Semi-StructMG: A Fast and Scalable Semi-Structured Algebraic Multigrid

Abstract

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.