TY - JOUR
T1 - An Efficient Iteration Based on Reduced Basis Method for Time-Dependent Problems with Random Inputs
AU - Dai , Dou
AU - Li , Qiuqi
AU - Song , Huailing
JO - CSIAM Transactions on Applied Mathematics
VL - 4
SP - 760
EP - 798
PY - 2025
DA - 2025/09
SN - 6
DO - http://doi.org/10.4208/csiam-am.SO-2024-0045
UR - https://global-sci.org/intro/article_detail/csiam-am/24502.html
KW - Reduced order model, time-dependent problems, random inputs, reduced basis, iteration method.
AB - <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>