## Abstract

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 language | English (US) |
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Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Unknown Journal |

Issue number | 453 |

State | Published - 1995 |

Externally published | Yes |

## ASJC Scopus subject areas

- Engineering(all)