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Communication-avoiding Krylov solvers for extreme scale nuclear CFD simulations

Idomura, Yasuhiro; Ina, Takuya*; Ali, Y.*; Imamura, Toshiyuki*

A new communication avoiding (CA) Krylov solver with a FP16 (half precision) preconditioner is developed for a semi-implicit finite difference solver in the Gyrokinetic Toroidal 5D full-f Eulerian code GT5D. In the solver, the bottleneck of global collective communication is resolved using a CA-Krylov subspace method, while the number of halo data communication is reduced by improving the convergence property using the FP16 preconditioner. The FP16 preconditioner is designed based on the physics properties of the operator and is implemented using the new support for FP16 SIMD operations on A64FX. The solver is ported on Fugaku (A64FX) and Summit (V100), which respectively show $$sim$$63x and $$sim$$29x speedups in socket performance compared to the conventional non-CA Krylov solver on JAEA-ICEX (Haswell).

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