### Abstract

Elliptic partial difference equations like Poisson's equation are used in many fields of application. However, the coefficientmatrix of the derived algebraic equation is large and sparse, and so its inversion is expensive. Various iterative methods are used to solve such a sparse matrix system. Although there have been many studies on solving the large sparse matrix system [1, 2, 3, 4, 5, 6, 7], there have been few reports on the implementation and performance of the iterative method with multicolor ordering. In this paper, a novel implementation technique to enhance the performance of the 2-colored SOR method is proposed, which eliminates the recursion for the standard 7-point stencil on the Cartesian grid in three dimensions. The performance of the multicolor SOR method is investigated on both a shared memory vector/parallel computer and a symmetric multiprocessor machine in a distributed memory environment.

Original language | English |
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Title of host publication | Parallel Computational Fluid Dynamics 2008 - Parallel Numerical Methods, Software Development and Applications |

Pages | 183-191 |

Number of pages | 9 |

DOIs | |

Publication status | Published - Jan 1 2011 |

Event | 20th International Series of Meetings on Parallel Computational Fluid Dynamics, CFD 2008 - Lyon, France Duration: May 19 2008 → May 22 2008 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 74 LNCSE |

ISSN (Print) | 1439-7358 |

### Other

Other | 20th International Series of Meetings on Parallel Computational Fluid Dynamics, CFD 2008 |
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Country | France |

City | Lyon |

Period | 5/19/08 → 5/22/08 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Engineering(all)
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Mathematics

### Cite this

*Parallel Computational Fluid Dynamics 2008 - Parallel Numerical Methods, Software Development and Applications*(pp. 183-191). (Lecture Notes in Computational Science and Engineering; Vol. 74 LNCSE). https://doi.org/10.1007/978-3-642-14438-7_19

**Multicolor SOR method with consecutive memory access implementation in a shared and distributed memory parallel environment.** / Ono, Kenji; Kawashima, Yasuhiro.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Parallel Computational Fluid Dynamics 2008 - Parallel Numerical Methods, Software Development and Applications.*Lecture Notes in Computational Science and Engineering, vol. 74 LNCSE, pp. 183-191, 20th International Series of Meetings on Parallel Computational Fluid Dynamics, CFD 2008, Lyon, France, 5/19/08. https://doi.org/10.1007/978-3-642-14438-7_19

}

TY - GEN

T1 - Multicolor SOR method with consecutive memory access implementation in a shared and distributed memory parallel environment

AU - Ono, Kenji

AU - Kawashima, Yasuhiro

PY - 2011/1/1

Y1 - 2011/1/1

N2 - Elliptic partial difference equations like Poisson's equation are used in many fields of application. However, the coefficientmatrix of the derived algebraic equation is large and sparse, and so its inversion is expensive. Various iterative methods are used to solve such a sparse matrix system. Although there have been many studies on solving the large sparse matrix system [1, 2, 3, 4, 5, 6, 7], there have been few reports on the implementation and performance of the iterative method with multicolor ordering. In this paper, a novel implementation technique to enhance the performance of the 2-colored SOR method is proposed, which eliminates the recursion for the standard 7-point stencil on the Cartesian grid in three dimensions. The performance of the multicolor SOR method is investigated on both a shared memory vector/parallel computer and a symmetric multiprocessor machine in a distributed memory environment.

AB - Elliptic partial difference equations like Poisson's equation are used in many fields of application. However, the coefficientmatrix of the derived algebraic equation is large and sparse, and so its inversion is expensive. Various iterative methods are used to solve such a sparse matrix system. Although there have been many studies on solving the large sparse matrix system [1, 2, 3, 4, 5, 6, 7], there have been few reports on the implementation and performance of the iterative method with multicolor ordering. In this paper, a novel implementation technique to enhance the performance of the 2-colored SOR method is proposed, which eliminates the recursion for the standard 7-point stencil on the Cartesian grid in three dimensions. The performance of the multicolor SOR method is investigated on both a shared memory vector/parallel computer and a symmetric multiprocessor machine in a distributed memory environment.

UR - http://www.scopus.com/inward/record.url?scp=78651576321&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651576321&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-14438-7_19

DO - 10.1007/978-3-642-14438-7_19

M3 - Conference contribution

AN - SCOPUS:78651576321

SN - 9783642144370

T3 - Lecture Notes in Computational Science and Engineering

SP - 183

EP - 191

BT - Parallel Computational Fluid Dynamics 2008 - Parallel Numerical Methods, Software Development and Applications

ER -