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

Journal Article · · SIAM Journal on Scientific Computing
 [1];  [2];  [3]; ;  [4]
  1. Univ. of Colorado, Boulder, CO (United States). Dept. of Computer Science
  2. Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
  3. Old Dominion Univ., Norfolk, VA (United States). Dept. of Computer Science
  4. Boeing Co., Seattle, WA (United States)
+ Show Author Affiliations
The authors 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. They 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. They 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.
Research Organization:
Argonne National Laboratory (ANL), Argonne, IL
Sponsoring Organization:
National Science Foundation, Washington, DC (United States); National Aeronautics and Space Administration, Washington, DC (United States); USDOE, Washington, DC (United States)
DOE Contract Number:
W-31109-ENG-38
OSTI ID:
599817
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 1 Vol. 19; ISSN 1064-8275; ISSN SJOCE3
Country of Publication:
United States
Language:
English

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Related Subjects

99 GENERAL AND MISCELLANEOUS
FINITE ELEMENT METHOD
ITERATIVE METHODS
NEWTON METHOD
NONLINEAR PROBLEMS
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS