Iterative Methods with Mixed-Precision Preconditioning for Ill-Conditioned Linear Systems in Multiphase CFD Simulations
TimeFriday, 19 November 20219:20am - 9:40am CST
DescriptionA 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).