再帰的構造を持つリオーダリングによるAMG-CG法の高速化

抄録

The Matrix Power Kernel (MPK) plays an important role in the Algebraic Multigrid-Conjugate Gradient (AMG-CG) method, when using the Chebyshev polynomial smoother. In this study, we propose a new kernel for the MPK, which combines a Depth-First Search (DFS)-based MPK implementation with a reordering that has a recursive structure. Our MPK implementation reduces the need for synchronization among OpenMP threads, thereby simplifying the implementation and improving the performance. Results from numerical experiments show that our method consistently reduces the cache misses and the computation time across all OpenMP thread conditions, outperforming the baseline methods. The proposed method also improves the acceleration rate of MPK.