Fast solution of Cahn–Hilliard variational inequalities using implicit time discretization and finite elements

Handle URI:
http://hdl.handle.net/10754/598318
Title:
Fast solution of Cahn–Hilliard variational inequalities using implicit time discretization and finite elements
Authors:
Bosch, Jessica; Stoll, Martin; Benner, Peter
Abstract:
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.
Citation:
Bosch 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.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Apr-2014
DOI:
10.1016/j.jcp.2013.12.053
Type:
Article
ISSN:
0021-9991
Sponsors:
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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorBosch, Jessicaen
dc.contributor.authorStoll, Martinen
dc.contributor.authorBenner, Peteren
dc.date.accessioned2016-02-25T13:18:37Zen
dc.date.available2016-02-25T13:18:37Zen
dc.date.issued2014-04en
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.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2013.12.053en
dc.identifier.urihttp://hdl.handle.net/10754/598318en
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.en
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.en
dc.publisherElsevier BVen
dc.subjectCahn-Hilliard equationen
dc.subjectDouble obstacle potentialen
dc.subjectMoreau-Yosida regularization techniqueen
dc.subjectPDE-constrained optimizationen
dc.subjectPreconditioningen
dc.subjectSemi-smooth Newton methoden
dc.titleFast solution of Cahn–Hilliard variational inequalities using implicit time discretization and finite elementsen
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionMax Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germanyen
dc.contributor.institutionTechnische Universitat Chemnitz, Chemnitz, Germanyen
kaust.grant.numberKUK-C1-013-04en
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