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 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. © 2014 Elsevier Inc.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: Parts of this work were performed while the first author was visiting the Oxford Centre for Collaborative Applied Mathematics (OCCAM), University of Oxford. This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). The authors would like to thank Christian Kahle, Michael Hinze as well as the anonymous referees for their helpful comments and suggestions.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.