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Coarse-grain parallelisation of multi-implicit Runge-Kutta methods
Trobec, Roman ; Orel, Bojan ; Slivnik, Boštjan
A parallel implementation for multi-implicit Runge-Kutta methods with real eigenvalues is described. The parallel method is analysed and the algorithm is devised. For the problem with ▫$d$▫ domains, ...the amount within the ▫$s$▫-stage Runge-Kutta method, associated with the solution of system, is proportional to ▫$(sd)^3$▫. The proposed parallelisation transforms the above systems to ▫$s$▫ independed sub-systems of dimension ▫$d$▫. The amount of work for the solution of such systems is proportional to ▫$sd^3$▫. The solution of ▫$d$▫ dimensional sub-systems is the most complex operation within the Runge-Kutta method. The described parallel algorithm is enabled to solve each sub-system on a separate processor or on a separate set of processors.
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