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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$$times$$ and 2.39$$times$$ from the conventional ones on Oakforest-PACS (KNL).

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