Extension of fixed point PDE solvers for optimal design by one-shot method - With first applications to aerodynamic shape optimization

Abstract

This paper concerns mathematical methods, algorithmic techniques and software tools for the transition from simulation to optimization. We focus in particular on applications in aerodynamics. The methodology is applicable to all areas of scientific computing, where large scale governing equations involving discretized PDEs are treated by custom made fixed point solvers. To exploit the domain specific experience and expertise invested in these simulation tools we propose to extend them in a semi-automated fashion. First they are augmented with an adjoint solvers to obtain (reduced) derivatives and then this sensitivity information is immediately used to determine optimization corrections.