Fast Iterative Solution of Reaction-Diffusion Control Problems Arising from Chemical Processes

John W. Pearson and Martin Stoll*

PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix systems, is a field of numerical analysis that has recently been attracting much attention. In this talk, we develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the incorporation of control constraints and application of the outer iteration to take account of the nonlinearity of the underlying PDEs. In our numerical results we illustrate that the proposed preconditioners perform rather robustly with respect to changes in the crucial system parameters such as mesh-size, regularization parameter or diffusion coefficients.

Mathematics Subject Classification: 65F08

Keywords: Preconditioning, PDE-constrained optimization, nonlinear programming, Krylov solvers

Minisymposion: Preconditioning for PDE-Constrained Optimization