A Hybrid GMRES Solver with Deflation for Ill-conditioned Adjoint Systems for Aerodynamic Shape Optimization

摘要

The aim of this paper is to demonstrate the framework in which the restarted GMRES method with deflation and the embedded inexact iterative method with domain decomposition as the global preconditioning act together to tackle the challenges associated with the solution of a large sparse ill-conditioned adjoint system of equations for aerodynamic shape optimization. Furthermore, using a dynamic approach to change the restart number and the deflated number, and the weighted-sum combination of 1st- and 2nd-order Jacobians, our numerical solver with restrictive memory storage can reach similar convergence levels with less computational time as compared to the full GMRES solver. The numerical verifications are demonstrated through solving adjoint systems of equations of a 2D NACA0012 airfoil and 3D Common Research Model (CRM) wing in viscous flows to demonstrate the applicability of this proposed framework for aerodynamic shape optimization problems.