
Accession Number : ADA314236
Title : Parallel NewtonKrylovSchwarz 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, XiaoChuan ; 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 twolevel 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, NewtonKrylovSchwarz (NKS), employs an inexact finitedifference 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 elliptichyperbolic 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 fillin in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributedmemory 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