PARALLEL NEWTON-KRYLOV-SCHWARZ ALGORITHMS FOR THE TRANSONIC FULL-POTENTIAL EQUATION

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potent ial equation of aerodynamics discretized in two dimensions with biline ar elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), emplo ys an inexact finite difference Newton method and a Krylov space itera tive method, with a two-level overlapping Schwarz method as a precondi tioner. We demonstrate that NKS, combined with a density upwinding con tinuation strategy for problems with weak shocks, is robust and econom ical for this class of mixed elliptic-hyperbolic nonlinear partial dif ferential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse gri d density, subdomain overlap, and the level of fill-in in the incomple te factorization, and report their effect on numerical convergence rat e, overall execution time, and parallel efficiency on a distributed-me mory parallel computer.