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Improving locality of explicit one-step methods on GPUs by tiling across stages and time steps

Title data

Korch, Matthias ; Werner, Tim:
Improving locality of explicit one-step methods on GPUs by tiling across stages and time steps.
In: Future Generation Computer Systems. Vol. 102 (2020) . - pp. 889-901.
ISSN 0167-739X
DOI: https://doi.org/10.1016/j.future.2019.07.075

Project information

Project title:
Project's official titleProject's id
Optimierungstechniken für explizite Verfahren zur GPU-beschleunigten Lösung von Anfangswertproblemen gewöhnlicher Differenzialgleichungen (OTEGO)KO 2252/3-1
Optimierungstechniken für explizite Verfahren zur GPU-beschleunigten Lösung von Anfangswertproblemen gewöhnlicher Differenzialgleichungen (OTEGO)KO 2252/3-2

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

The performance of explicit parallel methods solving large systems of ordinary differential equations (ODEs) on GPUs is often memory bound. Therefore, locality optimizations, such as kernel fusion, are desirable. This paper exploits a special property of a large class of right-hand-side (RHS) functions to enable the fusion of computations of blocks of components of dependent stages of the method. This allows the derivation of tilings of the stages not only within one time step, but also spanning several successive time steps. Our approach is based on a representation of the ODE method by a data flow graph and allows efficient GPU code with fused kernels to be generated automatically for user-defined tilings. In particular, we investigate two generalized tiling strategies, trapezoidal and hexagonal tiling, and two different partitionings, which are evaluated experimentally for several different high- and low-order Runge–Kutta (RK) methods.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: GPUs; Tiling; ODE methods; RK methods
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Computer Science > Chair Applied Computer Science II > Chair Applied Computer Science II - Univ.-Prof. Dr. Thomas Rauber
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
Date Deposited: 23 Oct 2020 08:22
Last Modified: 23 Oct 2020 08:22
URI: https://eref.uni-bayreuth.de/id/eprint/57909