## Globalized Newton-Krylov-Schwarz algorithms and software for parallel implicit CFD (1998)

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Venue: | Int. J. High Performance Computing Applications |

Citations: | 38 - 14 self |

### BibTeX

@ARTICLE{Gropp98globalizednewton-krylov-schwarz,

author = {W. D. Gropp and D. E. Keyes and L. C. Mcinnes and M. D. Tidriri},

title = {Globalized Newton-Krylov-Schwarz algorithms and software for parallel implicit CFD},

journal = {Int. J. High Performance Computing Applications},

year = {1998},

volume = {14},

pages = {102--136}

}

### Years of Citing Articles

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### Abstract

Key words. Newton-Krylov-Schwarz algorithms, parallel CFD, implicit methods Abstract. Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (ΨNKS) algorithmic framework is presented as a widely applicable answer. This article shows that, for the classical problem of three-dimensional transonic Euler flow about an M6 wing, ΨNKS can simultaneously deliver • globalized, asymptotically rapid convergence through adaptive pseudo-transient continuation and Newton’s method; • reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and • high per-processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of ΨNKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. We therefore distill several recommendations from our experience and from our reading of the literature on various algorithmic components of ΨNKS, and we describe a freely available, MPI-based portable parallel software implementation of the solver employed here. 1. Introduction. Disparate

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Citation Context ...ms have been brought together in freely available, widely portable, and widely distributed parallel software in the form of the Portable, Extensible Toolkit for Scientific Computation (PETSc) package =-=[4]-=-, through which the illustrative results of this paper have been obtained. We justify the broad scope of the presentation by the need to appreciate the framework as a whole. If any aspect of the #NKS ... |

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23 |
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23 |
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22 |
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Citation Context ...tioned with a global incomplete factorization) are competitive with multigrid methods for large-scale CFD problems; a similar comparison for the matrix-free form of such methods was given by Keyes in =-=[43]-=-. A study of the performance of the preconditioned NK matrix-free methods is given by Tidriri in [76] and [78]. Various practical aspects of NK methods in CFD were explored in [1, 7, 37, 53, 52, 60, 6... |

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Citation Context ...imality --- even without the benefit of a coarse grid component --- in the parabolic case. The term "Newton-Krylov-Schwarz" was coined in [15]. NKS methods have been taken up by Cai and coll=-=aborators [14, 16, 12, 13]-=-, Knoll and collaborators [47, 49, 48, 53, 50], Pernice and collaborators [63], and Tidriri [75, 77, 79], among many others. One of the main contemporary motivations for domain decomposition methods i... |

16 |
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Citation Context ...tion fronts, and multidisciplinary phenomena such as aeroelasticity. Local equilibration of wavespeeds (as in the "preconditioning" of [80]) and temporal subcycling (as in the "three-fi=-=eld" method of [27]-=-) are two strategies that permit explicit integration of the flowfields of some such problems; nevertheless, implicit solution methods are playing increasingly important roles in CFD. Whereas explicit... |

15 |
Domain decomposition on parallel computers’, Impact Comput
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(Show Context)
Citation Context ...de-andconquer concurrency. Scalability studies based on dimensionless ratios of communication and computation parameters for message-passing aspects of domain-decomposed iterative methods appeared in =-=[31, 32]-=-. Recently, the cache-based motivation for domain decomposition has become apparent [87]. Parallel implementations of NKS methods are also beginning to appear. We mention the shared-memory implementat... |

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Citation Context ...odest, reflecting the comparable situation for multigrid methods for di#cult flow problems. In this paper, we do not further consider coarse grids. We mention the Newton-based work of Venkatakrishnan =-=[84]-=- on Euler problems and the defect correction-based work of Jenssen & Weinerfelt on Euler [35] and NavierStokes [36]. In the former context, the convergence rate enhancement of the coarse grid is nearl... |

15 |
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Citation Context ...n and computation parameters for message-passing aspects of domain-decomposed iterative methods appeared in [31, 32]. Recently, the cache-based motivation for domain decomposition has become apparent =-=[87]-=-. Parallel implementations of NKS methods are also beginning to appear. We mention the shared-memory implementation of [54] and the distributed-memory implementations of [3], [14], and [16]. The most ... |