Chapter

Graph Theory and Sparse Matrix Computation

Volume 56 of the series The IMA Volumes in Mathematics and its Applications pp 57-84

Automatic Mesh Partitioning

  • Gary L. MillerAffiliated withSchool of Computer Science, Carnegie Mellon University
  • , Shang-Hua TengAffiliated withPalo Alto Research Center, Xerox Corporation
  • , William ThurstonAffiliated withDepartment of Mathematics, University of California
  • , Stephen A. VavasisAffiliated withDepartment of Computer Science, Cornell University

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Abstract

This paper describes an efficient approach to partitioning unstructured meshes that occur naturally in the finite element and finite difference methods. This 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.

Keywords

Center points domain decomposition finite element and finite difference meshes geometric sampling mesh partitioning nested dissection radon points overlap graphs separators stereographic projections