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

Abstract

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 paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects of 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 (Newton) iteration to take into account the nonlinearity of the underlying PDEs.