Robust and efficient solvers for coupled-adjoint linear systems are crucial to successful aerostructural optimization. Monolithic and partitioned strategies can be applied. The monolithic approach is expected to offer better robustness and efficiency for strong fluid-structure interactions. However, it requires a high implementation cost and convergence may depend on appropriate scaling and initialization strategies. On the other hand, the modularity of the partitioned method enables a straightforward implementation while its convergence may require relaxation. In addition, a partitioned solver leads to a higher number of iterations to get the same level of convergence as the monolithic one. The objective of this paper is to accelerate the fluid-structure coupled-adjoint partitioned solver by considering techniques borrowed from approximate invariant subspace recycling strategies adapted to sequences of linear systems with varying right-hand sides. Indeed, in a partitioned framework, the structural source term attached to the fluid block of equations affects the right-hand side with the nice property of quickly converging to a constant value. We also consider deflation of approximate eigenvectors in conjunction with advanced inner-outer Krylov solvers for the fluid block equations. We demonstrate the benefit of these techniques by computing the coupled derivatives of an aeroelastic configuration of the ONERA-M6 fixed wing in transonic flow. For this exercise the fluid grid was coupled to a structural model specifically designed to exhibit a high flexibility. All computations are performed using RANS flow modeling and a fully linearized one-equation Spalart-Allmaras turbulence model. Numerical simulations show up to 39% reduction in matrix-vector products for GCRO-DR and up to 19% for the nested FGCRO-DR solver.

翻译：耦合伴随线性系统的稳健高效求解器对于气动结构优化的成功至关重要。可采用整体求解策略与分区求解策略。对于强流固耦合问题，整体方法预期能提供更好的稳健性和效率，但其实现成本较高，且收敛性可能依赖于适当的缩放和初始化策略。另一方面，分区方法因其模块化特性而便于实现，但其收敛性可能需要松弛处理。此外，为达到与整体方法相同的收敛水平，分区求解器需要更多的迭代次数。本文旨在通过借鉴适用于变右侧向量线性系统序列的近似不变子空间循环回收技术，加速流固耦合伴随分区求解器。在分区框架中，附着于流体方程块的结构源项以快速收敛至常数的优良特性影响右侧向量。我们还考虑将近似特征向量消去技术与流体方程块的先进内外层Krylov求解器相结合。通过计算跨声速流中ONERA-M6固定翼气动弹性构型的耦合导数，我们验证了这些技术的有效性。本算例中，流体网格与专门设计以呈现高柔性的结构模型相耦合。所有计算均采用RANS流模型和完全线性化的单方程Spalart-Allmaras湍流模型。数值模拟显示，GCRO-DR求解器的矩阵-向量积减少了39%，而嵌套的FGCRO-DR求解器则减少了19%。