Numerical Algorithms

, Volume 67, Issue 3, pp 599–622 | Cite as

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

  • Bo Song
  • Yao-Lin Jiang
Original Paper


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.


Parareal algorithm Waveform relaxation Time-periodic problems Convergence analysis 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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