2017/04/23 by Gil Ariel, Hieu Nguyen, Ariel, Gil +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Mathematics and Applications #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1704.06882
openalex publication_date 2017/04/23 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
A weighted version of the parareal method for parallel-in-time computation of time dependent problems is presented. Linear stability analysis for a scalar weighing strategy shows that the new scheme may enjoy favorable stability properties with marginal reduction in accuracy at worse. More complicated matrix-valued weights are applied in numerical examples. The weights are optimized using information from past iterations, providing a systematic framework for using the parareal iterations as an approach to multiscale coupling. The advantage of the method is demonstrated using numerical examples, including some well-studied nonlinear Hamiltonian systems.