## Geometric Mesh Partitioning: Implementation and Experiments

Citations: | 102 - 19 self |

### BibTeX

@MISC{Gilbert_geometricmesh,

author = {John R. Gilbert and Gary L. Miller and Shang-Hua Teng},

title = { Geometric Mesh Partitioning: Implementation and Experiments},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

We investigate a method of dividing an irregular mesh into equal-sized pieces with few interconnecting edges. The method’s novel feature is that it exploits the geometric coordinates of the mesh vertices. It is based on theoretical work of Miller, Teng, Thurston, and Vavasis, who showed that certain classes of “well-shaped” finite element meshes have good separators. The geometric method is quite simple to implement: we describe a Matlab code for it in some detail. The method is also quite efficient and effective: we compare it with some other methods, including spectral bisection.

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Citation Context ...on the surface of a sphere in d + 1-space. If the mesh elements are well-shaped in a suitable sense, the theoretical algorithm provides a strong guarantee on the quality of the partition it generates =-=[34, 35, 41]-=-. In practice, our implementation produces partitions that are better than the theoretical guarantees and are competitive with those produced by other modern methods. The goal of this paper is to conv... |

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Citation Context ...ertia of the points. The idea of inertial weighting (in one form or another) has been suggested in conjuction with geometric coordinate bisection by several people [14, 42]. Gremban, Miller, and Teng =-=[23]-=- proved that one version of inertial weighting reduces the expected size of the separators in Theorem 1. We use inertial weighting (much more aggressively than the version analyzed by Gremban et al.) ... |

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Citation Context ...nds with a good C spectral code. 1 We do not mean to suggest that the geometric algorithm is the last word in mesh partitioning; several researchers have proposed refinements to spectral partitioning =-=[7, 8, 25]-=-, and some purely combinatorial methods such as Hendrickson and Leland's multilevel Kernighan-Lin [27] look very promising. However, we believe this data shows that geometric partitioning is at least ... |

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Citation Context ...nds with a good C spectral code. 1 We do not mean to suggest that the geometric algorithm is the last word in mesh partitioning; several researchers have proposed refinements to spectral partitioning =-=[7, 8, 25]-=-, and some purely combinatorial methods such as Hendrickson and Leland's multilevel Kernighan-Lin [27] look very promising. However, we believe this data shows that geometric partitioning is at least ... |

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