We investigate a domain decomposed multigrid technique, termed segmental refinement, for solving general nonlinear elliptic boundary value problems. We extend the method first proposed in 1994 by analytically and experimentally investigating its complexity. We confirm that communication of traditional parallel multigrid is eliminated on fine grids, with modest amounts of extra work and storage, while maintaining the asymptotic exactness of full multigrid. We observe an accuracy dependence on the segmental refinement subdomain size, which was not considered in the original analysis. We present a communication complexity analysis that quantifies the communication costs ameliorated by segmental refinement and report performance results with up to 64K cores on a Cray XC30.


  1. multigrid
  2. parallel multigrid
  3. distributed memory multigrid
  4. segmental refinement

MSC codes

  1. 68Q25
  2. 68R10
  3. 68U05

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Information & Authors


Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: C426 - C440
ISSN (online): 1095-7197


Submitted: 30 June 2014
Accepted: 16 May 2016
Published online: 4 August 2016


  1. multigrid
  2. parallel multigrid
  3. distributed memory multigrid
  4. segmental refinement

MSC codes

  1. 68Q25
  2. 68R10
  3. 68U05



Funding Information

U.S. Department of Energy http://dx.doi.org/10.13039/100000015 : DE-AC02-05CH11231

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