Abstract
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 use a sparse-grid collocation method to discretize in the stochastic space and multigrid techniques in the physical space. Numerical results show that the proposed preconditioners lead to significant computational savings, with the number of preconditioned conjugate gradient iterations decreasing as the resolution in the physical space increases.
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