Performance evaluation of a modified communication-avoiding generalized minimal residual method on many core platforms

Idomura, Yasuhiro   ; Ina, Takuya*; Mayumi, Akie ; Yamada, Susumu  ; Matsumoto, Kazuya*; Asahi, Yuichi*   ; Imamura, Toshiyuki*

We propose a modified communication-avoiding generalized minimal residual (CA-GMRES) method, which reduces both computation and memory access by 30% with keeping the same CA property as the original CA-GMRES method. These numerical properties, less communication and computation with higher arithmetic intensity, are promising features for future exascale machines with limited memory and network bandwidths. The modified CA-GMRES method is applied to a large scale non-symmetric matrix in an implicit solver of the gyrokinetic toroidal five dimensional Eulerian code GT5D, and its performance is estimated on the Oakforest-PACS (KNL). The numerical experiment shows that compared with the generalized conjugate residual method, computing kernels are accelerated by 1.5x, and the cost of data reduction communication is reduced from 12.5% to 1% of the total cost at 1,280 nodes.