A new parareal waveform relaxation algorithm for time-periodic problems

Abstract

We present a new parareal waveform relaxation algorithm for time-periodic problems which performs the parallelism both in sub-systems and in time. The new parareal waveform relaxation algorithm only needs to solve an initial-value coarse problem in each iteration instead of the periodic coarse problem in the classical parareal waveform relaxation algorithm. The convergence result of the new parareal waveform relaxation algorithm is then proved with a linear bound at most on the convergence factor. Numerical experiments including some parallel experiments illustrate our analysis and the effectiveness of the new parareal waveform relaxation algorithm finally.