Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD

Abstract

Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (ψNKS) algorithmic framework is presented as a widely applicable answer. This article shows that for the classical problem of three-dimensional transonic Euler flow about an M6 wing, ψNKS can simultaneously deliver globalized, asymptotically rapid convergence through adaptive pseudo-transient continuation and Newton’s method; reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and high per processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of ψNKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. The authors therefore distill several recommendations from their experience and reading of the literature on various algorithmic components of ψNKS, and they describe a freely available MPI-based portable parallel software implementation of the solver employed here.