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Research Group Leader (see New Webpage!) Dr. Martin Stoll

News Archive

Martin's News: New web page

August 1st, 2017
Please see my new web page for updated information.

Events: Workshop and meeting of GAMM activity group "Applied and Numerical Linear Algebra"

July 9th, 2015
The CSC research group organizes the annual GAMM ANLA workshop which takes place at the Max Planck Institute Magdeburg from 9.-10. July 2015

Events: Householder Symposium XIX

June 6th, 2014
The Householder Symposium XIX on numerical linear algebra took place in Spa (Belgium) from 06/08 - 06/13. The CSC group was represented by talks of Peter Benner, Martin Stoll and Patrick K├╝rschner as well as by a poster of Matthias Voigt.

Martin's News: New Research Group

August 1st, 2013
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

Events: European Numerical Mathematics and Advanced Applications (ENUMATH) conference 2013

July 26th, 2013
Peter Benner is member of the scientific committee of the ENUMATH 2013, August 26-30 2013, EPFL Lausanne (Switzerland). Martin Stoll, Peter Benner will give minisymposia, and H. Yücel, Y. Zhang and Martin Heß contributed talks.

New Preprint: Fast Solvers for Cahn-Hilliard Inpainting

June 26th, 2013
We consider the efficient solution of the modified Cahn-Hilliard equation for binary image inpainting using convexity splitting, which allows an unconditionally gradient stable time-discretization scheme. We look at a double-well as well as a double obstacle potential. For the latter we get a nonlinear system for which we apply a semi-smooth Newton method combined with a Moreau-Yosida regularization technique. At the heart of both methods lies the solution of large and sparse linear systems. We introduce and study block-triangular preconditioners using an efficient and easy to apply Schur complement approximation. Numerical results indicate that our preconditioners work very well for both problems and show that qualitatively better results can be obtained using the double obstacle potential.

New Preprint: A low-rank in time approach to PDE-constrained optimization

June 26th, 2013
The solution of time-dependent PDE-constrained optimization problems is a challenging task in numerical analysis and applied mathematics. All-at-once discretizations and corresponding solvers provide efficient methods to robustly solve the arising discretized equations. One of the drawbacks of this approach is the high storage demand for the vectors representing the discrete space-time cylinder. We here introduce a low-rank in time technique that exploits the low-rank nature of the solution. The theoretical foundations for this approach originate in the numerical treatment of matrix equations and can be carried over to PDE-constrained optimization. We illustrate how three different problems can be rewritten and used within a low-rank Krylov subspace solver with appropriate preconditioning.

CSC News: CSC at Preconditioning 2013

June 16th, 2013
The CSC group is participating at this years Preconditioning meeting in Oxford, UK. Jessica Bosch and Andrew Barker are giving contributed talks and Martin Stoll is giving a plenary lecture. Additionally. Andrew will spend the week prior to the meeting at OCCAM collaborating with John Pearson (Oxford) and Tyron Rees (RAL).

New Preprint: Jessica Bosch, Martin Stoll, Peter Benner: Fast solution of Cahn-Hilliard Variational Inequalities using Implicit Time Discretization and Finite Elements

December 20th, 2012
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.

New Preprint: Fast Iterative Solution of Reaction-Diffusion Control Problems Arising from Chemical Processes

September 20th, 2012
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.

Events: Kick-off meeting of the GAMM CSE activity group

September 17th, 2012
Peter Benner, Jens Saak und Martin Stoll are visiting the kick-off meeting of GAMM activity group Computational Science and Engineering (CSE) in Garching on September 17th and 18th.

New Visitor: John Pearson coming to Magdeburg for two months on ESF grant

June 29th, 2012
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.

Events: SIAM Applied Linear Algebra

June 16th, 2012
From June 18th to 22nd the SIAM Applied Linear Algebra conference 2012 is taking place in Valencia (Spain). The Computational Methods in Systems and Control Theory group is organizing two Minisymposia (Jens Saak and Martin Stoll) there. Moreover the group presents five invited Minisymposium talks (Peter Benner, Kapil Ahuja, Tobias Breiten, Jens Saak and Martin Stoll), as well as three contributed talks (Martin Hess, Patrick Kürschner und M. Sahadet Hossain) in several sections.

New visitor: Nick Higham visiting from Manchester

April 25th, 2012
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.

New visitor: Catherine Powell visiting from Manchester

April 9th, 2012
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.

New Preprint: Tyrone Rees, Martin Stoll:A fast solver for an H1 regularized optimal control problem

March 6th, 2012
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.

Thesis Topic: Bachelor Thesis

January 19th, 2012
This thesis deals with the study and implementation of shooting methods for PDE-constrained optimization problems. This approach will combine the numerical analysis of ODEs with efficient techniques used in numerical linear algebra.
Contact: Martin Stoll

New visitor: Bart Vandereycken visiting from EPFL

January 16th, 2012
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.

New visitor: Michael Saunders visiting from Stanford

January 11th, 2012
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.

New visitor: John Pearson visiting from Oxford

November 14th, 2011
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.

New preprint: John Pearson, Martin Stoll, Andy Wathen: Regularization-robust preconditioners for time-dependent PDE constrained optimization problems

September 14th, 2011
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.

New visitor: Fikriye Yilmaz (Gazi University, Ankara) visiting

July 25th, 2011
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"

New preprint: Martin Stoll: One-shot solution of a time-dependent time-periodic PDE-constrained optimization problem

July 19th, 2011
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.

Events: CSC-Aachen Workshop on parametric model order reduction

July 5th, 2011
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).

Thesis Topic: Diplom/Master Thesis

June 23rd, 2011
The main topic of the proposed dissertation is to develop and implement efficient iterative solvers for the numerical solution of Cahn-Hilliard problems. Please note that the description is in German but if you are interested anyway, please contact Martin Stoll (stollm@mpi...) for more details. This topic is already taken but similar ones can be offered for interested students. This news entry is expired.

CSC News: Peter Benner and Martin Stoll at Householder Symposium XVIII

June 12th, 2011
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.

New preprint: Martin Stoll, Andy Wathen (Oxford): All-at-once solution of time-dependent Stokes control

June 8th, 2011
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.
Logo SIAM Opt11

CSC News: Minisymposium at SIOPT 2011

May 16th, 2011
Roland Herzog (TU Chemnitz) and Martin Stoll are organizing a minisymposium on Preconditioning in PDE-Constrained Optimization at the SIAM Conference on Optimization, which takes place from May 16 until May 19, 2011, in Darmstadt. Peter Benner gives a talk in the minisymposium Model Order Reduction Techniques in PDE Constrained Optimization on System-theoretic Methods for Model Reduction of Linear and Nonlinear Parabolic Systems, too.

CSC News: David Knezevic visiting

May 9th, 2011
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).

CSC News: Melina Freitag visiting

May 2nd, 2011
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).

Martin's News: SIAM CSE Meeting

February 28th, 2011
Meet me at the SIAM CSE meeting in Reno, where I will talk about fast solvers for time-dependent control problems.

Martin's News: SIAM Optimization Meeting

February 1st, 2011
Roland Herzog (TU Chemnitz) and I are pleased to have our minisymposium on "Preconditioning in PDE-Constrained Optimization" for the SIAM optimization meeting accepted.
Martin Stoll, stollm@mpi-magdeburg.mpg.de