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.
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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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