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- Jessica Bosch, Martin Stoll, Peter Benner
- J. Comput. Physics
- 2014

We consider the efficient 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… (More)

- Tyrone Rees, Martin Stoll, Andrew J. Wathen
- Kybernetika
- 2010

The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different… (More)

- Andrew T. Barker, Martin Stoll
- Computer Physics Communications
- 2015

PDE-constrained optimization problems have a wide range of applications, but they lead to very large and ill-conditioned linear systems, especially if the problems are time dependent. In this paper we outline an approach for dealing with such problems by decomposing them in time and applying an additive Schwarz preconditioner in time, so that we can take… (More)

- Tyrone Rees, Martin Stoll
- Numerical Lin. Alg. with Applic.
- 2010

- Martin Stoll, Andrew J. Wathen
- SIAM J. Matrix Analysis Applications
- 2008

- John W. Pearson, Martin Stoll, Andrew J. Wathen
- SIAM J. Matrix Analysis Applications
- 2012

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… (More)

- John W. Pearson, Martin Stoll, Andrew J. Wathen
- Numerical Lin. Alg. with Applic.
- 2014

Optimal control problems with partial differential equations as constraints play an important role in many applications. The inclusion of bound constraints for the state variable poses a significant challenge for optimization methods. Our focus here is on the incorporation of the constraints via the Moreau-Yosida regularization technique. This method has… (More)

- Jessica Bosch, David Kay, Martin Stoll, Andrew J. Wathen
- SIAM J. Imaging Sciences
- 2014

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 non-linear system for which we apply a semi-smooth Newton method… (More)

- Martin Stoll, Andrew J. Wathen
- Numerical Lin. Alg. with Applic.
- 2012

Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal– dual active set method is used. We… (More)

- Hamdullah Yücel, Martin Stoll, Peter Benner
- Computers & Chemical Engineering
- 2013

In this paper, convection-diffusion-reaction models with nonlinear reaction mechanisms, which are typical problems of chemical systems, are studied by using the upwind symmetric interior penalty Galerkin (SIPG) method. The local spurious oscillations are minimized by adding an artificial viscosity diffusion term to the original equations. A discontinuity… (More)