Porting an aggregation-based algebraic multigrid method to GPUs

[摘要] We present a hybrid GPU-CPU version of the AGMG software, a popular algebraic multigrid (AMG) solver which implements an aggregation-based AMG method. With the new implementation, the solution stage runs on a GPU, except operations on the coarsest grid, which are executed on a CPU. To maximize the speedup, two novel %new features are introduced. On the one hand, $\ell_1$-Jacobi smoothing is combined with polynomial acceleration (or polynomial smoothing), leading to improved performance compared with standard $\ell_1$-Jacobi smoothing, while not requiring to compute eigenvalue estimates as standard polynomial smoothing does. On the other hand, besides the K-cycle used in standard AGMG, we introduce the relaxed W-cycle, which tends to combine the advantages of the K-cycle and the standard W-cycle. Numerical results show that the new implementation inherits the robustness of the original AGMG software, while bringing significant speedups on GPUs. A comparison with AmgX, a reference AMG solver from NVIDIA, suggests that the presented hybrid GPU-CPU version of AGMG is more robust and often significantly faster in the solution stage.

[学科分类] 数学（综合）

[关键词] multigrid;linear systems;iterative methods;AMG;preconditioning;parallel computing;GPU