Differential Equations Seminar: Sumaya Alzuhairy

Abstract: We investigate the design and analysis of multilevel preconditioners for optimal control problems constrained by elliptic equations with stochastic coefficients SPDECO.  Assuming a generalized polynomial chaos expansion for the stochastic components, our approach uses a non-intrusive and intrusive approach for the PDE. For the non-intrusive approach, we use a common strategy for solving optimal control of stochastic PDEs relies on stochastic collocation, which reduces the problem to multiple solves of optimal control problems constrained by deterministic PDEs. In particular, we use the discrete projection approach rather than the interpolation approach that has been used in most of the literature.  For the intrusive approach, we investigate an alternative approach where we use a stochastic Galerkin formulation and discretization of the PDE prior to solving the optimal control problem. Ultimately this requires solving a potentially very large linear system, which we then solve using specially designed multilevel algorithms.