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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:231

Article

Blank, Luise²  Sarbu, Lavinia²  Stoll, Martin¹ 

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

[2] Univ Regensburg, NWF I Math, D-93040 Regensburg, Germany

关键词: PDE-constrained optimization;    Allen-Cahn model;    Newton method;    Saddle point systems;    Preconditioning;    Krylov subspace solver;   

DOI  :  10.1016/j.jcp.2012.04.035

来源: Elsevier

【 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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free