This work compares the efficiency of several preconditioned GMRES methods (e.g. SGS, ILU(k), Restricted Schwarz additive (RAS)) to solve the adjoint linear system required for the goal-oriented mesh adaptation process. Adjoints equations are used for the goal-oriented mesh adaptation to compute the error estimate of a desired quantity of interest in order to adapt the mesh and reduce the spatial computational error. The goal-oriented mesh adaptation has been successfully applied to the Euler [2] and the RANS [1] equations. This method requires solving large linear systems which can be ill-conditioned and hard to converge on very fine anisotropic adapted meshes. It some cases it may also fail. Indeed, the adjoint problem is similar as solving the Navier-Stokes problem with a CFL equal to infinity. Here, the lack of mass matrix drastically reduces the diagonal dominance of the linear system matrix. Moreover, the parallel partitioning tends to reduce the efficiency of the preconditioner when the number of partitions increases. Currently, the method used to solve the adjoint system is a GMRES preconditioned with symmetric Gauss-Seidel (SGS) under-relaxations. Enhanced Krylov method like FGMRES and other preconditioners such as ILU(k) or RAS will be compared to the original method on several 3D industrial cases e.g. CRM in cruise condition, high-lift prediction, military aircraft. We will exhibit the method providing the more consistency in improving the convergence of the linear system. REFERENCES [1] F. Alauzet and L. Frazza. Feature-based and goal-oriented anisotropic mesh adaptation for RANS applications in aeronautics and aerospace. Journal of Computational Physics, 439:110340, August 2021. [2] F. Alauzet and O. Pironneau. Continuous and discrete adjoints to the Euler equations for fluids. International Journal for Numerical Methods in Fluids, 70(2):135–157, September 2012.