The convergence variability of parallel iterative solvers

Abstract

PurposeTo 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/approachThe 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.FindingsThe variability of iteration counts experienced by parallelised, element‐by‐element iterative solvers is caused by numerical precision and roundoff.Research limitations/implicationsA 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 implicationsThe authors believe that the variability in iteration count described for element‐by‐element methods presents no real difficulty to the engineering analyst.Originality/valueThe 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.