Solution of linear systems from an optimal control problem arising in wind simulation

Several solution strategies for a class of large, sparse linear systems with a block 2×2 structure arising from the finite element discretization of an optimal control problem in wind simulation are introduced and analyzed. Block preconditioners and a sparse direct solver on the original coupled system are compared with a preconditioned GMRES iteration applied to a reduced system (Schur complement). Theoretical and experimental results demonstrate the effectiveness of the reduced system approach.