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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:262

Article

Bosch, Jessica¹  Stoll, Martin¹  Benner, Peter^1,2 

[1] Max Planck Inst Dynam Complex Tech Syst, D-39106 Magdeburg, Germany

[2] Tech Univ Chemnitz, D-09126 Chemnitz, Germany

关键词: Cahn-Hilliard equation;    Double obstacle potential;    PDE-constrained optimization;    Moreau-Yosida regularization technique;    Semi-smooth Newton method;    Preconditioning;   

DOI  :  10.1016/j.jcp.2013.12.053

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free