Preconditioning for AllenCahn variational inequalities with non-local constraints
The solution of AllenCahn 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 primaldual 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.
preconditioning pde-constrained optimization saddle point systems allencahn model newton method krylov subspace solver