Diagonal Implicitly Iterated Runge Kutta Methods on Distributed Memory Multiprocessors

We investigate the parallel implementation of the diagonal implicitly iterated Runge Kutta DIIRK method an iteration method based on a predictor corrector scheme This method is appropriate for the solution of sti systems of ordinary di erential equations ODEs and provides embedded formulae to control the stepsize We discuss di erent strate gies for the implementation of the DIIRK method on distributed memory multiprocessors which mainly di er in the order of independent computations and the data distribution In particular we consider a consecutive implementation that executes the steps of each cor rector iteration in sequential order and distributes the resulting equation systems among all available processors and a group implementation that executes the steps in parallel by independent groups of processors The performance of these implementations depends on the right hand side of the ODE system For sparse functions the group implementation is superior and achieves medium range speedup values For dense functions the consecutive implementation is better and achieves good speedup values