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Communication avoiding multigrid preconditioned conjugate gradient method for extreme scale multiphase CFD simulations

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

A communication avoiding multigrid preconditioned conjugate gradient method (CAMGCG) is applied to the pressure Poisson equation in a multiphase CFD code JUPITER, and its computational performance and convergence property are compared against the conventional Krylov methods. The CAMGCG solver has robust convergence properties regardless of the problem size, and shows both communication reduction and convergence improvement, leading to higher performance gain than CA Krylov solvers, which achieve only the former. The CAMGCG solver is applied to extreme scale multiphase CFD simulations with 90 billion DOFs, and its performance is compared against the preconditioned CG solver. In this benchmark, the number of iterations is reduced to $$sim 1/800$$, and $$sim 11.6times$$ speedup is achieved with keeping excellent strong scaling up to 8,000 nodes on the Oakforest-PACS.

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