A Multigrid Solver for Saddle Point Problems in PDE-Constrained Optimization

Dr. René Simon

May 29, 2008, 3:30 p.m. HS 11

In this talk we consider a one-shot multigrid method for solving the discretized optimality system, also called the Karush-Kuhn-Tucker (KKT) system, of a PDE-constrained optimization problem. One of the most important ingredients of a multigrid iteration is an appropriate smoother. We discuss here the construction of additive Schwarz-type smoothers for a certain class of elliptic optimal control problems. The computational domain is divided into small patches. Each iteration step requires the solutions of several small local saddle point problems. Strategies for constructing such local problems are presented, which allow a rigorous multigrid convergence analysis. Finally, numerical experiments are shown which confirm the theoretical results.