An in‐depth introduction of multi‐workgroup tiling for improving the locality of explicit one‐step methods for ODE systems with limited access distance on GPUs. (22nd September 2020) - Korch, Matthias; Werner, Tim
Summary: This article considers a locality optimization technique for the parallel solution of a special class of large systems of ordinary differential equations (ODEs) by explicit one‐step methods on GPUs. This technique is based on tiling across the stages of the one‐step method and is enabled by the special structure of the class of ODE systems considered, that is, the limited access distance . The focus of this article is on increasing the range of access distances for which the tiling technique can provide a speedup by joining the memory resources and the computational power of multiple workgroups for the computation of one tile ( multi‐workgroup tiling ). In particular, this article provides an extended in‐depth introduction and discussion of the multi‐workgroup tiling technique and its theoretical and technical foundations together with a new tuning option (mapping stride) and new experiments. The experiments performed show speedups of the multi‐workgroup tiling technique compared with traditional single‐workgroup tiling for two different Runge–Kutta methods on NVIDIAs Kepler and Volta architectures.