## 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.

Original language | English (US) |
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Pages (from-to) | 246-265 |

Number of pages | 20 |

Journal | SIAM Journal on Scientific Computing |

Volume | 19 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1998 |

Externally published | Yes |

## Keywords

- Domain decomposition
- Finite elements
- Full potential equation
- Krylov space methods
- Newton methods
- Overlapping Schwarz preconditioner
- Parallel computing

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics