Heterogeneous sparse matrix–vector multiplication via compressed sparse row format

Sparse matrix–vector multiplication (SpMV) is one of the most important kernels in high-performance computing (HPC), yet SpMV normally suffers from ill performance on many devices. Due to performance, requires special care store and tune for a given device. Moreover, HPC facing heterogeneous hardware containing multiple different compute units, e.g., many-core CPUs GPUs. Therefore, an emerging goal has been produce formats methods that allow critical kernels, SpMV, be executed devices with portable minimal changes format method. This paper presents based CSR, named CSR-k, can tuned quickly outperforms average Intel MKL Xeon Platinum 838 AMD Epyc 7742 while still outperforming NVIDIA’s cuSPARSE Sandia National Laboratories’ KokkosKernels NVIDIA A100 V100 regular sparse matrices, i.e., matrices where number nonzeros per row variance ≤10, such as those commonly generated two three-dimensional finite difference element problems. In particular, CSR-k achieves this reordering by grouping rows into hierarchical structure super-rows super–super-rows are represented just few extra arrays pointers. its simplicity, model device, used select super-row sizes constant time.