Dynamic selection of implementation variants of sequential iterated runge-kutta methods with tile size sampling

• Authors: Natalia Kalinnik;Matthias Korch;Thomas Rauber
• Venue: Proceedings of the 2nd ACM/SPEC International Conference on Performance engineering
• Year: 2011

This paper describes an efficient self-adaptive procedure for iterated Runge-Kutta (IRK) methods, a class of solution methods for initial value problems (IVPs) of ordinary differential equations (ODEs). IRK methods execute a potentially large number of discrete time steps to compute the solution of the IVP. The performance of an IRK solver may strongly depend on the specific characteristics of the given IVP and the hardware architecture on which the solver is executed. To address this problem, this paper applies dynamic auto-tuning to the sequential execution of IRK methods. Auto-tuning is a promising technique to avoid time consuming and extensive manual tuning. Our self-adaptive IRK solver utilizes the time-stepping nature of the IRK method. It selects the fastest implementation variant for the given IVP on the target architecture from a candidate pool during the first time steps. Then, the fastest implementation variant is used to compute all remaining time steps. The different implementation variants in the candidate pool have been developed by modifications of the loop structure of the basic algorithm. For those implementation variants that use loop tiling, we consider different tile sizes during the auto-tuning phase to further improve the performance of the self-adaptive IRK solver. Runtime experiments demonstrate the efficiency of the self-adaptive IRK solver for different IVPs on different hardware architectures.