Recycling Krylov Subspaces for Efficient Partitioned Solution of Aerostructural Adjoint Systems

TL;DR

This paper introduces a novel approach to accelerate partitioned fluid-structure adjoint solvers by recycling Krylov subspaces and deflating eigenvectors, significantly reducing computational effort in aeroelastic simulations.

Contribution

It adapts invariant subspace recycling and eigenvector deflation techniques to improve the efficiency of partitioned coupled-adjoint solvers in aerostructural optimization.

Findings

Up to 39% reduction in matrix-vector products with GCRO-DR.

Up to 19% reduction with nested FGCRO-DR.

Effective acceleration demonstrated on ONERA-M6 wing in transonic flow.

Abstract

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.