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Abstract : |
Abstract. Domain decomposition (Krylov-Schwarz) iterative methods are natural for the parallel implicit solution of multidimensional systems of boundary value problems that arise in aerodynamics. They provide good data locality so that even a high-latency workstation network can be employed as a parallel machine. Matrix-free (Newton-Krylov) methods are natural when it is unreasonable to compute or store a true Jacobian. We call their combination Newton-Krylov-Schwarz and report experimental progress on two algorithmic aspects: the use of a coarse grid in additive Schwarz preconditioning and the use of mixed discretization schemes in the (implicitly defined) Jacobian and its preconditioner. Two model problems in two-dimensional compressible flow are considered: the full potential equation and the Euler equations. 1. Krylov-Schwarz Algorithms Fully implicit linear solvers in aerodynamics allow more rapid asymptotic approach to steady states than time-explicit, approximate factorization, or relaxation solvers that hold the outer nonlinear iteration to small time steps. Nevertheless, the, |
