Book ChapterDOI
Automatic Mesh Partitioning
Gary L. Miller,Shang-Hua Teng,William P. Thurston,Stephen A. Vavasis +3 more
- pp 57-84
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TLDR
An efficient approach to partitioning unstructured meshes that occur naturally in the finite element and finite difference methods that makes use of the underlying geometric structure of a given mesh and finds a provably good partition in random O(n) time is described.Abstract:
This paper describes an efficient approach to partitioning unstructured meshes that occur naturally in the finite element and finite difference methods. The approach makes use of the underlying geometric structure of a given mesh and finds a provably good partition in random O(n) time. It applies to meshes in both two and three dimensions. The new method has applications in efficient sequential and parallel algorithms for large-scale problems in scientific computing. This is an overview paper written with emphasis on the algorithmic aspects of the approach. Many detailed proofs can be found in companion papers.read more
Citations
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Journal ArticleDOI
Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems
TL;DR: In this paper, a multilevel version of RSB is introduced that attains about an order-of-magnitude improvement in run time on typical examples, and it is shown that RSB in its simplest form is expensive.
Journal ArticleDOI
Problem decomposition for adaptive hp finite element methods
Abani Patra,J. Tinsley Oden +1 more
TL;DR: Problem decomposition strategies for load balancing parallel computations on adaptive hp finite element discretizations are discussed in this work and a new ordering scheme for efficient recursive bisection of orderings is introduced.
Journal ArticleDOI
Fast and parallel mapping algorithms for irregular problems
TL;DR: These methods are very fast and provide good-quality mappings and are easily parallelizable, which make them useful for the parallelization of a number of irregular and adaptive applications.
Proceedings ArticleDOI
Performance evaluation of a new parallel preconditioner
TL;DR: A new class of preconditioners is developed that is based on the connectivity of the graphs corresponding to the matrices and are well-structured for parallel implementation, and outperform both diagonal scaling and incomplete Cholesky preconditionsers.
Proceedings ArticleDOI
A deterministic linear time algorithm for geometric separators and its applications
TL;DR: The deterministic algorithm hinges on the use of a new method forderiving the separator property of neighborhood systems and answers a majoralgorithmic open question posed by Miller, Teng, Thurston and Vavasis.
References
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Book
Sphere packings, lattices, and groups
TL;DR: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?
Book ChapterDOI
On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
TL;DR: This chapter reproduces the English translation by B. Seckler of the paper by Vapnik and Chervonenkis in which they gave proofs for the innovative results they had obtained in a draft form in July 1966 and announced in 1968 in their note in Soviet Mathematics Doklady.