### Abstract

We report on our efforts towards the design of efficient parallel hierarchical iterative methods for the solution of sparse and irregularly structured linear systems resulting from CFD applications. The solution strategies considered here share a central numerical kernel which consists in a linear multigrid by volume agglomeration method. Starting from this method, we study two parallel solution strategies. The first variant results from a direct intra-grid parallelization of multigrid operations on coarse grids. The second variant is based on an additive Schwarz domain decomposition algorithm which is formulated at the continuous level through the introduction of specific interface conditions. In this variant, the linear multigrid by volume agglomeration method is used to approximately solve the local systems obtained at each iteration of the Schwarz algorithm. As a result, the proposed hybrid domain decomposition/multigrid method can be viewed as a particular form of parallel multigrid in which multigrid acceleration is applied on a subdomain basis, these local calculations being coordinated by an appropriate domain decomposition iteration at the global level. The parallel performances of these two parallel multigrid methods are evaluated through numerical experiments that are performed on several clusters of PCs with different computational nodes and interconnection networks.

Language | English |
---|---|

Pages | 503-525 |

Number of pages | 23 |

Journal | Parallel Computing |

Volume | 30 |

Issue number | 4 |

DOIs | |

Publication status | Published - 30 Apr 2004 |

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### Keywords

- computational fluid dynamics (CFD)
- domain decomposition method
- multigrid method
- parallel computing
- triangular meshes

### Cite this

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**Parallel multigrid methods for the calculation of unsteady flows on unstructured grids : algorithmic aspects and parallel performances on clusters of PCs.** / Dolean, V.; Lanteri, S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Parallel multigrid methods for the calculation of unsteady flows on unstructured grids

T2 - Parallel Computing

AU - Dolean, V.

AU - Lanteri, S.

PY - 2004/4/30

Y1 - 2004/4/30

N2 - We report on our efforts towards the design of efficient parallel hierarchical iterative methods for the solution of sparse and irregularly structured linear systems resulting from CFD applications. The solution strategies considered here share a central numerical kernel which consists in a linear multigrid by volume agglomeration method. Starting from this method, we study two parallel solution strategies. The first variant results from a direct intra-grid parallelization of multigrid operations on coarse grids. The second variant is based on an additive Schwarz domain decomposition algorithm which is formulated at the continuous level through the introduction of specific interface conditions. In this variant, the linear multigrid by volume agglomeration method is used to approximately solve the local systems obtained at each iteration of the Schwarz algorithm. As a result, the proposed hybrid domain decomposition/multigrid method can be viewed as a particular form of parallel multigrid in which multigrid acceleration is applied on a subdomain basis, these local calculations being coordinated by an appropriate domain decomposition iteration at the global level. The parallel performances of these two parallel multigrid methods are evaluated through numerical experiments that are performed on several clusters of PCs with different computational nodes and interconnection networks.

AB - We report on our efforts towards the design of efficient parallel hierarchical iterative methods for the solution of sparse and irregularly structured linear systems resulting from CFD applications. The solution strategies considered here share a central numerical kernel which consists in a linear multigrid by volume agglomeration method. Starting from this method, we study two parallel solution strategies. The first variant results from a direct intra-grid parallelization of multigrid operations on coarse grids. The second variant is based on an additive Schwarz domain decomposition algorithm which is formulated at the continuous level through the introduction of specific interface conditions. In this variant, the linear multigrid by volume agglomeration method is used to approximately solve the local systems obtained at each iteration of the Schwarz algorithm. As a result, the proposed hybrid domain decomposition/multigrid method can be viewed as a particular form of parallel multigrid in which multigrid acceleration is applied on a subdomain basis, these local calculations being coordinated by an appropriate domain decomposition iteration at the global level. The parallel performances of these two parallel multigrid methods are evaluated through numerical experiments that are performed on several clusters of PCs with different computational nodes and interconnection networks.

KW - computational fluid dynamics (CFD)

KW - domain decomposition method

KW - multigrid method

KW - parallel computing

KW - triangular meshes

UR - http://www.scopus.com/inward/record.url?scp=2442648022&partnerID=8YFLogxK

UR - https://www.sciencedirect.com/journal/parallel-computing

U2 - 10.1016/j.parco.2004.03.002

DO - 10.1016/j.parco.2004.03.002

M3 - Article

VL - 30

SP - 503

EP - 525

JO - Parallel Computing

JF - Parallel Computing

SN - 0167-8191

IS - 4

ER -