Hybrid Parallel Approach of Splitting-Up Conjugate Gradient Method for Distributed Memory Multicomputers

  • Akiyoshi WakataniEmail author
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 70)


This paper describes several variants of SPCG (Splitting Up Conjugate Gradient) method suitable for parallel computing and evaluates the performance and the speed of convergence on a distributed-memory multicomputer. SP (Splitting-Up) preconditioner can be easily parallelized because other dimensions except for one dimension are independent. Among the variants, one of incomplete SPCG method, which does not carry out one of three tridiagonal matrix solvers, achieves the best performance, and this method is about 20 times faster than one-process version of the SPCG method on 32 CPU cores of the multicomputer.


Iterative methods Tridiagonal matrix solver Preconditioning 



We are grateful to Professor Tatsuo Nogi of Kyoto University for helpful discussions. I would like to express my gratitude to both professors. Tshis work was supported by JSPS KAKENHI Grant Number 18K02920. This research was also partially supported in part by MEXT, Japan.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Faculty of Informatics and IntelligenceKonan UniversityKobeJapan

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