## Differential Equations Seminar: Dr. Ana Maria Soane

#### U.S. Naval Academy

Monday, October 8, 2018 · 11 AM - Noon

**Title:**Multilevel preconditioners for optimal control problems with elliptic SPDE constraints.

**Abstract:**In this work we construct multigrid preconditioners to be used in the solution process of pathwise optimal control problems constrained by elliptic partial differential equations with random coefficients. We combine a sparse-grid collocation approach to discretize in the stochastic space with multigrid techniques in the physical space. Numerical results show that the proposed multigrid preconditioners lead to significant computational savings, with the number of preconditioned conjugate gradient iterations decreasing as the resolution increases.