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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.
| 229 | A fast solver for an H1 regularized PDE-constrained optimization problem; Andrew T Barker,Tyrone Rees, Martin Stoll; Accepted to Communications in Computational Physics : 2015. |
@article{BosSB14, 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; 2014. |
@article{BosKSetal14, 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; 2013. |
| 193 | One-shot solution of a time-dependent time-periodic PDE-constrained optimization problem; Martin Stoll; Accepted IMA Journal of Numerical Analysis; 2013. |
| 275 | A low-rank in time approach to PDE-constrained optimization; Martin Stoll, Tobias Breiten; Accepted SISC : 2013. |
| 245 | Fast Iterative Solution of Reaction-Diffusion Control Problems Arising from Chemical Processes; John W. Pearson, Martin Stoll; Submitted : Accepted SISC; 2012. |
| 194 | Regularization-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. |
| 169 | Preconditioning for Allen-Cahn variational inequalities with non-local constraints; Luise Blank; Lavinia Sarbu; Martin Stoll; Journal of Computational Physics, 231, 5406-5420 : 2012. https://dx.doi.org/10.1016/j.jcp.2012.04.035. |
| 166 | Preconditioning for partial differential equation constrained optimization with control constraints; Martin Stoll; Andy Wathen; Numerical Linear Algebra with Applications : 19:53–71; 2012. |
| 168 | Preconditioning for Allen-Cahn variational inequalities with non-local constraints; Luise Blank; Lavinia Sarbu; Martin Stoll; Oberwolfach report - not refereed : 2010. |
| 171 | All-at-once solution of time-dependent PDE-constrained optimization problems; Martin Stoll; Andy Wathen; Technical Report : 2010. |
| 163 | Preconditioning 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; 2010. |
| 165 | Block triangular preconditioners for PDE constrained optimization; Tyrone Rees; Martin Stoll; Numerical Linear Algebra with Applications Volume 17, Issue 6, pages 977–996, December 2010 : 2010. |
| 164 | All-at-once preconditioning in PDE-constrained optimization; Tyrone Rees; Martin Stoll; Andy Wathen; Kybernetika : Vol. 46 (2); 2010. |
| 162 | Computing the scattering amplitude; Gene H. Golub; Martin Stoll; Andy Wathen; Electronic Transactions on Numerical Analysis, Vol. 31 : 2008. |