Direct and Inverse Problems for PDEs with Random Coefficients - Abstract

Onwunta, Akwum

Efficient solvers for optimal control problems constrained by PDEs with uncertain inputs

joint work with P. Benner and M. Stoll We present an efficient approach for simulating optimization problems governed by partial differential equations involving random coefficients. This class of problems leads to prohibitively high dimensional saddle point systems with Kronecker product structure, especially when discretized with the stochastic Galerkin finite element method. Here, we derive and analyze robust Schur complement-based block diagonal preconditioners for solving the resulting stochastic Galerkin systems with low-rank iterative solvers. Finally, we illustrate the effectiveness of our solvers with numerical experiments.