Influence of locality on the scalability of method- and system-parallel explicit peer methods

Because the numerical solution of initial value problems (IVPs) of systems of ordinary differential equations (ODEs) can be computationally intensive, several parallel methods have been proposed in the past. One class of modern parallel IVP methods are the peer methods proposed by Schmitt and Weiner, some of which are publicly available in the software package EPPEER released in 2012. Since they possess eight independent stages, these methods offer natural parallelism across the method suitable for the typical numbers of CPU cores in modern multicore workstations. EPPEER is written in FORTRAN95 and uses OpenMP as parallel programming model.