Dozenten: | Günter Bärwolff, Rolf Dieter Grigorieff, Dietmar Hömberg, Volker Mehrmann, Reinhard Nabben, Caren Tischendorf, Fredi Tröltzsch, Petra Wittbold, Harry Yserentant |
Koordination: | Christian Mehl |
LV-Termine: | Di 16-18 in MA 313 oder n.V. |
Inhalt: | Vorträge von Mitarbeitern und Gästen zu aktuellen Forschungsthemen |
Vollständige Terminplanung: | ||||
Datum | Zeit | Raum | Vortragende(r) | Titel |
---|---|---|---|---|
Do 7.10.2004 | 16:15 | MA 313 | Prof. Dr. Raphael Loewy (Technion, Haifa, Israel) |
The minimum rank of a graph (Abstract) |
Mi 13.10.2004 | 13:00 | MA 313 | Dr. Jörg Liesen (TU Berlin) |
Konvergenz und numerisches Verhalten von Krylov-Raum-Verfahren (universitätsöffentlicher Habilitationsvortrag) |
Di 19.10.2004 | 16:15 | MA 313 | Dr. Olaf Schenk (Uni Basel, Schweiz) |
Symmetric Weighted Matchings and their Applications to Symmetric Indefinite Linear Systems (Abstract) |
Di 26.10.2004 | 16:15 | MA 313 | Dr. Daniel Kreßner (TU Berlin) |
Berlin's prospective contributions to LAPACK (Abstract) |
Di 2.11.2004 | 16:15 | MA 313 | Prof. Dr. Moshe Goldberg (Technion, Haifa, Israel) |
Stable Norms: From Theory to Applications and Back (Abstract) |
Di 9.11.2004 | 16:15 | MA 313 | Dr. François Courty (TU Berlin) |
Application of Optimization to PDE: from optimal shapes to optimal meshes (Abstract) |
Di 16.11.2004 | 16:15 | MA 001 | Dr. Cleve Moler (The MathWorks) |
Evolution of MATLAB (Talk within the scope of the 5th Colloquium of the DFG Research Center Matheon) (Abstract) |
Di 23.11.2004 | 16:15 | MA 313 | Prof. Dr. Frank Allgöwer (U. Stuttgart) |
Nonlinear Model Predictive Control: From Theory to Applications (Abstract) |
Mi 24.11.2004 | 16:15 | MA 313 | Prof. Dr. Valeria Simoncini (U. di Bologna, Italien) |
Structured Preconditioners for Saddle Point Problems (Abstract) |
Di 30.11.2004 | 16:15 | MA 313 | Prof. Dr. Volker Mehrmann (TU Berlin) |
A new algorithm to compute the Hamiltonian Schur form: The curse is lifted (Abstract) |
Mi 1.12.2004 | 16:15 | MA 313 | Luka Grubisic (Fernuniversität Hagen) |
Ritz value approximations for positive definite operators under realistic regularity assumptions (Abstract) |
Di 14.12.2004 | 16:15 | MA 313 | Dr. Alexander Mitin (TU Berlin) |
New methods for iterative calculation extreme eigenvalues of generalized symmetric eigenvalue problem with large matrices (Abstract) |
Mi 15.12.2004 | 16:15 | MA 313 | Dr. Kees Vuik (TU Delft, Niederlande) |
A parallel deflated Krylov solver for finite element problems (Abstract) |
Di 11.1.2005 | 16:15 | MA 313 | Prof. Dr. Sebastian Reich (Uni Potsdam) |
Partikelmethoden in der numerischen Wettervorhersage (Abstract) |
Di 18.1.2005 | 16:15 | H 1028 | Prof. Dr. Sergei Godunov (Novosibirsk, Russland) |
One dimensional matrix spectral portraits and their applications to Hamiltonian differential equations (Abstract) |
Mi 19.1.2005 | 16:15 | MA 313 | Dr. Noureddine Igbida (U. de Picardie, Amiens, Frankreich) |
On quasilinear elliptic problems with Neumann boundary condition (Abstract) |
Do 20.1.2005 | 11:15 | MA 313 | Prof. Dr. Sergei Godunov (Novosibirsk, Russland) |
Thermodynamics and equations of mathematical physics (Abstract) |
Di 25.1.2005 | 16:15 | MA 313 | Prof. Dr. Peter Eberhard (Uni Stuttgart) |
Contact Mechanics - Looking at the Two Extremes (Abstract) |
Mi 26.1.2005 | 16:15 | MA 313 | Dr. Thomas Kaminski (FastOpt GbR Hamburg) |
Automatic Differentiation of Navier-Stokes Solvers (Abstract) |
Di 1.2.2005 | 16:15 | MA 313 | Prof. Dr. Günter Bärwolff (TU Berlin) |
Some Experiences with the iterative solution of steady and unsteady Navier-Stokes equation (Abstract) |
Mo 7.2.2005 | 16:15 | MA 313 | Prof. Dr. Eli Turkel
(Tel Aviv University, Israel) |
High order accurate methods for Maxwell's equations with discontinuous coefficients (Abstract) |
Di 8.2.2005 | 16:15 | MA 313 | Dr. Karsten Eppler
(WIAS Berlin) |
Shape optimization for elliptic pde: The shape Hessian provides a proper preconditioning (Abstract) |
Di 1.3.2005 | 16:15 | MA 313 | Dr. Bor Plestenjak (Ljubljana, Slowenien) |
Multiparameter eigenvalue problems (Abstract) |
Mi 2.3.2005 | 15:15 | MA 313 | Prof. Dr. Daniel Hershkowitz (Technion, Haifa, Israel) |
Nonnegativity and Stability (Abstract) |
Mi 9.3.2005 | 16:15 | MA 313 | Prof. Dr. Daniel Szyld (Temple U, Philadelphia, PA, USA) |
Asyncronous power iterations for Markov chains and Google matrices (Abstract) |
Interessenten sind herzlich eingeladen!
Rückblick:
Abstracts zu den Vorträgen:
Abstract:
The benefit of nonsymmetric reorderings based on nonsymmetric maximum
weighted matchings for the factorization and preconditioning of nonsymmetric
linear systems is well-known by now and an important ingredient of direct
and preconditioned iterative linear solvers.
This talk will discuss the application of symmetric weighted matchings to
general symmetric indefinite systems. In the first part of the talk we will
demonstrate the effectiveness of various new pivoting factorization methods
[1] for solving sparse symmetric indefinite systems. We will demonstrate
numerical stability and accuracy of the algorithms and also show that a high
performance implementation is feasible.
In the second part of the talk we present symmetric preconditioning methods
for symmetric indefinite matrices based on these maximum weighted matchings
[2]. The emerging structure is exploited in a modified incomplete LDL^T
factorization scheme that uses 1x1 and 2x2 diagonal block pivoting. The
resulting symmetric incomplete indefinite factorizations are used as
preconditioners for Krylov-subspace linear solvers e.g SQMR. The objective
of the reordering is to maximize the diagonal element or the elements
directly alongside the diagonal. For a large class of matrices, such
reorderings allow the incomplete factorization method to choose a
numerically satisfying 1x1 or a 2x2 pivot.
We show the effectiveness of the resulting methods on a number of real world
symmetric indefinite linear systems ranging from augmented interior-point
optimizations matrices, to general symmetric saddle point problems and the
Anderson matrix eigenvalue problem, where it provides favorable performance
with a set of standard parameters.
[1] O.Schenk and K.Gärtner, On fast factorization pivoting methods for
sparse symmetric indefinite systems, Technical Report CS-2004-004,
Department of Computer Science, University of Basel. Submitted.
[2] M.Hagemann and O.Schenk, Weighted Matchings for the Preconditioning of
Symmetric Indefinite Linear Systems, Technical Report CS-2004-005,
Department of Computer Science, University of Basel. Submitted.
Abstract:
LAPACK is a comprehensive software library for solving linear systems and
eigenvalue problems. It provides well-tested, open source, reviewed code
implementing trusted algorithms that guarantee reliability, efficiency and
accuracy. LAPACK is working in the background of many other well-known
mathematical software packages such as Matlab or Mathematica.
The developers of LAPACK currently plan a major revision and extension,
and this talk describes software developed in the numerical analysis group
at TU Berlin that has been proposed to get included. These contributions
are as follows:
Abstract:
We show how MATLAB has evolved over the last 20 years from a simple matrix
calculator to a powerful technical computing environment. We demonstrate several
examples of MATLAB applications. We conclude with a few comments about possible
future developments.
Cleve Moler is the original author of MATLAB and one of the founders of the MathWorks. He is currently chairman and chief scientist of the company.
Abstract:
In the past decade model predictive control (MPC), also referred
to as receding horizon control, or moving horizon control, has
become a preferred control strategy for a large number of
industrial processes. The main reasons for this popularity include
the ability to explicitly handle constraints and to consider
multivariable processes with potentially many manipulated and
controlled variables. In this presentation we will give an overview
over the area of model predictive control with special emphasis on
nonlinear model predictive control. After a brief discussion of the history
and impact of MPC we will discuss recent results regarding system
theoretic properties like stability, robustness, output feedback and
performance of the closed loop. With a number of applications we will
demonstrate that by using specially tailored optimization methods
even large problems, having hundreds of states, can be controlled
efficiently using NMPC methods.
Abstract:
Saddle point linear systems arise in a variety of
applications. Due to the high indefiniteness of
the coefficient matrix, preconditioning is required to
speed up convergence. In most cases,
the structure of the matrix and the functional properties
of the associated operators can be conveniently
exploited to devise an effective preconditioner.
The quality of the preconditioner can be measured in terms
of optimality with respect to the given continuous problem
parameters, as well as in terms of computational speed.
In this talk we review some recent results on structured
preconditioners such as block diagonal, indefinite and
block triangular preconditioner. In addition, we
present a new algebraic framework that allows to analyze
a large class of computationally effective
preconditioners.
Abstract:
We show how to solve a long-standing open problem in numerical linear
algebra called van Loan's curse. We derive a new method for
computing the Hamiltonian Schur form of a Hamiltonian matrix. The
proposed method is numerically strongly backwards stable and of
complexity n^3. We demonstrate the properties of the new method
via several numerical examples.
Abstract:
We will present an abstract framework to obtain
the eigenvalue and eigenvector estimates for
the self adjoint operator defined by a positive
definite form in a Hilbert space. The estimate has a
form of a Temple-Kato like inequality. A Temple-Kato
like estimate is a combination of a bound on the part
of the spectrum one is not interested in and a measure
of the residual of the considered Ritz-vectors. The
obtained estimates involve "relative" quantities and
test vectors that are anywhere in the form (weak) domain
of the operator are allowed (think of Laplace operator
and linear finite elements).
The new estimates will be considered in the context of
finite element approximation methods for positive
definite operators. An abstract condition that is
needed to formulate a finite dimensional procedure
to asses the measure of the residual will be stated.
In the case of the Laplace (divergence form) operator
this condition essentially depends on the measure of
the oscillation of the considered Ritz-vector(s).
Several computational examples will be worked out in
detail.
Abstract:
New iterative methods derived by using Lagrange variational
approach will
be presented. A correction vector in this method is defined from a
solution of a system of linear equations. To simplify this system a star
approximation is introduced. This approximation results in numerical
algorithms with performances from the full to diagonal methods. Numerical
algorithms of new methods as well those of Davidson, Jacobi-Davidson, and
Newton methods with star approximation will be discussed. Numerical
examples that show performances of different methods will be presented.
Abstract:
It is well known that the convergence rate of the Conjugate Gradient method
is bounded as a function of the condition number of the system matrix to
which it is applied. If the condition number is large it is advisable to
solve,
instead, a preconditioned system. With respect to the known preconditioners at
least two problems remain:
Abstract:
Der Kern einer numerischen Wettervorhersage besteht aus
der Lösung der 3-dimensionalen Euler Gleichungen der Strömungsmechanik
auf der Erdkugel. Verlässliche Vorhersagen erfordern sowohl eine genaue
Reproduktion
von Erhaltungsgrössen, wie der Zirkulation und potentiellen
Wirbelfeldstärke, als
auch die Berücksichtigung der immanenten Zeit- und Längenskalen, die
sich
in verschiedenen Balance-Zuständen äußern. In dem Vortrag werde ich
Partikelmethoden als eine neue Alternative zu klassischen
gitterbasierten
Verfahren darstellen und speziellen Gesichtspunkte bzgl. der oben
genannten
Anforderung aus der Wettervorhersage diskutieren.
Abstract:
Symplectic matrices arise in a variety of applications of
linear Hamiltonian differential equations.
We consider a circular spectral dichotomy problem for symplectic matrices.
This problem is closely related to generalized Lyapunov equations.
An integral representation for the solutions of such equations can be used to
compute a matrix spectral portrait that gives a useful information on the
eigenvalue distribution in the complex plane. We present a numerical algorithm
for solving Lyapunov equations that also provides the spectral projections
onto the invariant subspaces of the matrix corresponding to the eigenvalues
inside and outside the circle.
Abstract:
Phenomenological thermodynamics is based on the postulate of
nonexistence of perpetual motion machines of the second kind.
As such a postulate for equations of continuum mechanics
one can consider a hypothesis of correctness of the Cauchy problem.
But in this case not for all solutions of nonlinear hyperbolic equations
the conservation laws are fulfilled. In this talk we consider some particular
models of continuum mechanics and describe different variants
of dissipative processes.
Abstract:
After some introductory remarks about the University of Stuttgart
and an overview about the Institute B of Mechanics and its current
research projects, some aspects of contact mechanics will be
described. On the one end of the formulations is the consideration
of deformable bodies with sometimes complicated shapes using the
Finite-Element method. Due to the complexity of the description
and the high computation times, we have to restrict ourselves to
few bodies and short simulation times. The other end of possible
contact formulations is in the consideration of granular media.
Here we have many bodies, where many bodies often means more than
100 000 particles in a system, but only simple geometries and hardly
any deformations. Obviously, this demands sophisticated algorithms
for neighborhood search and contact administration.
In the talk many examples will be shown and some effects and
critical issues will be discussed.
Abstract:
Automatic Differentiation (AD) is a technique to evaluate derivatives
of functions that are defined by numerical programmes.
In contrast to traditional derivative approximation by divided
differences,
AD employs the chain rule to provide accurate derivatives.
Basic concepts of AD such as forward and reverse modes are explained
and illustrated using simple examples.
The AD tools TAF and TAC++ are introduced,
and a number of large-scale applications for sensitivity studies,
state/parameter estimation, and uncertainty propagation are presented.
The selected examples focus on codes for
the simulation of the global oceanic and atmospheric circulation,
aerodynamic flows as well as the terrestrial biosphere.
Integrating an AD tool in such a modelling system
allows for quick updates of the derivative code after modifications of
the underlying model.
Abstract:
Based on a fv-discretization the Navier-Stokes equation will be solved by
an implicit time integration scheme (unsteady case) and a Newton method (steady case).
Experiences and consequences of different approximations of the convective terms and
the automatic evaluation of the Jacobian for the Newton method
using AD-tools will be presented.
Abstract:
Maxwell's equations contain a dielectric coefficient
that describes the particular media. For homogenous
materials the dielectric coefficient is constant within
the media. However, there is a jump in this coefficient
between differing media. This discontinuity frequently
significantly reduces the order of accuracy of the scheme.
We present an analysis and implementation of high (fourth) order
approximations of Maxwell equations, when there is
an interface between two media, and so the dielectric coefficient
is discontinuous. We consider not only the order of accuracy but
also the preservation of the zero divergence of the appropriate
electromagnetic fields. We analyze the one dimensional
system in frequency space.
Abstract:
The talk deals with algorithmic aspects of the numerical solution for elliptic
shape optimization problems. After introducing the shape problem and some basics
from the underlying shape calculus, the ``lack of regularity problem'' is
explained using the torsional rigidity of an elastic bar and the perimeter of a
domain as illustrational examples. The relation to properties of the shape Hessian
and to a proper preconditioning of related finite dimensional auxiliary
optimization problems is discussed as well. As a byproduct, further results
are presented about the numerical solution in 2d and 3d of the exterior
electromagnetic shaping problem, the electrical impedance tomography problem
and the free boundary problem like in electrochemical processing.
Abstract:
A complex square matrix A is said to be stable if the spectrum of A lies
in the open left or right half-plane. This, as well as other related types
of matrix stability, play an important role in various applications. As
such, matrix stability has been intensively investigated in the past two
centuries. A plausible way for finding necessary and/or sufficient
conditions for matrix stability is to examine classes of matrices that are
known to be stable, and to identify common properties of these classes.
Indeed, some well known classes of stable matrices share properties
associated with nonnegativity, such as positivity of the principal minors
(P-matrices) and weak sign symmetry. It was conjectured by Carlson that
the combination P-matrix + weak sign symmetry implies stability. This
conjecture was recently disproved by Holtz. However, if we replace the
weak sign symmetry by the stronger sign symmetry property, then it was
shown already by Carlson that P-matrix + sign symmetry implies stability.
The talk will review various results that relate positivity of the
principal minors, weak sign symmetry, sign symmetry and stability.
Abstract:
We report on our efforts to use parallel asynchronous iterative methods
for large Markov chains of the type used by web searches such as
the PageRank algorithm reportedly used by Google.
It is shown that the well developed theory of asynchronous
iterations can be used in this special case of parallel asynchronous
power method.
Numerical results illustrate the potential of these methods.
(joint work with Efstratios Gallopoulos and Giorgos Kollias, University of Patras, Greece)
Impressum | Christian Mehl 7.4.2005 |