Papers › A parallel-in-time method based on the Parareal algorithm and High-Order Dynamic Mode...
A parallel-in-time method based on the Parareal algorithm and High-Order Dynamic Mode Decomposition with applications to fluid simulations
Weifan Liu
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The high cost of sequential time integration is one major constraint that limits the speedup of a time-parallel algorithm like the Parareal algorithm due to the difficulty of coarsening time steps in a stiff numerical problem. To address this challenge, we develop a parallel-in-time approach based on the Parareal algorithm, in which we construct a novel coarse solver using a data-driven method based on Dynamic Mode Decomposition in place of a classic time marching scheme. The proposed solver computes an approximation of the solution using two numerical schemes of different accuracies in parallel, and apply High-Order Dynamic Mode Decomposition (HODMD) to reduce the cost of sequential computations. Compared to the original Parareal algorithm, the proposed approach allows for the construction of low-cost coarse solvers for many complicated stiff problems. We demonstrate through several numerical examples in fluid dynamics that the proposed method can effectively reduce the serial computation cost and improve the parallel speedup of long-time simulations which are hard to accelerate using the original Parareal algorithm.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections