The Journal of Supercomputing

, Volume 71, Issue 4, pp 1345–1356 | Cite as

A scalable multisplitting algorithm to solve large sparse linear systems



In this paper, we revisit the Krylov multisplitting algorithm presented in Huang and O’Leary (Linear Algebra Appl 194:9–29, 1993) which uses a sequential method to minimize the Krylov iterations computed by a multisplitting algorithm. Our new algorithm is based on a parallel multisplitting algorithm with few blocks of large size using a parallel GMRES method inside each block and on a parallel Krylov minimization to improve the convergence. Some large-scale experiments with a 3D Poisson problem are presented with up to 8,192 cores. They show the obtained improvements compared to a classical GMRES both in terms of number of iterations and in terms of execution times.


Large sparse linear systems Multisplitting algorithm  3D Poisson problem 



The authors would like to thank Mark Bull of the EPCC his fruitful remarks and the facilities of HECToR. This work has been partially supported by the Labex ACTION project (Contract “ANR-11-LABX-01-01”).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Femto-ST InstituteUniversity of Franche ComteBesançonFrance
  2. 2.Inria Bordeaux Sud-OuestTalenceFrance

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