Preconditioning for Allen-Cahn variational inequalities with non-local constraints

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• 作者：Luise Blank^a ; ¹ ; ^{luise.blank@mathematik.uni-regensburg.de} ; Lavinia Sarbu^a ; Martin Stoll^b ; ^{martin.stoll80@gmail.com}
• 关键词：PDE-constrained optimization ; Allen&ndash ; Cahn model ; Newton method ; Saddle point systems ; Preconditioning ; Krylov subspace solver
• 刊名：Journal of Computational Physics
• 出版年：2012
• 期刊代码：136_00219991
• 类别：cp
• 出版时间：20 June, 2012
• 卷：231
• 期：16
• 页码：5406-5420
• 文件大小：875 K

摘要

The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many applications. This problem can be solved both in its scalar and vector-valued form as a PDE-constrained optimization problem by means of a primal-dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate the competitiveness of this approach.