Dozenten: | Volker Mehrmann, Fredi Tröltzsch |
Koordination: | Christian Mehl |
LV-Termine: | Di 16-18 in MA 313 oder n.V. |
Inhalt: | Vorträge von Mitarbeitern und Gästen zu aktuellen Forschungsthemen |
Terminplanung: | ||||
Datum | Zeit | Raum | Vortragende(r) | Titel |
---|---|---|---|---|
Di 28.10.2003 | 16:15 | MA 313 | Dr. Luca Amodei (U. Paul Sabatier, Toulouse, Frankreich) |
Oblique projection methods for large scale algebraic Riccati equation |
Di 4.11.2003 | 16:15 | MA 313 | Dr. Matthias Bollhöfer (TU Berlin) |
Invers-Basierte algebraische Mehrgitter- und Zerlegungstechniken zur Vorkonditionierung linearer Gleichungen (universitätsöffentlicher Habilitationsvortrag) |
Di 11.11.2003 | 16:15 | MA 313 | Prof. Dr. Rainer Tichatschke (Uni Trier) |
Generalized Proximal-like Methods for Variational Inequalities (Abstract) |
Di 18.11.2003 | 16:15 | MA 313 | Dr. Shreemayee Bora (TU Berlin) |
The Effect of Linear Perturbation on the Spectra of Matrices (Abstract) |
Di 25.11.2003 | 16:15 | MA 313 | Dr. Martijn Anthonissen (TU Eindhoven, Niederlande) |
Adaptive Multilevel Grid Refinement based on Local Defect Correction with Application to Combustion (Abstract) |
Mi 3.12.2003 | 10:15 | MA 313 | Dr. René Pinnau (TU Darmstadt) |
Neue mathematische Methoden im Halbleiterdesign (Abstract) |
Di 9.12.2003 | 16:15 | MA 313 | Prof. Dr. Khakim Ikramov (U. Moskau, Russland) |
Malyshev's formula and its extension (Abstract) |
Do 18.12.2003 | 16:15 | MA 313 | Dr. Robert Shorten (National U of Ireland, Maynooth) |
On common quadratic Lyapunov functions (Abstract) |
Do 8.1.2004 | 10:15 | MA 313 |
Prof. Dr. Vasile Sima (Nation. Res. Inst. for Informatics, Bucharest, Romania) | Control Software |
Di 20.1.2004 | 16:15 | MA 313 | Dr. Achim Basermann (NEC Europe Ltd.) |
Parallel Flexible Iterative Solvers with Distributed Schur Complement Preconditioning for Equation Systems from Circuit Simulation (Abstract) |
Di 27.1.2004 | 16:15 | MA 313 | Dr. Alfio Borzi (Uni Graz, Österreich) |
On the multigrid solution of constrained elliptic optimal control problems |
Mi 28.1.2004 | 10:15 | MA 313 | Dr. Christian Mehl (TU Berlin) |
Das verallgemeinerte indefinite Hermitesche Eigenwertproblem (universitätsöffentlicher Habilitationsvortrag) |
Di 3.2.2004 | 16:15 | MA 313 | Prof. Dr. Ralph
Byers (U. of Kansas, Lawrence, KS, USA) |
Agressive Deflation and Questioning Conventional Wisdom in the QR algorithm (Abstract) |
Do 5.2.2004 | 10:15 | MA 313 | Prof. Dr. Rafikul Alam (Guwahati, India and Manchester, UK) |
A simple guaranteed method to compute the distance to the nearest defective matrices (Abstract) |
Di 10.2.2004 | 16:15 | MA 313 | Dr. Michael Karow (TU Berlin) |
Geometry of spectral value sets (Abstract) |
Di 17.2.2004 | 16:15 | MA 313 | Prof. Dr. Michael
Overton (New York U., NY, USA) |
Optimizing Matrix Stability and Controllability (Talk within the scope of the 3rd Colloquium of the DFG Research Center Mathematics for key technologies) (Abstract) |
Do 18.3.2004 | 13:00 | MA 313 | Prof. Dr. Axel Ruhe (KTH, Stockholm, Schweden) |
Variants of the rational Krylov algorithm for eigenproblems (Abstract) |
Interessenten sind herzlich eingeladen!
Weitere Vorträge siehe auch:
Rückblick:
Abstracts zu den Vorträgen:
Abstract:
A general framework for analyzing convergence of proximal-like
methods for variational inequalities with set-valued maximal
monotone operators is developed, including discretization of the space and data
approximation (operators and feasible sets).
This approach is devoted to
methods coupling successive approximation of the variational
inequality with the proximal point algorithm as well as to related
methods using regularization on a subspace and/or weak
regularization.
The convergence results are proved under mild assumptions with
respect to the original variational inequality and admit, in
particular, the use of the ε-enlargement of the operator
and the use of non-quadratic regularization functionals. The
latter permit us to deal with methods having an interior point
effect.
Taking into
account the specific structure of non-differentiable terms in
energy functionals of several problems in mathematical physics, we
analyze the construction of
ε-enlargements for some special operators.
The connection between proximal point method and the Auxiliary problem
principle will be issued, which leads to several splitting algorithms.
Abstract:
Given a matrix A of size n, and a fixed perturbation matrix E, the
effect of linear perturbations A+tE as t varies over the complex numbers,
on certain spectral properties of A is analyzed. The special effect of the
matrix E on these properties is exhibited. A geometric framework is
developed for spectral analysis of A+tE to achieve this goal.
It is shown that this framework leads to a better understanding of the
sensitivity of eigenvalues and spectral decompositions of A. Finally, a
set of necessary and sufficient conditions for the spectrum of A to be
equal to the spectrum of A+tE for all complex numbers t is provided.
Abstract:
Local defect correction (LDC) is an iterative method for solving elliptic boundary value
problems on composite grids based on simple data structures and simple
discretization stencils on uniform or tensor-product grids.
In the LDC method, the discretization on the
composite grid is based on a combination of standard discretizations
on several uniform grids with different grid sizes that cover different parts
of the domain.
LDC converges very fast; in practice, one or two iterations are sufficient
to reach the fixed point. The convergence behavior of the method has been
analyzed for a model problem, Poisson's
equation on the unit square with standard five-point
finite difference discretizations on uniform grids.
The standard LDC method has been combined with multi-level adaptive gridding
and domain decomposition. The domain decomposition algorithm
provides a natural way for parallelization and enables the usage of many small
tensor-product grids rather than a single large unstructured grid.
It has been shown that this may greatly reduce memory usage.
The properties above will be illustrated by applying the
adaptive multi-level LDC algorithm with domain decomposition
to a combustion problem. The mathematical model is a system of
nonlinear partial differential equations with
strongly nonlinear chemical source terms. The solutions of the
system have large gradients in a very small part of the domain and are
smooth elsewhere.
Abstract:
Modernes Halbleiterdesign stellt im wesentlichen drei Ansprüche an den angewandten
Mathematiker: Die Entwicklung von geeigneten Modellen zur Beschreibung der
physikalischen Effekte, die Bereitstellung von numerischen Verfahren zur Simulation der
Modellgleichungen und neuerdings die Umsetzung von Optimierungsstrategien zur schnellen
Berechnung von optimalen Designvorschlägen. In diesem Vortrag sollen die ersten
beiden Punkte anhand des Quanten Drift Diffusionsmodells erläutert werden. Es werden
insbesondere geeignete Zeit- und Ortsdiskretisierungen vorgestellt. Den dritten Punkt
betreffend wird ein neuer Optimierungsalgorithmus präsentiert, der es z.B. erlaubt das
optimale Design eines MESFET Bauteils mit äußerst geringem Aufwand zu berechnen.
Abstract:
Recent research on switched and hybrid systems has
resulted in a renewed interest in determining
conditions for the existence of a common quadratic
Lyapunov function for a finite number
of stable LTI systems. While efficient numerical
solutions to this problem have existed for some time,
compact analytical conditions for determining
whether or not such a function exists for
a finite number of matrices have yet to be
obtained. In this talk we present a geometric approach to
this problem. By making one simplifying assumption
we obtain a compact time-domain condition for the
existence of such a function for a pair of
matrices.
Our conditions also relate the existence of such a function
to the stability boundary of the underlying
switched linear system (thereby indicating that requiring
the existence of a such a function does not, in a
certain sense, lead to overly conservative stability conditions).
We show that classical Lyapunov results can be
obtained using our framework. In particular, we obtain
simple time-domain versions of the SISO
Kalman-Yacubovich-Popov lemma, the Circle Criterion, and stability
multiplier criteria. Finally, we indicate how our
approach can be used to analyse n-tuples of LTI systems
and present preliminary results on the existence of
common non-quadratic
Lyapunov functions of a certain
form.
Abstract:
For the solution of sparse linear systems from circuit simulation,
parallel flexible iterative methods with distributed Schur complement
preconditioning are presented. The parallel efficiency of the solvers is
increased by exploitation of parallel graph partitioning methods. The costs
of local, incomplete LU decompositions are decreased by fill-in reducing
reordering methods of the matrix. The efficiency of the parallel solvers is
demonstrated for real circuit simulation runs with NEC's circuit simulator
MUSASI.
Abstract:
Aggressive early deflation is a QR algorithm deflation
strategy that takes advantage of matrix perturbations
outside of the subdiagonal entries of the Hessenberg QR
iterate. It identifies and deflates converged eigenvalues
long before the classic small-subdiagonal strategy would.
The small-bulge multi-shift QR sweep with aggressive early
deflation maintains a high rate of execution of floating
point operations while significantly reducing the number
of operations required. We will discuss variations on
aggressive early deflation and revisit the question of
how best to choose shifts and where to expect deflations.
Abstract:
Let A be a simple matrix and d(A) be the distance of A from the set of defective
matrices. The determination of d(A) and a defective matrix A' such that
||A-A'|| = d(A) is widely known as Wilkinson's problem. We characterize the
nearest defective matrices, analyze their structure and describe a simple guaranteed way to compute
d(A).
Abstract:
The talk is a synopsis of my PhD thesis on spectral value sets.
These sets, also called structured pseudospectra, are unions
of spectra of perturbed matrices of the form A -> A+BDC, where
A,B and C are fixed matrices and the matrix D an element of a
given class of matrices (perturbation class). The content of
the talk is the following.
Abstract:
Rational Krylov is a development of the shifted and inverted
Arnoldi algorithm where several shifts (poles) are used in one
run. Two variants will be described. The first one transforms the
matrix pencil into a pencil of two Hessenberg matrices, the second
gives a new Arnoldi factorization each time the shift is moved. The
first is a natural alternative for Model reduction, while the second is
used to solve an eigenvalue problem that is nonlinear in the
eigenvalue parameter.
Results, taken from the thesis of Patrik Hager, are reported for
test examples coming from finite element approximations modelling
viscously damped vibrating structures.
Impressum | Christian Mehl 15.3.2004 |