Application of a Preconditioned Chebyshev Basis Communication-Avoiding Conjugate Gradient Method to a Multiphase Thermal-Hydraulic CFD Code.

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 PCBCG method is 1.38x and 1.17x faster than the P-CG and P-CACG methods at 2,000 processors, respectively.