Memory efficient hybrid algebraic solvers for linear systems arising from compressible flows

Abstract

This paper deals with the solution of sparse linear systems arising from design optimization in computational fluid dynamics. In this approach, a linearization of the discretized compressible Navier–Stokes equations is built, in order to evaluate the sensitivity of the entire flow with respect to each design parameter. This requires an efficient and robust parallel linear solver, to generate the exact flow derivatives: from the algebraic decomposition of the input matrix, a hybrid robust direct/iterative solver is generally defined with a Krylov subspace method as accelerator, a domain decomposition method as preconditioner and a direct method as subdomain solver. The goal of this paper is to reduce the memory requirements and indirectly, the computational cost at different steps of this scheme. To this end, we use a grid-point induced block approach for the data storage and the partitioning part, a Krylov subspace method based on the restarted GMRES accelerated by deflation, a preconditioner formulated with the restricted additive Schwarz method and an aerodynamic/turbulent fields split at the subdomain level. Numerical results are presented with industrial test cases to show the benefits of these choices.