A scalable multisplitting algorithm to solve large sparse linear systems
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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.
KeywordsLarge 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”).
- 2.Bahi JM, Contassot-Vivier S, Couturier R (2008) Parallel iterative algorithms: from sequential to grid computing, Chapman & Hall/CRC numerical analysis and scientific computing. Chapman & Hall/CRC, Boca Roton. ISBN 9781584888086Google Scholar
- 4.Brown N, Bull JM, Bethune I (2013) Solving large sparse linear systems using asynchronous multisplitting. Technical report, PRACE White paper number WP84Google Scholar
- 8.HECToR: UK National Supercomputing Service. http://www.hector.ac.uk