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

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    Type
    Article
    Authors
    Bosch, Jessica
    Stoll, Martin
    Benner, Peter
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2014-04
    Permanent link to this record
    http://hdl.handle.net/10754/598318
    
    Metadata
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    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.
    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.
    Publisher
    Elsevier BV
    Journal
    Journal of Computational Physics
    DOI
    10.1016/j.jcp.2013.12.053
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jcp.2013.12.053
    Scopus Count
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