@Article{JCM-28-676,
author = {Liping He},
title = {The Reduced Basis Technique as a Coarse Solver for Parareal in Time Simulations},
journal = {Journal of Computational Mathematics},
year = {2010},
volume = {28},
number = {5},
pages = {676--692},
abstract = {<p style="text-align: justify;">In this paper, we extend the reduced basis methods for parameter dependent problems to the parareal in time algorithm introduced by Lions et al. [12] and solve a nonlinear evolutionary parabolic partial differential equation. The fine solver is based on the finite element method or spectral element method in space and a semi-implicit Runge-Kutta scheme in time. The coarse solver is based on a semi-implicit scheme in time and the reduced basis approximation in space. Offline-online procedures are developed, and it is proved that the computational complexity of the on-line stage depends only on the dimension of the reduced basis space (typically small). Parareal in time algorithms based on a multi-grids finite element method and a multi-degrees finite element method are also presented. Some numerical results are reported.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1003-m2980},
url = {http://global-sci.org/intro/article_detail/jcm/8543.html}
}