Sparse matrix-vector multiplication (SpMV) is a fundamental building block for various numerical computing applications. However, most existing GPU-SpMV approaches may suffer from either long preprocessing overhead, load imbalance, format conversion, bad memory access patterns. In this paper, we proposed two new SpMV algorithms:flat andline-enhance, as well as their implementations, for GPU systems to overcome the above shortcomings. Our algorithms work directly on the CSR sparse matrix format. To achieve high performance: 1) for load balance, theflat algorithm uses non-zero splitting andline-enhance uses a mix of row and non-zero splitting; 2) memory access patterns are designed for both algorithms for data loading, storing and reduction steps; and 3) an adaptive approach is proposed to select appropriate algorithm and parameters based on matrix characteristics.

Summary The performance of sparse stiffness matrix‐vector multiplication is essential for large‐scale structural mechanics numerical simulation. Compressed sparse row (CSR) is the most common format for storing sparse stiffness matrices. However, the high sparsity of the sparse stiffness matrix makes the number of nonzero elements per row very small. Therefore, the CSR‐scalar algorithm, light algorithm, and HOLA algorithm in the calculation will cause some threads in the GPU to be in idle state, which will not only affect the computing performance but also waste computing resources. In this article, a new algorithm, CSR‐vector row, is proposed for fine‐grained computing optimization based on the AMD GPU architecture on heterogeneous supercomputers. This algorithm can set a vector to calculate a row based on the number of nonzero elements of the stiffness matrix. CSR‐vector row has efficient reduce operations, deep memory access optimization, better memory access, and calculation overlapping kernel function configuration scheme. The access bandwidth of the algorithm on AMD GPU is more than 700 GB/s. Compared with CSR‐scalar algorithm, the parallel efficiency of CSR‐vector row is improved by 7.2 times. And floating‐point computing performance is 41%–95% higher than that of light algorithm and HOLA algorithm. In addition, CSR‐vector row is used to calculate the examples from CFD, electromagnetics, quantum chemistry, power network, and semiconductor process, the memory access bandwidth and double floating‐point performance are also improved compared with rocSPARSE‐CSR‐vector.