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

By: Nasa, National Aeronautics and Space Adm

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. Cai, Xiao-Chuan and Gropp, William D. and Keyes, David E. and Melvin, Robin G. and Young, David P. Goddard Space Flight Center; Langley Research Center NAS1-19480; NAG5-2218; RTOP 505-90-52-01; W-31-109-eng-38; NSF ASC-954-57534; NSF ASC-92-17394; NSF ECS-95-27169; NSF ECS-89-57475...

• Format: Paperback
• Language: English
• ISBN: 1728929253
• ISBN13: 9781728929255
• Release Date: January 1
• Publisher: Independently Published
• Length: 32 Pages
• Weight: 0.22 lbs.
• Dimensions: 0.1" x 8.5" x 11.0"