Newton-Krylov-Schwarz algorithms for the 2D full potential equation
- Univ. of Colorado, Boulder, CO (United States)
- Argonne National Lab., IL (United States)
- Old Dominion Univ. Norfolk, VA (United States); and others
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 main 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, can be made robust 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 favorable choices for numerical convergence rate and overall execution time on a distributed-memory parallel computer.
- Research Organization:
- Front Range Scientific Computations, Inc., Lakewood, CO (United States)
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 440679
- Report Number(s):
- CONF-9604167--Vol.2; ON: DE96015307; CNN: Grant ASC-9457534; Grant ASC-9217394; Grant ECS-9527169; Grant NAG5-2218; Contract NAS1-19480; Grant ECS-8957475
- Country of Publication:
- United States
- Language:
- English
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