Keywords:Multiphase CFD code, Krylov subspace solver, Communication avoiding algorithm
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, in which point Jacobi preconditioning approximation is applied to boundary regions, 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. It is shown that on the K computer, the former hybrid approach 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, where the LP-CA-CG solver becomes 2x faster than the original CG solver by reducing the cost of global collective communications by 69 percent.