Multigrid methods for elliptic optimal control problems
Howard, Patricia A.
Master of Arts
Linear-quadratic optimal control problems governed by elliptic partial differential equations arise in a, variety of applications. The optimality conditions for these problems lead to large scale, symmetric indefinite linear systems of equations. For many applications these systems cannot be solved using direct numerical linear algebra techniques. Consequently, it is important to have efficient iterative methods for solving these optimality systems. This thesis studies multigrid methods for the solution of optimality systems arising in elliptic linear-quadratic optimal control problems. The formulation and application of multigrid methods are discussed. Their performance, both as an iterative method and as a preconditioner for GMRES, is investigated numerically. Several smoothing strategies within multigrid methods are studied for advection dominated problems.