An Architecture-Aware Heterogeneous Multigrid Solver for Geodynamic Simulations on the New-Generation Tianhe Supercomputer

Large-scale mantle convection simulations repeatedly solve sparse velocity-pressure systems, and the multigrid velocity solver often dominates the total runtime. This paper presents an MT-3000-oriented heterogeneous multigrid solver for CitcomCU on the new-generation Tianhe supercomputer. The solver keeps the original governing equations, finite-element discretization, Uzawa iteration, and geometric multigrid framework, while redesigning the dominant kernels and data movement for the explicitly managed memory hierarchy of MT-3000. The central design is an 8-color block Gauss-Seidel smoother co-designed with ELL-like node-based storage, topology-derived neighbor indexing, AM-aware row-wise streaming, ping-pong double buffering, host-accelerator collaboration, and communication-computation overlap. These techniques expose block-level parallelism, improve locality, and reduce avoidable DMA traffic without increasing the number of multigrid cycles in the tested cases. For the Busse1993 benchmark, the optimized solver remains consistent with the original CitcomCU implementation: after 4000 time steps, the full-domain relative L2 errors are 0.47% for temperature and 2.27% for the three-component velocity vector. Compared with the unmodified production CPU-based CitcomCU baseline, the complete heterogeneous execution mode achieves system-level speedups of up to 4.91x in average multigrid-cycle time and 4.71x in average complete-Uzawa-solve time per simulation step. Weak scaling maintains 59.54% efficiency on 12,800 processes, demonstrating the effectiveness of MT-3000-specific algorithmic and data-movement redesign for matrix-based geodynamic multigrid solvers.