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Analysis of a new parareal algorithm based on waveform relaxation method for time-periodic problems

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Abstract

We present a new parallel algorithm for time-periodic problems by combining the waveform relaxation method and the parareal algorithm, which performs the parallelism both in sub-systems and in time. In the new algorithm, the waveform relaxation propagator is chosen as a new fine propagator instead of the classical fine propagator. And because of the characteristic of time-periodic problems, the new parareal waveform relaxation algorithm needs to solve a periodic coarse problem at the coarse level in each iteration. The new algorithm is proved to converge linearly at most. Then the theoretic parallel efficiency of the new algorithm is also considered. Numerical experiments confirm our analysis finally.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, People’s Republic of China

    Bo Song & Yao-Lin Jiang

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  1. Bo Song
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  2. Yao-Lin Jiang
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Correspondence to Yao-Lin Jiang.

Additional information

This work was supported by the Natural Science Foundation of China (NSFC) under grant 11071192, 11371287 and the International Science and Technology (S&T) Cooperation Program of China under grant 2010DFA14700.

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Song, B., Jiang, YL. Analysis of a new parareal algorithm based on waveform relaxation method for time-periodic problems. Numer Algor 67, 599–622 (2014). https://doi.org/10.1007/s11075-013-9810-z

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  • DOI: https://doi.org/10.1007/s11075-013-9810-z

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