Parallel ILU Ordering and Convergence Relationships: Numerical Experiments

Abstract

We recently developed a parallel algorithm for computing ILU preconditioners, which was presented at Super Computing 1999. The algorithm has been shown to be highly scalable, in terms of execution time required for preconditioner factorization and application, for problems with up to 20 million unknowns running on up to 216 processors. However, since the algorithm reorders the matrix, and it is widely known that ordering can significantly affect convergence, questions were raised concerning the quality of the computed preconditioners. In this report we present experimental results demonstrating that the orderings imposed by the algorithm do not significantly degrade convergence, as long as the number of unknowns per subdomain is not too small. We report on two model problems, Poisson's equation, and a special case of the convection-diffusion equation, which other researchers have used for ordering and convergence studies. We show that convergence behavior is fairly flat as long as subdomains contain at least 512 nodes.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2000
Accession Number
ADA377210

Entities

People

  • Alex Pothen
  • David Hysom

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  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Computer Science
  • Computers
  • Convection
  • Convergence
  • Differential Equations
  • Diffusion
  • Education
  • Engineering
  • Equations
  • Graph Theory
  • Iterations
  • Linear Systems
  • Partial Differential Equations
  • Scalability
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