Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4639622 | Journal of Computational and Applied Mathematics | 2012 | 19 Pages |
Abstract
We report a new parallel iterative algorithm for semi-linear parabolic partial differential equations (PDEs) by combining a kind of waveform relaxation (WR) techniques into the classical parareal algorithm. The parallelism can be simultaneously exploited by WR and parareal in different directions. We provide sharp error estimations for the new algorithm on bounded time domain and on unbounded time domain, respectively. The iterations of the parareal and the WR are balanced to optimize the performance of the algorithm. Furthermore, the speedup and the parallel efficiency of the new approach are analyzed. Numerical experiments are carried out to verify the effectiveness of the theoretic work.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Jun Liu, Yao-Lin Jiang,