colloquium in Applied and Computational Mathematics

Titel Moments, model reduction and nonlinearity in solving linear algebraic problems
Referent:in, Affiliation Prof. Dr. Zdenek Strakos, Charles University, Prague, Czech Republic
Datum, Zeit 13. Oktober 2010, 16:15-17:15
Ort HG E 1.2
Unterlagen https://math.ethz.ch/ndb/00017/00816/abstract_strakos.pdffile_download
Moments, model reduction and nonlinearity in solving linear algebraic problemsread_more
HG E 1.2
27. Oktober 2010
16:15-17:15 		Dr. Maria Lopez-Fernandez
University of Zurich
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Zurich Colloquium in Applied and Computational Mathematics

Titel A quadrature based method for evaluating the exponential-type functions for exponential methods
Referent:in, Affiliation Dr. Maria Lopez-Fernandez, University of Zurich
Datum, Zeit 27. Oktober 2010, 16:15-17:15
Ort HG E 1.2
Abstract We present a quadrature-based method to evaluate exponential-like operators required by different kinds of exponential integrators. The method approximates these operators by means of a quadrature formula that converges like $O(e^{-cK})$, with $K$ the number of quadrature nodes, and it is useful when solving parabolic equations. The approach allows also the evaluation of the associated scalar mappings. The method is based on numerical inversion of sectorial Laplace transforms. Several numerical illustrations are provided to test the algorithm, including examples with a mass matrix and the application of the method inside the MATLAB package EXP4, an adaptive solver based on an exponential Runge--Kutta method.
A quadrature based method for evaluating the exponential-type functions for exponential methodsread_more
HG E 1.2
17. November 2010
16:15-17:15 		Dr. Michail Vlachos
IBM Research, Zürich
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Zurich Colloquium in Applied and Computational Mathematics

Titel Analyzing compressed weblog patterns
Referent:in, Affiliation Dr. Michail Vlachos, IBM Research, Zürich
Datum, Zeit 17. November 2010, 16:15-17:15
Ort HG E 1.2
Abstract Analysis of historical search patterns holds great importance for web search engines, because it can help to better understand the users' search behavior. Capturing the user search preferences over time can provide useful insights in applications such as discovery of news events, keyword recommendation and personalized ad targeting. A major bottleneck in analyzing historical sequential data is the growing size of data repositories. Therefore, there is a need to enable search and mining operations directly on the compressed data. In this talk we will present how to facilitate efficient search over compressed sequential data, with specific focus on weblog query patterns. Our approach guarantees optimally tight distance bounds, while at the same time being efficient and lightweight. This helps drastically reduce the search time compared to previous state of-the-art techniques. Additionally, we will explicate how to support other types of knowledge discovery operations, such as burst detection, query by-burst and query-by-periodicity. We will demonstrate extensions and applications of the presented technique for a multitude of areas.
Analyzing compressed weblog patternsread_more
HG E 1.2
24. November 2010
16:15-17:15 		Dr. Aziz Madrane
Bombardier Aerospace Systems, Montreal, Canada
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Zurich Colloquium in Applied and Computational Mathematics

Titel Overlapping unstructured hybrid grid chimera method
Referent:in, Affiliation Dr. Aziz Madrane, Bombardier Aerospace Systems, Montreal, Canada
Datum, Zeit 24. November 2010, 16:15-17:15
Ort HG E 1.2
Abstract Aerodynamic problems involving moving geometries have many applications, including store separation, high-speed train entering into a tunnel, simulation of full configurations of the helicopter and fast maneuvrability. Chimera method [1] offers the option of calculating these procedures. The solution process uses a grid system that discretizes the problem domain by using separately generated but overlapping unstructured grids that update and exchange boundary information through interpolation. However, such computations are complicated and time consuming [2].* *Parallel computing offers a very effective way to improve the productivity in doing computational fluid dynamics (CFD)*. *Therefore the purpose of this study is to develop an efficient parallel computation algorithm for analyzing the flowfield of complex geometries using overset grid technique [3],[4].* *The strategy adopted in the parallelization of the overset grids method including the use of hierarchical data structures and communication, will be described. Mathematical analysis of chimera method can be found in [5]. Numerical* *results are presented to demonstrate the efficiency of the resulting* *parallel overset grid method. *References:* [1] *Steger, J.L.* *and Benek, J.A*., On the Use of Composite Grid Schemes in Computational Aerodynamics, Computer Methods in Applied Mech. and Engeneering, 64, 301-320, (1987) [2] *Madrane, A.**, Heinrich R. and Gerhold T*., Implemetation of the Chimera method in the unstructured hybrid DLR finite volume Tau-Code. 6^th Overset Composite Grid and Solution Technology Symposuim. Ft.Walton Beach, Florida, USA, October 8-10, 2002. http://www.arl.hpc.mil/events/Overset2002/proceedings.html* * [3] *A.Madrane*, Parallel Implementation of a Dynamic Overset Unstructured Grid Approach. ECCOMAS2004, Jyvaskyla, Finland on 24-28 july 2004. _*http://www.mit.jyu. /eccomas2004/*_ [4]* A. Madrane, *http://www.arl.hpc.mil/events/Overset2006/program.html [5] *F. Brezzi, J.L. Lions, O. Pironneau*, Analysis of Chimera Method, C.R. Acad. Sci. Paris, t.332, Serie 1, pp. 655-660, 2001.
Overlapping unstructured hybrid grid chimera methodread_more
HG E 1.2
1. Dezember 2010
16:15-17:15 		Dr. Angela Kunoth
University of Paderborn, Germany
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Zurich Colloquium in Applied and Computational Mathematics

Titel Space-time adaptive wavelet methods for control problems constrained by parabolic PDEs
Referent:in, Affiliation Dr. Angela Kunoth, University of Paderborn, Germany
Datum, Zeit 1. Dezember 2010, 16:15-17:15
Ort HG E 1.2
Abstract Optimization problems constrained by partial differential equations (PDEs) are particularly challenging from a computational point of view: the first order necessary conditions for optimality lead to a coupled system of PDEs. Specifically, for the solution of control problems constrained by a parabolic PDE, one needs to solve a system of PDEs coupled {\em globally in time and space}. For these, conventional time-stepping methods quickly reach their limitations due to the enourmous demand for storage. For such a coupled PDE system, adaptive methods which aim at distributing the available degrees of freedom in an a-posteriori-fashion to capture singularities in the data or domain, with respect to both space and time, appear to be most promising. Here I propose an adaptive method based on wavelets. It builds on a recent paper by Schwab and Stevenson where a single linear parabolic evolution problem is formulated in a weak space-time form and where an adaptive wavelet method is designed for which convergence and optimal convergence rates (when compared to wavelet-best $N$ term approximation) can be shown. Our approach extends this paradigm to control problems constrained by evolutionary PDEs for which we can prove convergence and optimal rates for each of the involved unknowns (state, costate, and control).
Space-time adaptive wavelet methods for control problems constrained by parabolic PDEsread_more
HG E 1.2
8. Dezember 2010
16:15-17:15 		Prof. Dr. Andrew Stuart
University of Warwick, England
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Zurich Colloquium in Applied and Computational Mathematics

Titel Stochastic PDEs as limits of MCMC algorithms
Referent:in, Affiliation Prof. Dr. Andrew Stuart, University of Warwick, England
Datum, Zeit 8. Dezember 2010, 16:15-17:15
Ort HG E 1.2
Abstract Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have mainly been proved for target measures with a product structure, severely limiting their applicability. In this talk we study diffusion limits for a class of naturally occuring high dimensional measures, found from the approximation of measures on a Hilbert space which are absolutley continuous with respect to a Gaussian reference measure. The diffusion limit of a random walk Metropolis algorithm to an infinite dimensional Hilbert space valued SDE (or SPDE) is proved, facilitating understanding of the computational complexity of the algorithm. Variants on this idea are discussed and comparisons between different algorithms are made.
Stochastic PDEs as limits of MCMC algorithmsread_more
HG E 1.2
15. Dezember 2010
16:15-17:15 		Dr. Euan Spence
University of Bath, England
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Zurich Colloquium in Applied and Computational Mathematics

Titel Boundary integral equation methods for high frequency scattering
Referent:in, Affiliation Dr. Euan Spence, University of Bath, England
Datum, Zeit 15. Dezember 2010, 16:15-17:15
Ort HG E 1.2
Abstract Much research effort in recent years has been focused on designing effective numerical methods for high frequency acoustic scattering. The main difficulty is that as the frequency increases the solution becomes more oscillatory, leading to a rapid increase of degrees of freedom in conventional methods to maintain accuracy. One way around this difficulty is to use the high frequency asymptotics of the solution of the scattering problem to design approximation spaces that take into account the high oscillation of the solution. Once these hybrid asymptotic-numerical methods have been designed, an interesting question is whether stability of these methods can be established with bounds that are explicit in the frequency. One strategy for proving stability of boundary integral methods for these high frequency problems is to seek to prove that the integral operator is coercive. This talk will present some recent results on proving coercivity for a wide class of domains, and independent of the (high) frequency. This is joint work with Timo Betcke and Simon Chandler-Wilde (University of Reading), Ivan Graham (University of Bath) and Valery Smyshlyaev (University College London).
Boundary integral equation methods for high frequency scatteringread_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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