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GPU optimization of matrix solvers

Ali, Y.*; Onodera, Naoyuki   ; Idomura, Yasuhiro   ; Ina, Takuya*; Imamura, Toshiyuki*

Krylov solvers can account for up to $$sim$$ 90% of the total computing cost in extreme scale nuclear CFD simulations. In order to accelerate such CFD codes, we ported the conventional Preconditioned Conjugate Gradient (PCG) and the two latest communication avoiding algorithms, the Preconditioned Chebyshev Basis communication-avoiding Conjugate Gradient (P-CBCG) and the Communication-Avoiding Generalized Minimal RESidual (CA-GMRES) methods, on to GPUs. In this talk, we discuss a trade-off between the performance portability and the performance improvement for implementations using OpenACC and CUDA, and show performance tests on the latest GPU supercomputers.

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