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

Authors:
Luise Blank;Lavinia Sarbu;Martin Stoll
Affiliations:
Universität Regensburg, NWF I - Mathematik, 93040 Regensburg, Germany;Universität Regensburg, NWF I - Mathematik, 93040 Regensburg, Germany;Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

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.