Multigrid Poisson solver for a block-structured adaptive mesh refinement method on CPU and GPU supercomputers

Onodera, Naoyuki   ; Idomura, Yasuhiro   ; Asahi, Yuichi   ; Hasegawa, Yuta   ; Shimokawabe, Takashi*; Aoki, Takayuki*

This paper presents performance studies of a multigrid (MG) Poisson solver on a block-structured adaptive mesh refinement (block-AMR) method on CPU and GPU supercomputers. The block-AMR method is efficient solutions of the nuclear reactor which is composed of complicated structures. We implement a three-stage V-cycle MG method and the calculation is accelerated by using a mixed precision techniques. For a large-scale Poisson problem with cells, the developed MG-CG method reduced the number of iterations to less than 30% and achieved 2 times speedup compared with the original preconditioned CG method on the GPU-supercomputer TSUBAME. This kind of performance studies are useful for designing advanced preconditioners in terms of robustness, computational precision, thread parallelization, and cache size on each architecture.