Primal-dual active set methods for Allen-Cahn variational inequalities with nonlocal constraints

摘要

We propose and analyze a primal-dual active set method for discretized versions of the local and nonlocal Allen-Cahn variational inequalities. An existence result for the nonlocal variational inequality is shown in a formulation involving Lagrange multipliers for local and nonlocal constraints. Local convergence of the discrete method is shown by interpreting the approach as a semismooth Newton method. Properties of the method are discussed and several numerical simulations demonstrate its efficiency.