Accession Number : ADA314236

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

Descriptive Note : Contract rept.,

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Cai, Xiao-Chuan ; Gropp, William D. ; Keye, David E. ; Melvin, Robin G. ; Young, David P.

PDF Url : ADA314236

Report Date : MAY 1996

Pagination or Media Count : 28

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.

Descriptors :   *ALGORITHMS, *FINITE ELEMENT ANALYSIS, MATHEMATICAL MODELS, OPTIMIZATION, DISTRIBUTED DATA PROCESSING, PARALLEL PROCESSING, COMPUTATIONAL FLUID DYNAMICS, FINITE DIFFERENCE THEORY, COMPRESSIBLE FLOW, NONLINEAR SYSTEMS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, CONVERGENCE, SYSTEMS ANALYSIS, NONLINEAR ANALYSIS, NUMERICAL METHODS AND PROCEDURES, APPLIED MATHEMATICS, INVISCID FLOW, HYPERBOLIC DIFFERENTIAL EQUATIONS, AERODYNAMICS, TRANSONIC FLOW, POTENTIAL THEORY.

Subject Categories : Operations Research
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE