Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P. Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation. (English) Zbl 0917.76035 SIAM J. Sci. Comput. 19, No. 1, 246-265 (1998). The authors study several aspects of the parallel implementation of a Krylov-Schwarz domain decomposition algorithm for the finite element solution of the nonlinear full potential equation of aerodynamics. They employ a combined algorithm, called Newton-Krylov-Schwarz (NKS) algorithm, and demonstrate that the NKS procedure, 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. Numerical results for some subsonic and transonic flows are given and discussed. Reviewer: S.Nocilla (Torino) Cited in 55 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76H05 Transonic flows 76G25 General aerodynamics and subsonic flows 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65Y05 Parallel numerical computation Keywords:Krylov space method; overlapping Schwarz preconditioner; Krylov-Schwarz domain decomposition algorithm; density upwinding continuation; weak shocks; mixed elliptic-hyperbolic nonlinear partial differential equations PDFBibTeX XMLCite \textit{X.-C. Cai} et al., SIAM J. Sci. Comput. 19, No. 1, 246--265 (1998; Zbl 0917.76035) Full Text: DOI