<span class="var-sub_title">Communication Avoiding Multigrid Preconditioned Conjugate Gradient Method for Extreme Scale Multiphase CFD Simulations</span> SC18 Proceedings

The International Conference for High Performance Computing, Networking, Storage, and Analysis

9th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems


Communication Avoiding Multigrid Preconditioned Conjugate Gradient Method for Extreme Scale Multiphase CFD Simulations

Authors: Yasuhiro Idomura (Japan Atomic Energy Agency)

Abstract: A communication avoiding (CA) multigrid preconditioned conjugate gradient method (CAMGCG) is applied to the pressure Poisson equation in a multiphase CFD code JUPITER, and its computational performance and convergence property are compared against CA Krylov methods. A new geometric multigrid preconditioner is developed using a preconditioned Chebyshev iteration smoother, in which no global reduction communication is needed, halo data communication is reduced by a mixed precision approach, and eigenvalues are computed using the CA Lanczos method. The CAMGCG solver has robust convergence properties regardless of the problem size, and shows both communication reduction and convergence improvement, leading to higher performance gain than CA Krylov solvers, which achieve only the former. The CAMGCG solver is applied to extreme scale multiphase CFD simulations with ~90 billion DOFs, and it is shown that compared with a preconditioned CG solver, the number of iterations, and thus, All\_Reduce is reduced to ~1/800, and ~11.6x speedup is achieved with keeping excellent strong scaling up to 8,000 KNLs on the Oakforest-PACS.

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