A New AINV Preconditioner for the CG Method in Hybrid CPU-GPU Computing Environment

• Item type: Trans(1)
• 公開日: 2022-09-27
• タイトル: A New AINV Preconditioner for the CG Method in Hybrid CPU-GPU Computing Environment
• タイトル / 言語: en
• タイトル: A New AINV Preconditioner for the CG Method in Hybrid CPU-GPU Computing Environment
• 言語: eng
• キーワード / 主題Scheme: Other
• キーワード / 主題: Iterative linear solver, Conjugate gradient method, Sparse approximate inverse preconditioning, AINV preconditioner, Multi-threading, Graphics processing units
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_6501
• 資源タイプ: journal article
• 著者所属: Graduate School of Information Science and Technology, Hokkaido University
• 著者所属: Information Initiative Center, Hokkaido University
• 著者所属: Information Initiative Center, Hokkaido University
• 著者所属(英): en
• 著者所属(英): Graduate School of Information Science and Technology, Hokkaido University
• 著者所属(英): en
• 著者所属(英): Information Initiative Center, Hokkaido University
• 著者所属(英): en
• 著者所属(英): Information Initiative Center, Hokkaido University
• 著者名: Kengo, Suzuki; Takeshi, Fukaya; Takeshi, Iwashita
• 著者名(英): Kengo, Suzuki; Takeshi, Fukaya; Takeshi, Iwashita
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: In the last few decades, graphics processing units (GPUs) have been used to efficiently solve linear systems by means of preconditioned Krylov subspace methods. The preconditioner is required to have a high degree of parallelism to exploit the potential of GPUs for massive data processing. An approximate inverse (AINV) preconditioner is suitable for GPU implementation because its preconditioning operations mainly consist of sparse matrix-vector multiplication. However, an AINV algorithm, the algorithm to construct the AINV preconditioner, usually requires more time than construction algorithms for other preconditioners, such as the ILU/IC factorization. Therefore, it is necessary to improve the AINV algorithm to make AINV preconditioning more attractive. In this study, we propose a new version of the AINV algorithm: the SD-AINV algorithm, by introducing a statically defined approximation based on nonzero element positions of a coefficient matrix. The SD-AINV algorithm is expected to run faster than the AINV algorithm because the approximation reduces the computational cost of the AINV algorithm. In addition, the approximation enables parallel implementations of the SD-AINV algorithm using nodal/block multi-color ordering. Numerical experiments show that the SD-AINV algorithm constructs the preconditioner faster than the conventional AINV algorithm without significantly degrading the performance of the preconditioned conjugate gradient method.; ------------------------------; This is a preprint of an article intended for publication Journal of; Information Processing(JIP). This preprint should not be cited. This; article should be cited as: Journal of Information Processing Vol.30(2022) (online); ------------------------------
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: In the last few decades, graphics processing units (GPUs) have been used to efficiently solve linear systems by means of preconditioned Krylov subspace methods. The preconditioner is required to have a high degree of parallelism to exploit the potential of GPUs for massive data processing. An approximate inverse (AINV) preconditioner is suitable for GPU implementation because its preconditioning operations mainly consist of sparse matrix-vector multiplication. However, an AINV algorithm, the algorithm to construct the AINV preconditioner, usually requires more time than construction algorithms for other preconditioners, such as the ILU/IC factorization. Therefore, it is necessary to improve the AINV algorithm to make AINV preconditioning more attractive. In this study, we propose a new version of the AINV algorithm: the SD-AINV algorithm, by introducing a statically defined approximation based on nonzero element positions of a coefficient matrix. The SD-AINV algorithm is expected to run faster than the AINV algorithm because the approximation reduces the computational cost of the AINV algorithm. In addition, the approximation enables parallel implementations of the SD-AINV algorithm using nodal/block multi-color ordering. Numerical experiments show that the SD-AINV algorithm constructs the preconditioner faster than the conventional AINV algorithm without significantly degrading the performance of the preconditioned conjugate gradient method.; ------------------------------; This is a preprint of an article intended for publication Journal of; Information Processing(JIP). This preprint should not be cited. This; article should be cited as: Journal of Information Processing Vol.30(2022) (online); ------------------------------
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AA11833852
• 書誌情報: 情報処理学会論文誌コンピューティングシステム（ACS）; 巻 15, 号 2, 発行日 2022-09-27
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 1882-7829
• 出版者 / 言語: ja
• 出版者: 情報処理学会