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

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

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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