We present a parallel multigrid technique that efficiently solves optimal control problems in two and three spatial dimensions. Both linear and nonlinear problems are considered. The nonlinear problems result in singular optimal control systems. These systems are characterized by indefiniteness of the state equations and the possibility of multiple solutions. Control is required to avoid blow-up and to drive the system to a desired target configuration.

      A robust parallel nonlinear multigrid method is implemented to realize our control strategy and demonstrate robustness with respect to the optimization parameterization. We apply this method to a steady state solid fuel ignition model to verify its usefulness.