A parareal algorithm based on waveform relaxation
Parareal algorithms are variants of multiple shooting methods and time-multigrid methods. The authors combine the known parareal and waveform relaxation (WR) techniques to develop a new parallel algorithm, which can be carried out in parallel in sub-systems and time. A sharp upper bound on errors is presented, which indicates the superlinear convergence of the algorithm. The performance of the new algorithm is optimized by balancing both methods. In addition, it is observed by numerical experiments that lower computational cost is needed than with the classical parareal algorithm to achieve the same accuracy. However, a future deferred correction strategy may promote the efficiency of the combination of the two different parallel approaches.
scientific article; zbMATH DE number 6107084