Parallel spherical harmonic transforms on heterogeneous architectures (graphics processing units/multi-core CPUs)

摘要

Spherical harmonic transforms (SHT) are at the heart of many scientific and practical applications rangingrnfrom climate modelling to cosmological observations. In many of these areas, new cutting-edge sciencerngoals have been recently proposed requiring simulations and analyses of experimental or observational datarnat very high resolutions and of unprecedented volumes. Both these aspects pose formidable challenge forrnthe currently existing implementations of the transforms. This paper describes parallel algorithms for computingrnSHT with two variants of intra-node parallelism appropriate for novel supercomputer architectures,rnmulti-core processors and Graphic Processing Units (GPU). It also discusses their performance, alone andrnembedded within a top-level, Message Passing Interface-based parallelisation layer ported from the S~2HATrnlibrary, in terms of their accuracy, overall efficiency and scalability. We show that our inverse SHT run onrnGeForce 400 Series GPUs equipped with latest Compute Unified Device Architecture architecture (Fermi)rnoutperforms the state of the art implementation for a multi-core processor executed on a current Intel Corerni7-2600K. Furthermore, we show that an Message Passing Interface/Compute Unified Device Architecturernversion of the inverse transform run on a cluster of 128 Nvidia Tesla S1070 is as much as 3 times fasterrnthan the hybrid Message Passing Interface/OpenMP version executed on the same number of quad-corernprocessors Intel Nehalem for problem sizes motivated by our target applications. Performance of the directrntransforms is however found to be at the best comparable in these cases.We discuss in detail the algorithmicrnsolutions devised for the major steps involved in the transforms calculation, emphasising those with a majorrnimpact on their overall performance and elucidates the sources of the dichotomy between the direct and therninverse operations.