Dynamic Iterations for the Solution of Ordinary Differential Equations on Multicore Processors

In the past few years, there has been a trend of providing increased computing power through greater number of cores on a chip, rather than through higher clock speeds. In order to exploit the available computing power applications need to be parallelized efficiently We consider the solution of Ordinary Differential Equations (ODE) on multicore processors. Conventional parallelization strategies distribute the state space amongst the processors, and are efficient only when the state space of the ODE system is large. However users of a desktop system with multicore processors may wish to solve small ODE systems. Dynamic iterations, parallelized along the time domain, appear promising for such applications. However they have been of limited usefulness because of their slow convergence. They also have a high memory requirement when the number of time steps is large. We propose a hybrid method that combines conventional sequential ODE solvers with dynamic iterations. We show that it has better convergence and also requires less memory. Empirical results show a factor of two to four improvement in performance over an equivalent conventional solver on a single node. The significance of this paper lies in proposing a new method that can enable small ODE systems, possibly with long time spans, to be solved faster on multicore processors.