DOMAIN DECOMPOSITION IN TIME FOR PDE-CONSTRAINED OPTIMIZATION∗

Abstract. PDE-constrained optimization problems have a wide range of applications, but they lead to very large and ill-conditioned linear systems, especially if the problems are time dependent. In this paper we outline an approach for dealing with such problems by decomposing them in time and applying an additive Schwarz preconditioner in time, so that we can take advantage of parallel computers to deal with the very large linear systems. We then illustrate the performance of our method on a variety of problems. Key words. PDE-constrained optimization, space-time methods, preconditioning, Schur com-plement, domain decomposition, parallel computing