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The convergence variability of parallel iterative solvers

Ian M. Smith (School of Mechanical, Aeronautical and Construction Engineering, University of Manchester, Manchester, UK)
Lee Margetts (Manchester Computing, University of Manchester, Manchester, UK)

Engineering Computations

ISSN: 0264-4401

Article publication date: 1 February 2006




To investigate the cause of a well‐known phenomenon associated with a range of parallel iterative solvers – the variability in the number of iterations required to achieve convergence.


The conclusions are based on extensive experiments undertaken using parallel computers. Recently published works are also used to provide additional examples of variability in iteration count.


The variability of iteration counts experienced by parallelised, element‐by‐element iterative solvers is caused by numerical precision and roundoff.

Research limitations/implications

A theoretical examination of the phenomenon may bring to light a methodology in which the iteration count could be limited to the lower end of the variable range – thus reducing solution times.

Practical implications

The authors believe that the variability in iteration count described for element‐by‐element methods presents no real difficulty to the engineering analyst.


The paper gives a detailed account of the phenomenon and is useful both to developers of parallel iterative solvers and to the analysts that use them in practice.



Smith, I.M. and Margetts, L. (2006), "The convergence variability of parallel iterative solvers", Engineering Computations, Vol. 23 No. 2, pp. 154-165.



Emerald Group Publishing Limited

Copyright © 2006, Emerald Group Publishing Limited

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