Automated extension of fixed point PDE solvers for optimal design with bounded retardation (I)

To exploit the domain specific experience and expertise invested in high-fidelity simulation tools we propose to extend them in a semi-automated fashion. First they are augmented with adjoint solvers to obtain (reduced) derivatives and then this sensitivity information is immediately used to determine optimization corrections. In other words, rather than applying an outer optimization loop we prefer the "one-shot" strategy of pursuing optimality simultaneously with the goals of primal and adjoint feasibilty. To complete an optimization run in a small multiple of the number of iterations required for a simulation run it must be ensured that the contractivity factor of the combined "one-shot" scheme is only a certain fraction closer to 1 than that of the user supplied fixed point solver. We focus on applications in aerodynamics to optimize wing shapes and in climate studies to identify parameters.