Summary We present in this paper a comprehensive performance study of highly efficient extreme scale direct numerical simulations of secondary flows, using an optimized version of Nek5000. Our investigations are conducted on various Cray XC40 systems, using a very high‐order spectral element method. Single‐node efficiency is achieved by auto‐generated assembly implementations of small matrix multiplies and key vector‐vector operations, streaming lossless I/O compression, aggressive loop merging, and selective single precision evaluations. Comparative studies across different Cray XC40 systems at scale, Trinity (LANL), Cori (NERSC), and ShaheenII (KAUST) show that a Cray programming environment, network configuration, parallel file system, and burst buffer all have a major impact on the performance. All three systems possess a similar hardware with similar CPU nodes and parallel file system, but they have different theoretical peak network bandwidths, different OSs, and different versions of the programming environment. Our study reveals how these slight configuration differences can be critical in terms of performance of the application. We also find that with 9216 nodes (294 912 cores) on Trinity XC40 the applications sustain petascale performance, as well as 50% of peak memory bandwidth over the entire solver (500 TB/s in aggregate). On 3072 Xeon Phi nodes of Cori, we reach 378 TFLOP/s with an aggregated bandwidth of 310 TB/s, corresponding to time‐to‐solution 2.11× faster than obtained with the same number of (dual‐socket) Xeon nodes.

Many modern highly scalable scientific simulations packages rely on small matrix multiplications as their main computational engine. Math libraries or compilers are unlikely to provide the best possible kernel performance. To address this issue, we present a library which provides high performance small matrix multiplications targeting all recent x86 vector instruction set extensions up to Intel AVX-512. Our evaluation proves that speed-ups of more than 10× are possible depending on the CPU and application. These speed-ups are achieved by a combination of several novel technologies. We use a code generator which has a built-in architectural model to create code which runs well without requiring an auto-tuning phase. Since such code is very specialized we leverage just-in-time compilation to only build the required kernel variant at runtime. To keep ease-of-use, overhead, and kernel management under control we accompany our library with a BLAS-compliant frontend which features a multi-level code-cache hierarchy.