A preconditioner freeze strategy for numerical solution of compressible flows

Abstract

SUMMARYIt is well known that Krylov-Schwarz methods are well suited for solving linear systems of equations in high-latency, distributed memory environments and constitute powerful tools when combined with Newton-Krylov methods to solve Computational Fluid Dynamics problems. Nevertheless, the computational costs related to the Jacobian and the preconditioner evaluation can sometimes be prohibitive. In this work a strategy to reduce these costs is presented, based on evaluating a new preconditioner only after it had been frozen for several time steps. Numerical experiments show the computational gain achieved with the proposed strategy.

A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows

“…The second preconditioning strategy consists of a measure to automatically determine whether it is preferred to compute a new preconditioner [35]. The preconditioner update strategy is based on the principle that the accuracy of the preconditioner influences the number of iterations of the Krylov subspace solver.…”

“…The preconditioner freeze strategy in [35] is modified in the sense that computational times for rejected time steps are ignored by the algorithm. Also, the number of stages per time step differs per time integration scheme.…”