Dynamic optimization of multiscale PDE/kMC process systems using nonlinear order reduction and tabulation techniques

The problem of dynamic optimization for multiscale systems comprising of coupled continuum and discrete descriptions is considered. The solution of such problems is challenging owing to large computational requirements of the multiscale process model. This problem is addressed by developing a reduced multiscale model. This is achieved by combining order reduction techniques for dissipative partial-differential equations with adaptive tabulation of microscopic simulation data. The optimization problem is subsequently formulated and solved using standard search algorithms. The proposed method is applied to a representative catalytic oxidation process where optimal inlet concentration profiles are computed to guide the microscopic system from one stable stationary state to another stable stationary state.