Variations on algebraic recursive multilevel solvers (ARMS) for the solution of CFD problems

Yousef Saad, Azzeddine Soulaimani, Ridha Touihri

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This paper presents results using preconditioners that are based on a number of variations of the Algebraic Recursive Multilevel Solver (ARMS). ARMS is a recursive block ILU factorization based on a multilevel approach. Variations presented in this paper include approaches which incorporate inner iterations, and methods based on standard reordering techniques. Numerical tests are presented for three-dimensional incompressible, compressible and magneto-hydrodynamic (MHD) problems.

Original languageEnglish (US)
Pages (from-to)305-327
Number of pages23
JournalApplied Numerical Mathematics
Issue number2-3
StatePublished - Nov 2004

Bibliographical note

Funding Information:
The work of Azzeddine Soulaimani and Rida Touihri has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Yousef Saad acknowledges support from the Army Research Office under contract DA/DAAD19-00-1-0485, the NSF under grants ACI-0305120, INT-0003274, and the Minnesota Supercomputing Institute. The authors would like to thank Masha Sosonkina for her help in comparing ARMS with the Algebraic Multigrid method (AMG) on the IBM SP.


  • ARMS
  • Algebraic multilevel iterations
  • Compressible
  • Flexible GMRES
  • ILUT
  • Incompressible
  • MHD flows
  • Preconditioners


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