Parallel Newton--Krylov--Schwarz Algorithms for the Transonic Full Potential Equation

Authors:
Xiao-Chuan Cai;William D. Gropp;David E. Keyes;Robin G. Melvin;David P. Young
Affiliations:
-;-;-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
1998

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Abstract

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton--Krylov--Schwarz (NKS), employs an inexact finite difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.