HOMEContact | Local | Impressum | German
Minerva Logo of the MPG
Photo of the Institute
Banner Max-Planck-Institut
Research Group Computational Methods in Systems and Control Theory
MPI Magdeburg > Computational Methods in Systems and Control Theory > Projects > Efficient Solution and Preconditioning of linear systems

Diese Seite wird nicht mehr aktualisiert. Bitte besuchen Sie unsere neue Webpräsenz.

This page is not updated any longer. Please visit our new website.

Efficient Solution and Preconditioning of linear systems


  • Martin Stoll
    Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg,
    Computational Methods in Systems and Control Theory,
    Tel: +49 (0)391-6110-805
    E-mail: stollm@mpi-magdeburg.mpg.de

Project Description

Roadmap The complexity of differential equation models describing real-world problems and their discretization makes the computation of the approximate solution a challenging task. For the solution of the PDE problem often referred to as the forward problem many iterative algorithms and preconditioning strategies have been proposed. As more often these problems become only the constraints in an optimization problem the preconditioning strategies have to be adjusted to deal with the higher complexity and different mathematical properties. We therefore study in addition to general linear system saddle point systems (often referred to as KKT systems as the correspond to the first order optimality conditions). The efficient solution of many linear systems is also essential for parameter-dependent problems that appear in the context of the reduced basis method. There a reduced model is build up using the solution of a linear system for certain values of the parameter.

Duration and Funding

  • since October 2010: MPI Magdeburg
  • September-October 2012: ESF OPTPDE

Related Publications

229A fast solver for an H1 regularized PDE-constrained optimization problem;
Andrew T Barker,Tyrone Rees, Martin Stoll;
Accepted to Communications in Computational Physics  :  
author = {Bosch, J. and Stoll, M. and Benner, P.},
title = {Fast solution of {C}ahn--{H}illiard variational inequalities using implicit time discretization and finite elements},
journal = {J. Comput. Phys.},
volume = {262},
pages = {38--57},
year = {2014},
doi = {https://dx.doi.org/10.1016/j.jcp.2013.12.053},
url = {https://www.sciencedirect.com/science/article/pii/S0021999114000084} }
Fast solution of Cahn-Hilliard Variational Inequalities using Implicit Time Discretization and Finite Elements;
Jessica Bosch, Martin Stoll, Peter Benner: ;
Journal of Computational Physics  :  Vol. 262, pp. 38-57;
author = {Bosch, J. and Kay, D. and Stoll, M. and Wathen, A.~J.},
title = {Fast Solvers for {C}ahn--{H}illiard Inpainting},
journal = {SIAM J. Imaging Sci.},
volume = {7},
number = {1},
pages = {67--97},
year = {2014},
doi = {10.1137/130921842},
url = {https://dx.doi.org/10.1137/130921842} }
Fast Solvers for Cahn-Hilliard Inpainting;
Jessica Bosch, David Kay, Martin Stoll, Andrew J. Wathen;
SIAM Journal on Imaging Sciences  :  Vol. 7, No. 1, pp. 67-97;
193One-shot solution of a time-dependent time-periodic PDE-constrained optimization problem;
Martin Stoll;
Accepted IMA Journal of Numerical Analysis;
275A low-rank in time approach to PDE-constrained optimization;
Martin Stoll, Tobias Breiten;
Accepted SISC  :  
245Fast Iterative Solution of Reaction-Diffusion Control Problems Arising from Chemical Processes;
John W. Pearson, Martin Stoll;
Submitted  :  Accepted SISC;
194Regularization-robust preconditioners for time-dependent PDE constrained optimization problems;
John W. Pearson, Martin Stoll, Andy Wathen;
SIAM Journal on Matrix Analysis and Applications  :  Vol. 33, No. 4, pp. 1126-1152;
SIAM; 2012.
169Preconditioning for Allen-Cahn variational inequalities with non-local constraints;
Luise Blank; Lavinia Sarbu; Martin Stoll;
Journal of Computational Physics, 231, 5406-5420  :  
166Preconditioning for partial differential equation constrained optimization with control constraints;
Martin Stoll; Andy Wathen;
Numerical Linear Algebra with Applications  :  19:53–71;
168Preconditioning for Allen-Cahn variational inequalities with non-local constraints;
Luise Blank; Lavinia Sarbu; Martin Stoll;
Oberwolfach report - not refereed  :  
171All-at-once solution of time-dependent PDE-constrained optimization problems;
Martin Stoll; Andy Wathen;
Technical Report  :  
163Preconditioning saddle point problems with applications in optimization;
N.I.M. Gould; H.S. Dollar; Martin Stoll; Andy Wathen;
SIAM Journal of Scientific Computing, 32(2010), pp. 249-270  :  Vol. 31;
165Block triangular preconditioners for PDE constrained optimization;
Tyrone Rees; Martin Stoll;
Numerical Linear Algebra with Applications Volume 17, Issue 6, pages 977–996, December 2010  :  
164All-at-once preconditioning in PDE-constrained optimization;
Tyrone Rees; Martin Stoll; Andy Wathen;
Kybernetika  :  Vol. 46 (2);
162Computing the scattering amplitude;
Gene H. Golub; Martin Stoll; Andy Wathen;
Electronic Transactions on Numerical Analysis, Vol. 31  :  
Thomas Mach, thomas.mach@googlemail.com