The development of the LRnLA algorithm for cross stencil numerical schemes for the CUDA GPU model of parallelism

Abstract

Abstract This document describes the recent progress in the constructing of a 3D and time (3D1T) spatial and temporal blocking algorithm for cross stencil numerical scheme implementation. This method serves the purpose of raising the operational intensity of the memory-bound problems and increasing the performance limit at least several times compared to the algorithm without temporal blocking. The method of construction of LRnLA algorithms involves choosing the prism shape that subdivides the dependency graph of the problem into a series of tasks with prescribed dependencies between each other. The algorithm is adjusted to the GPU architecture, taking into account all available levels of parallelism. The proposed algorithm had been implemented and called DiamondCandy. The obtained efficiency in our current implementation is 59% of the limit estimated by theoretical analysis.