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Application of a preconditioned Chebyshev basis communication-avoiding conjugate gradient method to a multiphase thermal-hydraulic CFD code

前処理付チェビシェフ基底省通信共役勾配法の多相熱流体CFDコードへの適用

井戸村 泰宏; 伊奈 拓也*; 真弓 明恵; 山田 進; 今村 俊幸*

Idomura, Yasuhiro; Ina, Takuya*; Mayumi, Akie; Yamada, Susumu; Imamura, Toshiyuki*

前処理付チェビシェフ基底省通信共役勾配(P-CBCG)法を多相熱流体CFDコードJUPITERにおける圧力ポアソン方程式に適用し、8,208台のKNLプロセッサを搭載したOakforest-PACS上で計算性能と収束特性を前処理付共役勾配(P-CG)法や前処理付省通信共役勾配(P-CACG)法と比較した。P-CBCG法は収束特性のロバースト性を維持しつつ集団通信回数を削減する。このロバースト性向上により、P-CACG法と比べて一桁以上大きい省通信ステップ数を実現する。2,000プロセッサを用いた場合、P-CBCG法はP-CG法, P-CACG法と比べてそれぞれ1.38倍, 1.17倍高速であることを示した。

A preconditioned Chebyshev basis communication-avoiding conjugate gradient method (P-CBCG) is applied to the pressure Poisson equation in a multiphase thermal-hydraulic CFD code JUPITER, and its computational performance and convergence properties are compared against a preconditioned conjugate gradient (P-CG) method and a preconditioned communication-avoiding conjugate gradient (P-CACG) method on the Oakforest-PACS, which consists of 8,208 KNLs. The P-CBCG method reduces the number of collective communications with keeping the robustness of convergence properties. Compared with the P-CACG method, an order of magnitude larger communication-avoiding steps are enabled by the improved robustness. It is shown that the P-CBCG method is $$1.38times$$ and $$1.17times$$ faster than the P-CG and P-CACG methods at 2,000 processors, respectively.

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