## Semicoarsening Multigrid On Distributed Memory Machines (0)

Venue: | SIAM Journal on Scientific Computing |

Citations: | 51 - 6 self |

### BibTeX

@ARTICLE{Brown_semicoarseningmultigrid,

author = {Peter N. Brown and Robert D. Falgout and Jim E. Jones and Jim and E. Jones},

title = {Semicoarsening Multigrid On Distributed Memory Machines},

journal = {SIAM Journal on Scientific Computing},

year = {},

volume = {21},

pages = {1823--1834}

}

### OpenURL

### Abstract

. This paper presents the results of a scalability study for a three dimensional semicoarsening multigrid solver on a distributed memory computer. In particular, we are interested in the scalability of the solver; how the solution time varies as both problem size and number of processors are increased. For an iterative linear solver, scalability involves both algorithmic issues and implementation issues. We examine the scalability of the solver theoretically by constructing a simple parallel model and experimentally by results obtained on a IBM SP. The results are compared with those obtained for other solvers on the same computer. 1. Introduction. This paper focuses on our work in developing a parallel solver for the linear systems arising from nite dierence, nite volume, or nite element discretizations of the diusion equation, r (Dru) + u = f; (1) on logically rectangular grids. In R n , the diusion coeÆcient D is a symmetric positive denite n n matrix and 0. We re...

### Citations

83 |
Black box multigrid
- Dendy
- 1982
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Citation Context ...bility of the method on distributed memory machines. Alternative multigrid methods which are robust for anisotropic and discontinuous coe��cients include algebraic multigrid [10], black box multig=-=rid [4]-=-, and multiple semicoarsened multigrid [9]. The rest of this paper is organized as follows. In section 2 we describe the semicoarsening multigrid algorithm. In section 3 we describe our parallel imple... |

68 |
Algebraic Multigrid (AMG
- Ruge, Stueben
- 1986
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Citation Context ... 3D problems and the scalability of the method on distributed memory machines. Alternative multigrid methods which are robust for anisotropic and discontinuous coe��cients include algebraic multig=-=rid [10]-=-, black box multigrid [4], and multiple semicoarsened multigrid [9]. The rest of this paper is organized as follows. In section 2 we describe the semicoarsening multigrid algorithm. In section 3 we de... |

59 |
Multigrid methods
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- 1987
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Citation Context ...k the sequential processing of grid levels; to reduce communications within a standard V-cycle; and to create additional, useful work for processors that would otherwise go idle on coarser grids. See =-=[7]-=- for a brief survey. In our implementation, we have not made any algorithmic changes. The parallel and serial codes produce identical numerical results. In investigating the parallel performance of th... |

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Citation Context .... In section 4 we present numerical results investigating the solver's algorithmic and implementation scalability. We compare the implementation scalability of our solver to that of ParFlow multigrid =-=[1]-=- and a simple matrix vector product. In Section 5, based on the model and numerical experiments, we present some conclusions about the scalability of the solver. 2. SMG: semicoarsening multigrid. The ... |

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Citation Context ...1]. This algorithm's parallel performance has been investigated by other authors on various parallel machines: Bandy, Dendy and Spangenberg [3] (2D and 3D results on the CM-5); Dendy, Ida and Rutledge=-=[5-=-] (2D results on the CM-2); Smith and Weiser [12](2D results on the Intel iPSC/2 hypercube). Our work diers from these previous studies in its emphasis on 3D problems and the scalability of the method... |

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Citation Context ...een investigated by other authors on various parallel machines: Bandy, Dendy and Spangenberg [3] (2D and 3D results on the CM-5); Dendy, Ida and Rutledge[5] (2D results on the CM-2); Smith and Weiser =-=[12-=-](2D results on the Intel iPSC/2 hypercube). Our work diers from these previous studies in its emphasis on 3D problems and the scalability of the method on distributed memory machines. Alternative mul... |

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Citation Context ...for constant coe��cient anisotropic problem. algorithm for harder problems involving anisotropic and discontinuous coe��cients has been demonstrated experimentally in the literature, for examp=-=le, see [2]-=-. In the rest of this paper, we assume algorithmic scalability for SMG and investigate its implementation scalability. We investigate the implementation scalability of our SMG code on the initial deli... |

5 |
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- 1998
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Citation Context ...rithmically scalable, but in our applications, special attention must be paid to the potential anisotropic and discontinuous coe��cients. Our multigrid algorithm is based on the work of Steve Scha=-=er [11]-=-. This algorithm's parallel performance has been investigated by other authors on various parallel machines: Bandy, Dendy and Spangenberg [3] (2D and 3D results on the CM-5); Dendy, Ida and Rutledge[5... |

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Some multigrid algorithms for elliptic problems on data parallel machines
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- 1998
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Citation Context ...multigrid algorithm is based on the work of Steve Schaer [11]. This algorithm's parallel performance has been investigated by other authors on various parallel machines: Bandy, Dendy and Spangenberg [=-=3-=-] (2D and 3D results on the CM-5); Dendy, Ida and Rutledge[5] (2D results on the CM-2); Smith and Weiser [12](2D results on the Intel iPSC/2 hypercube). Our work diers from these previous studies in i... |

1 |
Parallel performance of contaminate transport code on the IBM SP/2. unpublished manuscript
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Citation Context ...5 0.6 0.7 0.8 0.9 1 Number of Processors (Problem Size) o- 100x100x100 x- 75x75x75 +- 50x50x50 *- 25x25x25 Fig. 1. Scaled e��ciency as predicted by model: equation (12) andswere obtained from data=-= in [8]. -=-The value for f re ects the measured 13.5 M op rate of the relaxation routine obtained on a single processor for a problem on a 50 50 50 grid. The model suggests that the scaled e��ciency of the... |

1 |
The improved robustness of multigrid solvers based on multiple semicoarsened grids
- Naik, Rosendale
- 1993
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Citation Context ... machines. Alternative multigrid methods which are robust for anisotropic and discontinuous coe��cients include algebraic multigrid [10], black box multigrid [4], and multiple semicoarsened multig=-=rid [9]-=-. The rest of this paper is organized as follows. In section 2 we describe the semicoarsening multigrid algorithm. In section 3 we describe our parallel implementation and develop a model for predicti... |