Comparison of parallel implementations of Runge-Kutta solvers: Message passing vs. threads

Abstract

This chapter discusses the comparison of parallel implementations of runge-kutta (RK) solvers. The parallel solution of systems of ordinary differential equations (ODEs) by explicit RK methods, such as embedded and iterated RK methods, is discussed. Experiments with embedded and iterated RK methods on a Sun Fire SMP have shown that C/Pthreads implementations are often faster than C/MPI implementations, because the multi-broadcast operations used in the MPI implementations are more expensive than the barrier operations required in the Pthreads implementations. Though the Java implementations are slower than the C implementations, they show similar scalability. Experiments on a Cray T3E have resulted in lower speed-ups due to the slower communication network. Thus, small or medium size SMPs seem to be a more efficient environment for the execution of embedded and iterated RK methods.