TY - JOUR
T1 - Novel Partitioned Time-Stepping Algorithms for Fast Computation of Random Interface-Coupled Problems with Uncertain Parameters
AU - Sun , Yizhong
AU - Wang , Jiangshan
AU - Zheng , Haibiao
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 145
EP - 180
PY - 2024
DA - 2024/02
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2023-0109
UR - https://global-sci.org/intro/article_detail/nmtma/22914.html
KW - Scalar auxiliary variable, ensemble algorithm, random interface-coupled problems, implicit-explicit partitioned method, data-passing partitioned method.
AB - <p style="text-align: justify;">The simulation of multi-domain, multi-physics mathematical models with
uncertain parameters can be quite demanding in terms of algorithm design and computation costs. Our main objective in this paper is to examine a physical interface
coupling between two random dissipative systems with uncertain parameters. Due
to the complexity and uncertainty inherent in such interface-coupled problems, uncertain diffusion coefficients or friction parameters often arise, leading to considering random systems. We employ Monte Carlo methods to produce independent
and identically distributed deterministic heat-heat model samples to address random systems, and adroitly integrate the ensemble idea to facilitate the fast calculation of these samples. To achieve unconditional stability, we introduce the scalar
auxiliary variable (SAV) method to overcome the time constraints of the ensemble
implicit-explicit algorithm. Furthermore, for a more accurate and stable scheme,
the ensemble data-passing algorithm is raised, which is unconditionally stable and
convergent without any auxiliary variables. These algorithms employ the same coefficient matrix for multiple linear systems and enable easy parallelization, which
can significantly reduce the computational cost. Finally, numerical experiments are
conducted to support the theoretical results and showcase the unique features of the
proposed algorithms.</p>