Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

Xiao Chuan Cai, William D. Gropp, David E. Keyes, Robin G. Melvin, David P. Young

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)246-265
Number of pages20
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - Jan 1998
Externally publishedYes


  • Domain decomposition
  • Finite elements
  • Full potential equation
  • Krylov space methods
  • Newton methods
  • Overlapping Schwarz preconditioner
  • Parallel computing

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation'. Together they form a unique fingerprint.

Cite this