Parallel implicit methods for aerodynamics

Abstract. Domain decomposition (Krylov-Schwarz) iterative methods are natural for the parallel implicit solution of multidimensional systems of bound-ary value problems that arise, for instance, in aerodynamics. They provide good data locality so that even a high-latency workstation network can be em-ployed as a parallel machine. Matrix-free (Newton-Krylov) methods are natu-ral when it is unreasonable to compute or store a true Jacobian. We call their combinationNewton-Krylov-Schwarz and report experimental progress on two algorithmic aspects: the use of a coarse grid in additive Schwarz precondition-ing and the use of mixed discretization schemes in the (implicitly dened) Jacobian and its preconditioner. Two model problems in two-dimensional compressible ow are considered: the full potential equation, and the Euler equations. 1. Krylov-Schwarz Algorithms Fully implicit linear solvers in aerodynamics allow more rapid asymptotic ap-proach to steady states than time-explicit, approximate factorization, or relaxatio