A Schur–Newton–Krylov solver for steady-state aeroelastic analysis and design sensitivity analysis

This paper presents a Newton–Krylov approach applied to a Schur complement formulation for the analysis and design sensitivity analysis of systems undergoing fluid–structure interaction. This solution strategy is studied for a three-field formulation of an aeroelastic problem under steady-state conditions and applied to the design optimization of three-dimensional wing structures. A Schur–Krylov solver is introduced for computing the design sensitivities. Comparing the Schur–Newton–Krylov solver with conventional Gauss–Seidel schemes shows that the proposed approach significantly improves robustness and convergence rates, in particular for problems with strong fluid–structure coupling. In addition, the numerical efficiency of the aeroelastic sensitivity analysis can be typically improved by more than a factor of 1.5, especially if high accuracy is required.