Regular Article
Optimal Coarsening of Unstructured Meshes

https://doi.org/10.1006/jagm.1998.0990Get rights and content

Abstract

A bounded aspect-ratio coarsening sequence of an unstructured meshM0is a sequence of meshesM1,…,Mksuch that:

  • is a bounded aspect-ratio mesh, and

  • is an approximation ofthat has fewer elements,

where a mesh is called a bounded aspect-ratio mesh if all its elements are of bounded aspect-ratio. The sequence is node-nested if the set of the nodes ofMiis a subset of that ofMi  1. The problem of constructing good quality coarsening sequences is a key step for hierarchical and multilevel numerical calculations. In this paper, we give an algorithm for finding a bounded aspect-ratio, node-nested, coarsening sequence that is of optimal size: that is, the number of meshes in the sequence, as well as the number of elements in each mesh, are within a constant factor of the smallest possible.

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    *

    E-mail:glmiller,[email protected]. Supported in part by NSF Grants CCR-9505472 and CCR-9706572.

    E-mail:[email protected]. Work done while at Carnegie Mellon University.

    E-mail:[email protected]. Supported in part by the DOE Accelerated Strategic Computing Initiative (ASCI), Center for Simulation of Advanced Rockets, an NSF CAREER award (CCR-9502540), an Alfred P. Sloan Research Fellowship. Part of the work was done while at Department of Computer Science, University of Minnesota, Minneapolis, MN 55455.

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