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 strategies 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 corrector 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 ...

• Type: Conference
• Year: 1995
• Where: PDP
• Authors: Thomas Rauber, Gudula Rünger
• Keywords: Consecutive Implementation, Distributed And Parallel Computing, Group Implementation, Implementation, PDP 1995