Newton-Krylov-Schwarz Methods in CFD

Abstract

Newton-Krylov methods are potentially well suited for the implicit solution of nonlinear problems whenever it is unreasonable to compute or store a true Jacobian. Krylov-Schwarz iterative methods are well suited for the parallel implicit solution of multidimensional systems of boundary value problems that arise in CFD. They provide good data locality so that even a high-latency workstation network can be employed as a parallel machine. We call the combination of these two methods Newton-Krylov-Schwarz and report numerical experiments on some algorithmic and implementation aspects: the use of mixed discretization schemes in the (implicitly defined) Jacobian and its preconditioner, the selection of the differencing parameter in the formation of the action of the Jacobian, the use of a coarse grid in additive Schwarz preconditioning, and workstation network implementation. Three model problems are considered: a convection-diffusion problem, the full potential equation, and the Euler equations.