@Article{CSIAM-AM-6-760,
author = {Dai , DouLi , Qiuqi and Song , Huailing},
title = {An Efficient Iteration Based on Reduced Basis Method for Time-Dependent Problems with Random Inputs},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2025},
volume = {6},
number = {4},
pages = {760--798},
abstract = {<p style="text-align: justify;">In this paper, we propose an efficient iterative method called RB-iteration,
based on reduced basis (RB) techniques, for addressing time-dependent problems with
random input parameters. This method reformulates the original model such that the
left-hand side is parameter-independent, while the right-hand side remains parameterdependent, facilitating the application of fixed-point iteration for solving the system.
High-fidelity simulations for time-dependent problems often demand considerable
computational resources, rendering them impractical for many applications. RB-iteration enhances computational efficiency by executing iterations in a reduced order
space. This approach results in significant reductions in computational costs. We conduct a rigorous convergence analysis and present detailed numerical experiments for
the RB-iteration method. Our results clearly demonstrate that RB-iteration achieves
superior efficiency compared to the direct fixed-point iteration method and provides
enhanced accuracy relative to the classical proper orthogonal decomposition (POD)
greedy method.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2024-0045},
url = {http://global-sci.org/intro/article_detail/csiam-am/24502.html}
}