Numerik-Oberseminar WS 2003/04

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

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:


Abstracts zu den Vorträgen:

Prof. Dr. Rainer Tichatschke, Universität Trier
Generalized Proximal-like Methods for Variational Inequalities
Di 11.11.2003, 16:15 Uhr in MA 313

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.

Dr. Shreemayee Bora, TU Berlin
The Effect of Linear Perturbation on the Spectra of Matrices
Di 18.11.2003, 16:15 Uhr in MA 313

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.

Dr. Martijn Anthonissen, TU Eindhoven, Niederlande
Adaptive Multilevel Grid Refinement based on Local Defect Correction with Application to Combustion
Di 25.11.2003, 16:15 Uhr in MA 313

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.

Dr. René Pinnau, TU Darmstadt
Neue mathematische Methoden im Halbleiterdesign
Mi 3.12.2003, 10:15 Uhr in MA 313

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.

Dr. Robert Shorten, National University of Ireland, Maynooth, Ireland
On common quadratic Lyapunov functions
Di 18.12.2003, 16:15 Uhr in MA 313

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.

Dr. Achim Basermann, (NEC Europe Ltd.)
Parallel Flexible Iterative Solvers with Distributed Schur Complement Preconditioning for Equation Systems from Circuit Simulation
Di 20.1.2004, 16:15 Uhr in MA 313

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.

Prof. Dr. Ralph Byers, University of Kansas, Lawrence, KS, USA (on sabbatical at TU Berlin)
Agressive Deflation and Questioning Conventional Wisdom in the QR algorithm
Di 3.2.2004, 16:15 Uhr in MA 313

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.

Prof. Dr. Rafikul Alam, Guwahati, India and Manchester, UK
A simple guaranteed method to compute the distance to the nearest defective matrices
Do 5.2.2004, 10:15 Uhr in MA 313

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).

Dr. Michael Karow, TU Berlin
Geometry of spectral value sets
Do 5.2.2004, 10:15 Uhr in MA 313

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.

  1. The general framework (the connection between spectral value sets, stability radii and μ-functions)
  2. Real perturbations, real perturbation values and hermitian-symmetric inequalities
  3. Real pseudospectra of normal matrices
  4. Pseudospectra of upper triangular matrices and an open problem
  5. Root sets of uncertain polynomials
  6. Spectral value sets for composite systems and the eigenvalue inclusion theorem of Brualdi
  7. Eigenvalue condition numbers for structured perturbations
  8. An almost trivial remark on the distance of a matrix pair (A,B) to the set of uncontrollable pairs

Prof. Dr. Axel Ruhe, KTH Stockholm, Sweden
Variants of the rational Krylov algorithm for eigenproblems
Do 18.3.2004, 10:00 Uhr in MA 313

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