Novel Partitioned Time-Stepping Algorithms for Fast Computation of Random Interface-Coupled Problems with Uncertain Parameters  

作　　者：Yizhong Sun Jiangshan Wang Haibiao Zheng 

机构地区：[1]School of Mathematical Sciences,East China Normal University,Shanghai,China [2]School of Mathematical Sciences,Ministry of Education Key Laboratory of Mathematics and Engineering Applications,Shanghai Key Laboratory of PMMP,East China Normal University,Shanghai,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期145-180,共36页高等学校计算数学学报（英文版）

摘　　要：The simulation of multi-domain,multi-physics mathematical models with uncertain parameters can be quite demanding in terms of algorithm design and com-putation 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,un-certain diffusion coefficients or friction parameters often arise,leading to consid-ering random systems.We employ Monte Carlo methods to produce independent and identically distributed deterministic heat-heat model samples to address ran-dom systems,and adroitly integrate the ensemble idea to facilitate the fast calcu-lation 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 co-efficient 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.

关 键 词：Scalar auxiliary variable ensemble algorithm random interface-coupled problems implicit-explicit partitioned method data-passing partitioned method 

分 类 号：O24[理学—计算数学]