The International Conference for High Performance Computing, Networking, Storage, and Analysis
The International Conference for High Performance Computing, Networking, Storage, and Analysis
Workshop:12th Workshop on Latest Advances in Scalable Algorithms for Large Scale Systems
Authors: Takuya Ina (RIKEN Center for Computational Science (R-CCS)), Yasuhiro Idomura (Japan Atomic Energy Agency), Toshiyuki Imamura (RIKEN Center for Computational Science (R-CCS)), and Susumu Yamashita and Naoyuki Onodera (Japan Atomic Energy Agency)
Abstract: A new mixed-precision preconditioner based on the iterative refinement (IR) method is developed for the preconditioned conjugate gradient (P-CG) solver and the multigrid preconditioned conjugate gradient (MGCG) solver in the multi-phase thermal-hydraulic CFD code JUPITER. In the IR preconditioner, mixed-precision computing is designed to avoid influences of the roundoff errors in computing ill-conditioned matrices. Linear systems are normalized within the dynamic range of FP16. All data is stored in FP16 to reduce memory access, while all computation is performed in FP32, which keeps the similar convergence property as FP32, while the computational performance is close to FP16. The developed solvers are optimized on Fugaku (A64FX), and applied to ill-conditioned matrices with 90 billion DOFs in JUPITER. The P-CG and MGCG solvers with the new IR preconditioner show excellent strong scaling up to 8,000 CPUs, where 5.7x and 3.4x speedups are respectively achieved from the conventional solvers on Oakforest-PACS (KNL).