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dc.contributor.authorBosch, Jessica
dc.contributor.authorStoll, Martin
dc.contributor.authorBenner, Peter
dc.date.accessioned2016-02-25T13:18:37Z
dc.date.available2016-02-25T13:18:37Z
dc.date.issued2014-04
dc.identifier.citationBosch J, Stoll M, Benner P (2014) Fast solution of Cahn–Hilliard variational inequalities using implicit time discretization and finite elements. Journal of Computational Physics 262: 38–57. Available: http://dx.doi.org/10.1016/j.jcp.2013.12.053.
dc.identifier.issn0021-9991
dc.identifier.doi10.1016/j.jcp.2013.12.053
dc.identifier.urihttp://hdl.handle.net/10754/598318
dc.description.abstractWe 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.
dc.description.sponsorshipParts 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.
dc.publisherElsevier BV
dc.subjectCahn-Hilliard equation
dc.subjectDouble obstacle potential
dc.subjectMoreau-Yosida regularization technique
dc.subjectPDE-constrained optimization
dc.subjectPreconditioning
dc.subjectSemi-smooth Newton method
dc.titleFast solution of Cahn–Hilliard variational inequalities using implicit time discretization and finite elements
dc.typeArticle
dc.identifier.journalJournal of Computational Physics
dc.contributor.institutionMax Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
dc.contributor.institutionTechnische Universitat Chemnitz, Chemnitz, Germany
kaust.grant.numberKUK-C1-013-04


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