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Die CSC Gruppe organisiert den diesjährigen GAMM ANLA Workshop, der im Max-Planck-Institut Magdeburg am 9.-10. Juli 2015 stattfinden wird.

Das Householder-Symposium XIX zu numerischer linearer Algebra fand vom 08. - 13. Juni 2014 in Spa (Belgien) statt. Die CSC-Gruppe war mit Vorträgen von Peter Benner, Martin Stoll und Patrick Kürschner, sowie einem Poster von Matthias Voigt vertreten.

From the beginning of August I will head the research group Numerical Linear Algebra for Dynamical Systems. More infos will appear on the new institute webpage due in December 2013

Mitglied des Wissenschaftlichen Komitees der ENUMATH 2013, 26.-30. August, 2013, EPFL Lausanne (Schweiz). Martin Stoll und Peter Benner sprechen in Minisymposia. H. Yücel, Y. Zhang und Martin Heß geben Sektionsvorträge.

Wir stellen verschiedene Techniken zum Inpainting in der Bildverarbeitung vor, die auf der Cahn-Hilliard Gleichung basieren. Weiterhin konstruieren wir schnelle Loeser, um diese Probleme effizient zu behandeln.

Niedrigrank Algorithmen fuer Optimierungsprobleme mit PDE-Nebenbedingungen werden vorgestellt.

Die CSC-Gruppe ist auf der diesjährigen Tagung Preconditioning in Oxford, UK. Jessica Bosch und Andrew Barker geben contributed Talks und Martin Stoll hält einen Plenarvortrag. Andrew verbringt die Woche vor der Konferenz in Zusammenarbeit mit John Pearson (Oxford) und Tyron Rees (RAL).

We consider the effcient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At the heart of this method lies the solution of large and sparse linear systems for which we propose the use of preconditioned Krylov subspace solvers using an effective Schur complement approximation. Numerical results illustrate the competitiveness of this approach.

PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs.

Peter Benner, Jens Saak und Martin Stoll nehmen am Kick of Meeting des GAMM Fachausschuss Computational Science and Engineering (CSE) in Garching am 17. und 18.September teil.

John Pearson (University of Oxford) will be coming to Magdeburg in September and October of 2012. He will be working with Martin Stoll on the fast solution of optimal control problems coming from the modelling of chemical processes. His research visit is kindly funded by the ESF OPTPDE program. This visit is part of an ongoing project between Oxford and Magdeburg.

This paper presents the results obtained within the SPP1253 project: Optimal Control-Based Feedback Stabilization in Multi-Field Flow Problems .

Vom 18. bis 21. Juni findet im spanischen Valencia die SIAM applied linear Algebra Konferenz 2012 statt. Die Arbeitsgruppe Computational Methods in Systems and Control Theory ist dort mit zwei organisierten Minisymposien (Jens Saak und Martin Stoll), fünf Vorträgen in Minisymposien (Peter Benner, Kapil Ahuja, Tobias Breiten, Jens Saak und Martin Stoll) und weiteren drei Sektionsvorträgen (Martin Hess, Patrick Kürschner und M. Sahadet Hossain) vertreten.

Nick Higham from the University of Manchester will be visiting the CSC group from the 25th of April. Nick will give a presentation as part of the MPI colloquium series joint with the Department of Mathematics colloquium series. The title of his presentation is Recent Progress in Matrix Functions and the talk will be given on Thursday, April 26, 2012 at 5 pm here at the MPI. Nick is the Richardson Professor of Applied Mathematics and an expert on many things in Numerical Analysis with a particular focus on Numerical Linear Algebra as well as Numerical Software. He is the vice president of SIAM, a fellow of the Royal Society and SIAM fellow.

Catherine Powell from the University of Manchester will be visiting the CSC group after Easter. She will give a presentation titled Efficient solvers for saddle point problems with random data on Tuesday the 10th of April at 2pm. Catherine is an expert on Uncertainty Quantification with a particular focus on computational fluid dynamics.

In this paper we consider a PDE-constrained optimization problem where an H1 regularization control term is introduced. We address both time-independent and time-dependent versions. We introduce bound constraints on the state, and show how these can be handled by a Moreau-Yosida penalty function. We propose Krylov solvers and preconditioners for the different problems and illustrate their performance with numerical examples.

In dieser Arbeit geht es um die numerische Umsetzung von Schiessverfahren für PDE-beschränkte Steuerungsprobleme.
Contact: Martin Stoll

Bart Vandereycken is visiting from EPFL from the 16th to the 20th of January. Bart will give a talk titled "Riemannian algorithms for rank-structured matrices and tensors" on Tuesday at 2pm. Please come along. Bart is the recipient of the 2011 Householder prize, which is awarded only every 3 years. He is an expert on optimization on manifolds and matrix equations.

Michael Saunders is visiting the CSC group from Stanford. He will give a presentation on Thursday at 2pm at the MPI titled "CG and MINRES: A tale of two solvers". Michael is an expert on numerical optimization and numerical linear algebra among other things. He is an ISI highly cited researcher in both mathematics and computer science. He will arrive on Wednesday and stay until Sunday.

John Pearson is visiting the CSC group from the 14th to the 18th of November. He is giving a seminar titled Preconditioned Iterative Methods for Optimal Control Problems on Thursday the 17th at 3pm. He will also be working with Martin Stoll on the fast solution of nonlinear optimal control problems.

In this article, we motivate, derive and test effective preconditioners to be used with the minres algorithm for solving a number of saddle point systems, which arise in PDE constrained optimization problems. We consider the distributed control problem involving the heat equation with two different functionals, and the Neumann boundary control problem involving Poisson equation and the heat equation. Crucial to the effectiveness of our preconditioners in each case is an effective approximation of the Schur complement of the matrix system. In each case, we state the problem being solved, propose the preconditioning approach, prove relevant eigenvalue bounds, and provide numerical results which demonstrate that our solvers are effective for a wide range of regularization parameter values, as well as mesh sizes and time-steps.

Fikriye Yilmaz from Gazi University in Ankara is visiting the CSC group. She is going to work with Martin Stoll on optimal control problems for PDEs and is giving a presentation in the CSC seminar on Wednesday at 11 am. The title for her talk is "All-at-once solution of optimal control for Burgers equation"

In this paper we describe the efficient solution of a PDE-constrained optimization problem subject to the time-periodic heat equation. We propose a space-time formulation for which we develop a monolithic solver. We present preconditioners well suited to approximate the Schur-complement of the saddle point system associated with the first order conditions. This means that in addition to a Richardson iteration based preconditioner we also introduce a preconditioner based on the tensor product structure of the PDE discretization, which allows the use of a FFT based preconditioner. We also consider additional bound constraints that can be treated using a semi-smooth Newton method. Moreover, we introduce robust preconditioners with respect to the regularization parameter. Numerical results will illustrate the competitiveness and flexibility of our approach.

Model reduction is a crucial and important technique in many applications such as chemical or mechanical engineering. Important contributions have been made over the last decades and today much of the research is devoted to developing techniques for generating reduced order models for parameter dependent problems. The Computational Methods in Systems and Control Theory group at the MPI Magdeburg and the RWTH Aachen (research groups of Martin Grepl and Karen Veroy-Grepl) are joining forces for a day, 5th of July 2011, to discuss the latest developments and state-of-the art methods to generate accurate and efficient reduced models for problems coming from a variety of applications. The workshop is going to be held in our big seminar room and we invite you to join us for the whole day or parts of it.

For more information see the workshop webpage or contact Martin Stoll (stollm@mpi-magdeburg.mpg.de).

Die Cahn-Hilliard Gleichung ist eine partielle Differentialgleichung 4. Ordnung, die in vielen Bereichen wie Materialwissenschaften, Geophysik und Chemie von grosser Bedeutung ist, da sie die numerische Simulation von Verfestigunsprozessen ermöglicht. Das Lösen von Cahn-Hilliard Gleichungen ist kompliziert, doch glücklicherweise wurden in den letzten Jahren Fortschritte erzielt, die sich dabei hauptsächlich auf das Formulieren der Cahn-Hilliard Gleichung als Optimierungsproblem mit partiellen Differentialgleichungen stützen. Grundlage dieser Verfahren sind nichtglatte Optimierungsverfahren. Die Kosten dieser Methoden werden im wesentlichen durch das Lösen der grossen, schwach-besetzten Newton-Systeme bestimmt. In vielen Fällen sind noch keine hinreichend effizienten Verfahren bekannt, die es erlauben, diesen Schritt drastisch zu beschleunigen. Das Thema der Arbeit soll sich deshalb der effizienten Lösung dieser Gleichungssysteme mittels iterativer, vorkonditionierter Löser widmen. Das Thema ist bereits vergeben. Ähnliche Themen können gern aufgestellt werden (am besten per Email an Martin Stoll (stollm@mpi...) wenden). Dieser News-Eintrag ist nicht mehr aktuell.

Peter Benner and Martin Stoll will participate in the Householder Symposium XVIII on Numerical Linear Algebra to be held on June 12-17, 2011, at the Granlibakken Conference Center & Lodge in Tahoe City, California. In his plenary lecture Peter Benner will talk about Rational Krylov Subspaces for Nonlinear Model Reduction. Martin Stoll will present a poster on Preconditioning for time-dependent optimal control problems.

The Householder Symposia are one of the longest running conference series in applied mathematics and attendance is by invitation only. The first meeting goes back to 1961 in Gatlinburg and therefore, the first meetings were called Gatlinburg Conference. The series was renamed in 1969 to honor Alston Householder for his groundbreaking contributions to Numerical Mathematics and is now held every 3 years.

The solution of time-dependent PDE-constrained optimization problems subject to unsteady flow equations presents a challenge to both algorithms and computers. In this paper we present an all-at-once approach where we solve for all time-steps of the discretized unsteady Stokes problem at once. The most desirable feature of this approach is that for all steps of an iterative scheme we only need approximate solutions of the discretized Stokes operator. This leads to an efficient scheme which exhibits mesh-independent behaviour.

Roland Herzog (TU Chemnitz) und Martin Stoll organisieren ein Minisymposium zum Thema Preconditioning in PDE-Constrained Optimization auf der SIAM Conference on Optimization, die vom 16.-19.05.2011 in Darmstadt stattfindet. Peter Benner trägt außerdem im Minisymposium Model Order Reduction Techniques in PDE Constrained Optimization über System-theoretic Methods for Model Reduction of Linear and Nonlinear Parabolic Systems vor.

David Knezevic (MIT) will be visiting us from the 9th to the 11th of May. David is an expert on the analysis and implementation of the Certified Reduced Basis Method. He is one of the developers of the finite element package libmesh. His PhD at Oxford was on the numerical simulation of dilute polymeric fluids. David gives a seminar talk on The Certified Reduced Basis Method: Real-time Simulation of Parametrized Systems (05/09/11, 15:30).

Melina Freitag (University of Bath) will be visiting us in the first week of May (02-06). Melina is an expert on eigenvalue problems and their numerical solution with a particular focus on preconditioned inverse iteration. She has also worked extensively on inverse problems in weather forecasting in collaboration with the Met Office. Melina gives an seminar talk on Preconditioned inverse iteration and shift-invert Arnoldi method (05/03/11, 15:00).

Meet me at the SIAM CSE meeting in Reno, where I will talk about fast solvers for time-dependent control problems.

Roland Herzog (TU Chemnitz) and I are pleased to have our minisymposium on "Preconditioning in PDE-Constrained Optimization" for the SIAM optimization meeting accepted.