Parallel implementation of Runge-Kutta integrators with low storage requirements

Abstract

This paper considers the parallel solution of large systems of ordinary differential equations (ODEs) which possess a special access pattern by explicit Runge-Kutta (RK) methods. Such systems may arise, for example, from the semi-discretization of partial differential equations (PDEs). We propose an implementation strategy based on a pipelined processing of the stages of the RK method that does not impose restrictions on the choice of coefficients of the RK method. This approach can be implemented with low storage while still allowing efficient step control by embedded solutions. © 2009 Springer.