Additive Schwarz preconditioners for a state constrained elliptic distributed optimal control problem discretized by a partition of unity method (1811.07809v1)

Abstract: We present additive Schwarz preconditioners for a class of elliptic optimal control problems discretized by a partition of unity method. The discrete problem is solved by a primal-dual active set algorithm, where the auxiliary system in each iteration is solved by a preconditioned conjugate gradient method based on additive Schwarz preconditioners. Condition number estimates are given and verified by a numerical example.