Efficient Preconditioners for PDE-Constrained Optimization with Uncertainty

This paper addresses the computational challenges of solving optimal control problems governed by PDEs with uncertain coefficients. The authors propose hierarchical preconditioners to accelerate iterative solvers, improving efficiency for large-scale problems arising from uncertainty quantification. The focus on both steady-state and time-dependent applications highlights the broad applicability of the method.

• •Develops efficient hierarchical preconditioners for optimal control problems with uncertain coefficients.
• •Integrates finite element discretization, stochastic Galerkin approximation, and advanced time-discretization schemes.
• •Exploits sparsity in generalized polynomial chaos expansions.
• •Demonstrates improved convergence of iterative solvers compared to existing methods.
• •Applicable to both steady-state and time-dependent optimal control problems.