Zurich colloquium in applied and computational mathematics

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Autumn Semester 2011

Date / Time

Speaker

Title

Location

21 September 2011
16:15-17:15

Prof. Dr. Tucker Carrington
Queen's University, Ontario, Canada

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Using sparse grids to solve the vibrational Schrödinger equation
Speaker, Affiliation	Prof. Dr. Tucker Carrington, Queen's University, Ontario, Canada
Date, Time	21 September 2011, 16:15-17:15
Location	HG E 1.2
Abstract	I shall review computational techniques for solving the vibrational Schroedinger equation and present new ideas for using sparse grids to cope with the curse of dimensionality. Mathematicians not interested in solving the Schrödinger equation might appreciate: 1) how to do quadratures with a sparse grid without summing contributions to the integral from each of the grids that compose the sparse grid; 2) how to exploit the structure of nested grids to evaluate matrix-vector produces efficiently.

Using sparse grids to solve the vibrational Schrödinger equationread_more

HG E 1.2

28 September 2011
16:15-17:15

Dr. Xavier Claeys
ISAE Toulouse, France

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Multi-trace boundary integral formulation of the first kind for acoustic scattering by composite structures
Speaker, Affiliation	Dr. Xavier Claeys, ISAE Toulouse, France
Date, Time	28 September 2011, 16:15-17:15
Location	HG E 1.2
Abstract	We study the scattering of acoustic waves by a penetrable object composed of several adjacent parts with different material properties. Starting from an already well known single trace integral formulation of the first kind for this problem, we derive a new boundary integral formulation of the first kind where all unknowns are doubled on each interface. This formulation is immune to spurious resonnances, and it satisfies a stability property that ensures quasi optimal convergence of conforming Galerkin boundary element methods. Besides the operator of this formulation satisfies a relation similar to the standard Calderon identity.

Multi-trace boundary integral formulation of the first kind for acoustic scattering by composite structuresread_more

HG E 1.2

12 October 2011
16:15-17:15

PD Dr. Steffen Börm
CAU Kiel, Deutschland

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Matrix-Galerkin
Speaker, Affiliation	PD Dr. Steffen Börm, CAU Kiel, Deutschland
Date, Time	12 October 2011, 16:15-17:15
Location	HG E 1.2
Abstract	Certain mathematical problems from control theory or the investigation of stochastic PDEs lead to matrix equations. Storing the $n \times n$ solution matrix in the standard way requires ${\mathcal O}(n^2)$ units of storage, so this representation becomes unusable if $n$ grows large. In this talk, an alternative approach is discussed: the matrix is approximated in a data-sparse representation requiring only ${\mathcal O}(n k)$ units of storage, where $k$ is a parameter controlling the accuracy of the approximation. A Galerkin approach can be employed to compute the approximation. The talk outlines the fundamental idea, demonstrates how a number of fundamental properties of the resulting system can be derived, and discusses algorithms for solving this system.

Matrix-Galerkinread_more

HG E 1.2

26 October 2011
16:15-17:15

Prof. Dr. Eric Vanden-Eijnden
Courant Institute, New York

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Dimension reduction, coarse-graining and data assimilation in high-dimensional dynamical systems: modeling and computation
Speaker, Affiliation	Prof. Dr. Eric Vanden-Eijnden, Courant Institute, New York
Date, Time	26 October 2011, 16:15-17:15
Location	HG E 1.2

Dimension reduction, coarse-graining and data assimilation in high-dimensional dynamical systems: modeling and computation

HG E 1.2

23 November 2011
16:15-17:15

Prof. Dr. Mustafa Khammash
D-BSSE, ETH Zurich

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Stochastic gene expression: mathematical modeling, analysis, and control
Speaker, Affiliation	Prof. Dr. Mustafa Khammash, D-BSSE, ETH Zurich
Date, Time	23 November 2011, 16:15-17:15
Location	HG E 1.2
Abstract	Mathematical modeling of genetic networks is key to understanding life at the most basic level. One of the challenges to the analysis and synthesis of such networks is that the cellular environment in which they function is abuzz with noise arising from the random nature of biochemical reactions at the molecular level. Cellular noise results in random fluctuations within individual living cells and is a source of variability among genetically identical populations. In this talk, we present a stochastic modeling paradigm for modeling genetic networks based on continuous-time discrete (infinite) state Markov models. We discuss some of the key computational methods for the simulation, approximation, and analysis of such models and how they can be used to enhance our fundamental understanding of stochastic biological phenomena. A quantitive understanding of the stochastic nature of gene expression leads naturally to the development of methods for feedback control of genetic circuits. We describe novel analytical and experimental work demonstrating the feasibility of such control. We end with adiscussion of some open computational problems in the field.

Stochastic gene expression: mathematical modeling, analysis, and controlread_more

HG E 1.2

30 November 2011
16:15-17:15

Dr. Claudia Schillings
Dept. Math., University of Trier, Germany

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	On the treatment of uncertainties in aerodynamic design
Speaker, Affiliation	Dr. Claudia Schillings, Dept. Math., University of Trier, Germany
Date, Time	30 November 2011, 16:15-17:15
Location	HG E 1.2
Abstract	Uncertainties pose problems for the reliability of numerical computations and their results in all technical contexts one can think of. They have the potential to render worthless even highly sophisticated numerical approaches, since their conclusions do not realize in practice due to unavoidable uncertainty in parameter values, initial and boundary conditions, geometry, etc. The proper treatment of these uncertainties within a numerical context is a very important challenge. In this talk, we discuss a novel approach towards aleatory uncertainties for the specific application of optimal aerodynamic design under uncertainties. An appropriate robust formulation of the underlying deterministic problem and efficient approximation techniques of the probability space are investigated. Finally, algorithmic approaches based on multiple-setpoint ideas in combination with one-shot methods are presented as well as numerical results.

On the treatment of uncertainties in aerodynamic designread_more

HG E 1.2

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

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09