Parallel multigrid methods are widely used as preconditioned for solving large sparse linear systems. Most multigrids rely on general sparse matrix formats, which prevent them from achieving optimal performance. There is an emerging trend towards semi-structured multigrids that balance flexibility with performance. However, existing libraries often fall short in terms of speed and scalability for semi-structured problems. To address these limitations, we have designed and implemented Semi-StructMG. It employs multi-dimensional coarsening to reduce complexity and simplify communication patterns. It also considers the special role of inter-block connections in smoothers and triple-matrix products to improve convergence under large-scale parallelism. We evaluated Semi-StructMG using two benchmark problems and four real-world applications from petroleum reservoir simulation, ship manufacturing, numerical weather prediction, and ocean modeling. Compared to hypre's multigrids, Semi-StructMG achieves the fastest time-to-solution across all cases, with average speedups of 5.97x, 15.2x, and 3.85x over SSAMG, Split, and BoomerAMG, respectively. Additionally, Semi-StructMG significantly improves both strong and weak scaling efficiencies in all tests. These results suggest that it can serve as an effective alternative to SSAMG and Split.

Half-precision hardware support is now almost ubiquitous. In contrast to its active use in AI, half-precision is less commonly employed in scientific and engineering computing. The valuable proposition of accelerating scientific computing applications using half-precision prompted this study. Focusing on solving sparse linear systems in scientific computing, we explore the technique of utilizing FP16 in multigrid preconditioners. Based on observations of sparse matrix formats, numerical features of scientific applications, and the performance characteristics of multigrid, this study formulates four guidelines for FP16 utilization in multigrid. The proposed algorithm demonstrates how to avoid FP16 overflow through scaling. A setup-then-scale strategy prevents FP16’s limited accuracy and narrow range from interfering with the multigrid’s numerical properties. Another strategy, recover-and-rescale on the fly, reduces the memory footprint of hotspot kernels. The extra precision-conversion overhead in mix-precision kernels is addressed by the transformation of storage formats and SIMD implementation. Two ablation experiments validate the effectiveness of our algorithm and parallel kernel implementation on ARM and X86 architectures. We further evaluate three idealized and five real-world problems to demonstrate the advantage of utilizing FP16 in a multigrid preconditioner. The average speedups are approximately 2.75x and 1.95x in preconditioner and end-to-end workflow, respectively.