Schurras: A restricted version of the overlapping schur complement preconditioner

L. I. Zhongze, Yousef Saad

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


This paper presents a preconditioner based on solving approximate Schur complement systems with the overlapping restricted additive Schwarz (RAS) methods. The construction of the preconditioner, called SchurRAS, is as simple as in the standard RAS. The communication requirements for each application of the preconditioning operation are also similar to those of the standard RAS approach. In the particular case when the degree of overlap is one, then SchurRAS and RAS involve exactly the same communication volume per step. In addition, SchurRAS has the same degree of parallelism as RAS. In some numerical experiments with a model problem, the convergence rate of the method was found to be similar to that of the multiplicative Schwarz (MS) method. The Schur-based RAS usually outperforms the standard RAS both in terms of iteration count and CPU time. For a few two-dimensional scaled problems, SchurRAS was about twice as fast as the stardard RAS on 64 processors.

Original languageEnglish (US)
Pages (from-to)1787-1801
Number of pages15
JournalSIAM Journal on Scientific Computing
Issue number5
StatePublished - 2006


  • Additive Schwarz preconditioned restricted additive Schwarz preconditioner
  • Distributed sparse linear systems
  • Domain decomposition
  • Parallel preconditioning
  • Schur complement techniques


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