Globalized Newton-Krylov-Schwarz algorithms and software for parallel implicit CFD

Implicit solution methods are important in applications modeled by PDEs wit h disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, parallelization is essential. T he pseudo-transient matrix-free Newton-Krylov-Schwarz (Psi NKS) algorithmic framework is presented as a widely applicable answer. This article shows t hat for the classical problem of three-dimensional transonic Euler flow abo ut an M6 wing, Psi NKS can simultaneously deliver globalized, asymptoticall y rapid convergence through adaptive pseudo-transient continuation and Newt on's method; reasonable parallelizability for an implicit method through de ferred synchronization and favorable communication-to-computation scaling i n the Krylov linear solver; and high per processor performance through atte ntion to distributed memory and cache locality, especially through the Schw arz preconditioner. Two discouraging features of Psi NKS methods are their sensitivity to the coding of the underlying PDE discretization and the larg e number of parameters that must be selected to govern convergence. The aut hors therefore distill several recommendations from their experience and re ading of the literature on various algorithmic components of Psi NKS, and t hey describe a freely available MPI-based portable parallel software implem entation of the solver employed here.