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Onodera, Naoyuki; Idomura, Yasuhiro; Ali, Y.*; Yamashita, Susumu; Shimokawabe, Takashi*; Aoki, Takayuki*
Proceedings of Joint International Conference on Supercomputing in Nuclear Applications + Monte Carlo 2020 (SNA + MC 2020), p.210 - 215, 2020/10
This paper presents a GPU-based Poisson solver on a block-based adaptive mesh refinement (block-AMR) framework. The block-AMR method is essential for GPU computation and efficient description of the nuclear reactor. In this paper, we successfully implement a conjugate gradient method with a state-of-the-art multi-grid preconditioner (MG-CG) on the block-AMR framework. GPU kernel performance was measured on the GPU-based supercomputer TSUBAME3.0. The bandwidth of a vector-vector sum, a matrix-vector product, and a dot product in the CG kernel gave good performance at about 60% of the peak performance. In the MG kernel, the smoothers in a three-stage V-cycle MG method are implemented using a mixed precision RB-SOR method, which also gave good performance. For a large-scale Poisson problem with 
cells, the developed MG-CG method reduced the number of iterations to less than 30% and achieved 
2.5 speedup compared with the original preconditioned CG method.
Idomura, Yasuhiro; Ina, Takuya*; Yamashita, Susumu; Onodera, Naoyuki; Yamada, Susumu; Imamura, Toshiyuki*
Proceedings of 9th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA 2018) (Internet), p.17 - 24, 2018/11
Times Cited Count：9 Percentile：90.27(Computer Science, Theory & Methods)A communication avoiding (CA) multigrid preconditioned conjugate gradient method (CAMGCG) is applied to the pressure Poisson equation in a multiphase CFD code JUPITER, and its computational performance and convergence property are compared against CA Krylov methods. In the JUPITER code, the CAMGCG solver has robust convergence properties regardless of the problem size, and shows both communication reduction and convergence improvement, leading to higher performance gain than CA Krylov solvers, which achieve only the former. The CAMGCG solver is applied to extreme scale multiphase CFD simulations with 
billion DOFs, and it is shown that compared with a preconditioned CG solver, the number of iterations is reduced to 
, and 
speedup is achieved with keeping excellent strong scaling up to 8,000 nodes on the Oakforest-PACS.
Idomura, Yasuhiro
no journal, ,
Communication-avoiding (CA) algorithms are key technologies towards extreme scale CFD simulations on future exascale machines, which are characterized by accelerated computation and relatively low communication bandwidth. In order to resolve this communication bottleneck, we developed two types of CA-based sparse matrix solvers on extreme scale nuclear simulations such as the five dimensional (5D) fusion plasma turbulence code GT5D and the 3D multi-phase thermal-hydraulic code JUPITER. One is a CA Krylov method, in which multiple basis vectors are generated and orthogonalized at once. By using this approach, one can avoid the bottleneck of All_Reduce communication, which is required at each iteration in the conventional Krylov method. The other is a CA multigrid (MG) method, in which the number of iteration or All_Reduce is reduced by improving the convergence property. In addition, MG implementation with a mixed precision approach reduces both computation and communication. By applying these CA solvers, the performances of GT5D and JUPITER were dramatically improved, and the strong scaling was extended up to the full system size of the Oakforest-PACS, which consists of 8,208 KNLs.
