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Kolloquium der Arbeitsgruppe Modellierung • Numerik • Differentialgleichungen

Wintersemester 2014/15
Verantwortliche Dozenten:
Alle Professoren der
Arbeitsgruppe Modellierung • Numerik • Differentialgleichungen
Koordination:
Dr. Christian Schröder, Dr. Hans-Christian Kreusler
Termine:
Di 16-18 Uhr in MA 313 und nach Vereinbarung
Inhalt:
Vorträge von Gästen und Mitarbeitern zu aktuellen Forschungsthemen

Beschreibung

Das Kolloquium der Arbeitsgruppe "Modellierung, Numerik, Differentialgleichungen" im Institut der Mathematik ist ein Kolloquium klassischer Art. Es wird also von einem breiten Kreis der Professoren und Mitarbeiter aus allen zugehörigen Lehrstühlen, insbesondere Angewandte Funktionalanalysis, Numerische Lineare Algebra, und Partielle Differentialgleichungen, besucht. Auch Studierende nach dem Bachelorabschluss zählen schon zu den Teilnehmern unseres Kolloquiums.

Aus diesen Gründen freuen wir uns insbesondere über Vorträge, die auf einen nicht spezialisierten Hörerkreis zugeschnitten sind und auch von Studierenden nach dem Bachelorabschuss bereits mit Profit gehört werden können.

Terminplanung / schedule
Datum
date
Zeit
time
Raum
room
Vortragende(r)
speaker
Titel
title
Einladender
invited by
Di 28.10.14
16:15
MA 313
Arnd Meyer (TU Chemnitz)
Coordinate free formulations of the classic shell models (Abstract)
F. Tröltzsch
Di 4.11.14
16:15
MA 313
Andreas Prohl
(U Tübingen) 
Numerical Analysis of the stochastic cubic Schroedinger equation (Abstract)
E. Emmrich
Di 18.11.14
16:15
MA 313
Michael L. Overton
(Courant Institute, NYU)
Fast Approximation of the H_infinity Norm via Optimization over Spectral Value Sets (Abstract)
V. Mehrmann
Di 9.12.14
t.b.a.
t.b.a.
Sina Ober-Blöbaum
(U Paderborn, FU Berlin)
to be announced
rooms 313, 315 not available
V. Mehrmann
Di 16.12.14
16:15
MA 313
Aneta Wróblewska-Kamińska
(Polish Academy of Sciencees)
to be announced
E. Emmrich
Mi 17.12.14
Sjoerd Verduyn Lunel
(U Utrecht)
to be announced
V. Mehrmann
Di 20.01.15
16:15
MA 313
Peter Casazza
(U of Missouri)
to be announced
G. Kutyniok
Di 27.01.15
16:15
MA 313
Stefan Ulbrich
to be announced
F. Tröltzsch
Di 3.02.15
16:15
MA 313
Christian Engström
(Umeå U, Sweden)
Rational operator functions and applications to photonic crystals (Abstrakt)
K. Schmidt

Abstracts zu den Vorträgen:

Arnd Meyer (TU Chemnitz)

Coordinate free formulations of the classic shell models
Dienstag, den 28.10.2014, 16.15 Uhr in MA 313
Abstract:

We consider the classic linear shell equations of Koiter and Naghdi. These are given and investigated by using the tensor coefficients of the approximate linear strain tensors leading to rather complicate differential terms strongly dependent on the parametrization of the shell mid-surface. If these tensors are completely written with their tensor bases, we are able to find a coordinate free meaning of these complicate terms based on the metric and curvature tensor of the mid-surface and on the surface gradient operator. This notation has low effects on well established FE-calculations of shell deformations, but can be useful in new developments in discrete differential geometry.

Preceding this talk there will be coffee, tea, and biscuits at 15:45 in room MA 315 - everybody's welcome.

Andreas Prohl (U Tübingen)

Numerical Analysis of the stochastic cubic Schroedinger equation
Dienstag, den 4.11.2014, 16.15 Uhr in MA 313
Abstract:

In der vorgestellten stochastischen nichtlinearen Schroedingergleichung wechselwirken dispersive, nichtlineare, und Rauscheffekte, was die Konstruktion einer konvergenten numerischen Diskretisierung nichttrivial macht. Im Vortrag fasse ich aktuelle Resultate zu diesem Thema zusammen und zeige Probleme auf, die im Vergleich zur Numerik der deterministischen Schroedingergleichung zu loesen sind, um schliesslich ein optimal konvergentes Verfahren zu konstruieren. Ein wesentliches Hilfsmittel hierfür ist eine gleichmaessige Schranke fuer den Hamiltonian der Diskretisierung. Die vorgestellten Resultate sind einer aktuellen Arbeit mit C. Chen und J. Hong (Chinese Academy of Sciences, Beijing) entnommen.

Preceding this talk there will be coffee, tea, and biscuits at 15:45 in room MA 315 - everybody's welcome.

Michael L. Overton (Courant Institute, NYU)

Nonsmooth Optimization and Crouzeix's Conjecture
Dienstag, den 18.11.2014, 16.15 Uhr in MA 313
Abstract:

The H_infinity norm of a transfer matrix function for a continuous-time control system is the maximum of the norm of the transfer matrix on the imaginary axis, or equivalently, the reciprocal of the largest value of epsilon such that the associated epsilon-spectral value set is contained in the left half-plane. We start by defining spectral value sets and discussing some of their fundamental properties, including the intricate relationship between the singular vectors of the transfer matrix and the eigenvectors of the corresponding perturbed system matrix. We then introduce an iterative method for approximating the epsilon-spectral value set abscissa (the maximum of the real part of the points in the set), characterizing the fixed points of the iteration, and explain how the procedure can be combined with a Newton-bisection outer iteration to approximate the H_infinity norm. We then explain why this idealized algorithm sometimes breaks down instead introduce a method called hybrid expansion-contraction to address this deficiency. Under reasonable assumptions, the new algorithm finds locally maximal values of the norm of the transfer matrix on the imaginary axis and although these are only lower bounds on the H_infinity norm, it typically finds good approximations in cases where we can test this. It is much faster than the standard Boyd-Balakrishnan-Bruinsma-Steinbuch algorithm to compute the H_infinity norm when the system matrices are large and sparse. The main work required by the algorithm is the computation of the rightmost eigenvalues of a sequence of matrices that are rank-one perturbations of a sparse matrix. Joint work with Nicola Guglielmi (L’Aquila), Mert Gürbüzbalaban (MIT) and Tim Mitchell (NYU).

Preceding this talk there will be coffee, tea, and biscuits at 15:45 in room MA 315 - everybody's welcome.

Christian Engström (Umeå U, Sweden)

Rational operator functions and applications to photonic crystals
Dienstag, den 3.02.2015, 16.15 Uhr in MA 313
Abstract

Operator functions with a nonlinear dependence of a spectral parameter describe a large number of processes in science. In particular, when dispersion is present the operator function is nonlinear. This nonlinearity is rational in several areas of physics and here we study functions that have applications in electromagnetic field theory. We establish variational principles and provide two-sided estimates for all the eigenvalues of a class of rational operator functions. Moreover, we apply the new theory to an unbounded operator function used to model photonic crystals. These nano-sized structures can be used to control the flow of light and are for example used in integrated optics. The operator function is discretised with a high order finite element method and several examples illustrate the general theory. In particular, we show the connection between eigenvalue accumulation at the poles and a numerical approximation of the corresponding singular sequence. This talk is based on a joint work with Heinz Langer and Christiane Tretter.

Preceding this talk there will be coffee, tea, and biscuits at 15:45 in room MA 315 - everybody's welcome.

Zusatzinformationen / Extras