Scientific Programming

Scientific Programming / 2004 / Article

Open Access

Volume 12 |Article ID 175169 |

Thomas Rauber, Gudula Rünger, "Improving Locality for ODE Solvers by Program Transformations", Scientific Programming, vol. 12, Article ID 175169, 22 pages, 2004.

Improving Locality for ODE Solvers by Program Transformations

Received20 Oct 2004
Accepted20 Oct 2004


Runge-Kutta methods are popular methods for the solution of ordinary differential equations and implementations are provided by many scientific libraries. The performance of Runge-Kutta methods depends on the specific application problem to be solved, but also on the characteristics of the target machine. For processors with a memory hierarchy, the locality of data referencing pattern has a large impact on the efficiency of a program. In this paper, we describe program transformations for Runge-Kutta methods resulting in implementations with improved locality behavior for systems of ODEs. The transformations are based on properties of the solution method but are independent from the specific application problem or the specific target machine so that the resulting implementation is suitable as library function. We show that the locality improvement leads to performance gains on different recent microprocessors.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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