Block Diagonal Parareal Preconditioner for Parabolic Optimal Control Problems

Marcus Sarkis | Schaerer, Christian | Mathew , Tarek

Keywords: Preconditioner | Finite Element | Parareal | Parabolic Optimal Control | KKT System

We describe an iterative algorithm for the solution of a large scale linear-quadratic parabolic optimal control problem. Unlike Ricatti equation based methods, we determine the control variable by an iterative procedure which solves a large saddle point system obtained by an {\it all at once} discretization strategy involving the state (primal) variables, the control variables and the adjoint (dual) variables. We derive a reduced symmetric indefinite linear system involving the control variables and auxiliary variables, and solve it using a preconditioned MINRES iteration, with a symmetric positive definite block diagonal preconditioner based on the parareal algorithm. Theoretical and numerical results show that the preconditioned algorithm has adequate convergence properties and parallel scalability.

Anexos:

• schaerer_mini_10TR.pdf