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Left-preconditioned communication avoiding CG solver for multiphase CFD code JUPITER

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

The left-preconditioned communication avoiding conjugate gradient (LP-CA-CG) method is applied to the pressure Poisson equation in the multiphase CFD code JUPITER. Two LP-CA-CG solvers with block Jacobi preconditioning and with underlap preconditioning are developed. The former is developed based on a hybrid CA approach, in which CA is applied only to global collective communications for inner product operations. The latter is a full CA approach, in which CA is applied also to local point-to-point communications in sparse matrix-vector (SpMV) operations and preconditioning. CA-SpMV requires additional computation for overlapping regions. It is shown that on the K computer, the LP-CA-CG solvers with block Jacobi preconditioning is faster, because the performance of local point-to-point communications scales well, and the convergence property becomes worse with underlap preconditioning. The LP-CA-CG solver shows good strong scaling up to 30,000 nodes.

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