Applicability of dynamic selection of implementation variants of sequential iterated Runge-Kutta methods

Abstract

Iterated Runge-Kutta (IRK) methods are a class of solution methods for initial value problems (IVPs) of ordinary differential equations (ODEs). The main advantage of IRK methods is that the stages within each corrector step are independent. This provides an additional degree of parallelism as well as an additional degree of freedom in the organization of the computational structure. The performance of implementations of IRK methods strongly depends on the characteristics of the IVP and the target architecture. Therefore, it is important that an IRK solver can adapt to these characteristics, such as the coupling structure of the ODE system and parameters of the cache hierarchy. In this paper, we focus on autotuning techniques for the sequential execution of IRK methods. We present a self-adapting IRK solver, which exploits the time-stepping nature of the solution procedure to select the best implementation from a candidate pool at run-time. Runtime experiments show that this technique can successfully be applied to differently structured IVPs on different architectures.