## Porting an aggregation-based algebraic multigrid method to GPUs

Abdeselam El Haman Abdeselam, Artem Napov, and Yvan Notay

### Abstract

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.

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### Key words

multigrid, linear systems, iterative methods, AMG, preconditioning, parallel computing, GPU

### AMS subject classifications

65F10, 65N22, 65Y05, 65Y10

### Links to the cited ETNA articles

 [20] Vol. 37 (2010), pp. 123-146 Yvan Notay: An aggregation-based algebraic multigrid method

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