Geometric Mesh Partitioning: Implementation and Experiments
TL;DR: A method of dividing an irregular mesh into equal-sized pieces with few interconnecting edges is investigated, based on theoretical work of Miller, Teng, Thurston, and Vavasis, who showed that certain classes of "well-shaped" finite-element meshes have good separators.
read more
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 \sc 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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
•Book
Iterative Methods for Sparse Linear Systems
Yousef Saad
- 01 Apr 2003
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
George Karypis,Vipin Kumar +1 more
TL;DR: This work presents a new coarsening heuristic (called heavy-edge heuristic) for which the size of the partition of the coarse graph is within a small factor of theSize of the final partition obtained after multilevel refinement, and presents a much faster variation of the Kernighan--Lin (KL) algorithm for refining during uncoarsening.
Recent Advances in Graph Partitioning
Aydin Buluc,Henning Meyerhenke,Ilya Safro,Peter Sanders,Christian Schulz +4 more
- 01 Nov 2016
TL;DR: In this article, the authors survey recent trends in practical algorithms for balanced graph partitioning, point to applications, and discuss future research directions, and present a survey of the most popular algorithms.
Parallel sparse matrix-vector and matrix-transpose-vector multiplication using compressed sparse blocks
Aydin Buluc,Jeremy T. Fineman,Matteo Frigo,John R. Gilbert,Charles E. Leiserson +4 more
- 11 Aug 2009
TL;DR: In this article, a storage format for sparse matrices, called compressed sparse blocks (CSB), is introduced, which allows both Ax and A,x to be computed efficiently in parallel, where A is an n×n sparse matrix with nnzen nonzeros and x is a dense n-vector.
How Good is Recursive Bisection
Horst D. Simon,Shang-Hua Teng +1 more
TL;DR: It is shown that for some important classes of graphs that occur in practical applications, such as well-shaped finite-element and finite-difference meshes, RB is within a constant factor of the optimal one "almost always."
264
References
An efficient heuristic procedure for partitioning graphs
Brian W. Kernighan,Shou-De Lin +1 more
TL;DR: A heuristic method for partitioning arbitrary graphs which is both effective in finding optimal partitions, and fast enough to be practical in solving large problems is presented.
5.5K
The design and application of upwind schemes on unstructured meshes
Timothy J. Barth,Dennis C. Jespersen +1 more
- 01 Jan 1989
TL;DR: Cell-centered and mesh-vertex upwind finite-volume schemes are developed which utilize multi-dimensional monotone linear reconstruction procedures which differ from existing algorithms (even on structured meshes).
2.4K
Partitioning sparse matrices with eigenvectors of graphs
TL;DR: In this paper, it is shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph.