The performance of parallel iterative solvers

A performance model is constructed for parallel iterative numerical methods under the assumption of a message-passing computing system. Arguments are given for the fact that the speedup of parallel iterative methods is mainly influenced by the speedup at one iterative step. Using the theoretical model, it is proved why explicit iterative methods for ordinary differential equations are inefficient in implementation on distributed memory multiprocessor systems. Numerical tests on parallel and distributed computing environments confirm the correctness of the theoretical model at least in the case of iterative methods for ordinary differential equations and time-dependent partial differential equations.