NDLI: Left-preconditioned communication-avoiding conjugate gradient methods for multiphase CFD simulations on the K computer

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Left-preconditioned communication-avoiding conjugate gradient methods for multiphase CFD simulations on the K computer

Content Provider	ACM Digital Library
Author	Idomura, Yasuhiro Yamada, Susumu Ina, Takuya Mayumi, Akie Imamura, Toshiyuki
Abstract	The left-preconditioned communication avoiding conjugate gradient (LP-CA-CG) method is applied to the pressure Poisson equation in the multiphase CFD code JUPITER. The arithmetic intensity of the LP-CA-CG method is analyzed, and is dramatically improved by loop splitting for inner product operations and for three term recurrence operations. 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. CA-preconditiong is enabled by underlap preconditioning, which approximates preconditioning for overlapping regions by point Jacobi preconditioning. It is shown that on the K computer, the former 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 achieved higher performance than the original CG solver by reducing the cost of global collective communications by 69 percent.
Starting Page	17
Ending Page	24
Page Count	8
ISBN	9781509052226
DOI	10.1109/ScalA.2016.7
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2016-11-13
Access Restriction	Subscribed
Subject Keyword	Fluid dynamics Sparse matrices Gradient method Optimization
Content Type	Text
Resource Type	Article

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