Fast solution of CahnHilliard variational inequalities using implicit time discretization and finite elements
We consider the efficient solution of the CahnHilliard 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 MoreauYosida 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.
semi-smooth newton method moreauyosida regularization technique preconditioning cahnhilliard equation double obstacle potential pde-constrained optimization