Aerodynamic applications of Newton-Krylov-Schwarz solvers

David E. Keyes*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


Parallel implicit solution methods are increasingly important in aerodynamics, since reliable low-residual solutions at elevated CFL number are prerequisite to such large-scale applications of aerodynamic analysis codes as aeroelasticity and optimization. In this chapter, a class of nonlinear implicit methods and a class of linear implicit methods are defined and illustrated. Their composition forms a class of methods with strong potential for parallel implicit solution of aerodynamics problems. Newton-Krylov methods are suited for nonlinear problems in which it is unreasonable to compute or store a true Jacobian, given a strong enough preconditioner for the inner linear system that needs to be solved for each Newton correction. In turn, Krylov-Schwarz iterative methods are suited for the parallel implicit solution of multidimensional systems of linearized boundary value problems. Schwarz-type domain decomposition preconditioning provides good data locality for parallel implementations over a range of granularities. These methods are reviewed separately, illustrated with CFD applications, and composed in a class of methods named Newton-Krylov-Schwarz.

Original languageEnglish (US)
Pages (from-to)1-20
Number of pages20
JournalUnknown Journal
Issue number453
StatePublished - 1995
Externally publishedYes
EventProceedings of the 14th International Conference on Numerical Methods in Fluid Dynamics - Bangalore, India
Duration: Jul 11 1994Jul 15 1994

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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