Iterative methods with mixed-precision preconditioning for ill-conditioned linear systems in multiphase CFD simulations

Ina, Takuya*; Idomura, Yasuhiro   ; Imamura, Toshiyuki*; Yamashita, Susumu   ; Onodera, Naoyuki   

A new mixed-precision preconditioner based on the iterative refinement (IR) method is developed for preconditioned conjugate gradient (P-CG) and multigrid preconditioned conjugate gradient (MGCG) solvers in a multi-phase thermal-hydraulic CFD code JUPITER. In the IR preconditioner, all data is stored in FP16 to reduce memory access, while all computation is performed in FP32. The hybrid FP16/32 implementation 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 in JUPITER. The P-CG and MGCG solvers with the new IR preconditioner show excellent strong scaling up to 8,000 nodes, and at 8,000 nodes, they are respectively accelerated up to 4.86 and 2.39 from the conventional ones on Oakforest-PACS (KNL).