Novel Ensemble Domain Decomposition Method for the Random Stokes-Darcy Coupled Problems with Uncertain Parameters

Date and Time

• Time：11:00 am-12:00 am
• Date： Monday, November 6, 2023
• Venue：MB441, SIP North Campus
• Language： English
• Speaker：Haibiao Zheng (East China Normal University)

Abstract

This talk presents a novel ensemble domain decomposition method for fast-solving the Stokes-Darcy coupled models with random hydraulic conductivity and body force. To address such random systems, we employ the Monte Carlo method to generate a set of independent and identically distributed deterministic model samples. In the traditional Monte Carlo method, more accurate numerical approximate require larger samples in probability space and smaller mesh size in the physical space. Then the computational cost increases significantly, which is the product of the number of samples and the computational cost of each sample, as the mesh size becomes smaller for the more accurate numerical approximate. Therefore we adopt the multi-level Monte Carlo (MLMC) method to dramatically reduce the computational cost in the probability space because of the number of samples. Furthermore, to facilitate the fast calculation of these samples, we adroitly integrate the ensemble idea with the domain decomposition method. This approach not only allows multiple linear problems to share a standard coefficient matrix but also enables easy-to-use and convenient parallel computing.

Speaker

Zheng Haibiao, School of Mathematical Sciences, East China Normal University, associate professor; assistant to the dean of Zhangjiang Institute of Mathematics, East China Normal University Branch, and deputy director of the Department of Applied Mathematics, School of Mathematical Sciences. Ph.D. from Xi'an Jiaotong University, jointly trained doctoral candidate at the University of Pittsburgh, USA, visiting scholar at the University of Cambridge, UK. Main research directions: computable modeling and high-performance algorithms for complex multi-physics problems; published more than 40 high-level academic papers in internationally renowned journals such as SIAM series, Comput. Meth. Appl. Mech. Eng., J. Comput. Phy. article, and won the second prize of Shaanxi Provincial Science and Technology Award twice (2015, 2023, second completer).