The convergence variability of parallel iterative solvers

, and . Engineering Computations (Swansea, Wales) 23 (2): 154--165 (2006)


Purpose - 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. Design/methodology/approach - 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. Findings - 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. Originality/value - 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.

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