走向现代数学学术报告 - 侯江勇副教授（No. 733)

题目：Domain Decomposition Methods for the Dual-Porosity-Navier-Stokes Model

报告人：侯江勇 副教授（西北大学）

时间：2024年9月13日 14:30

地点：东海岸校区-D实209

摘要：In this talk, we propose and analyze the Dual-Porosity-Navier-Stokes model, which describes both Dual-Porosity flow and free flow (governed by Navier-Stokes equation) coupled through four interface conditions, including the Beavers-Joseph interface condition. Then we propose a domain decomposition method for efficiently solving such a large complex system. Robin boundary conditions are used to decouple the Dual-Porosity equations from the Navier-Stokes equations in the coupled system. Based on the two decoupled sub-problems, a parallel Robin-Robin domain decomposition method is constructed and then discretized by finite elements. We analyze the convergence of the domain decomposition method with the finite element discretization and investigate the effect of Robin parameters on the convergence, which also provide instructions for how to choose the Robin parameters in practice. Three cases of Robin parameters are studied, including a difficult case which was not fully addressed in the literature, and the optimal geometric convergence rate is obtained. Furthermore, optimized Schwarz methods are proposed for the dual-porosity-Stokes model and optimized Robin parameters are obtained to improve the convergence of proposed algorithms. Numerical experiments are presented to verify the theoretical conclusions, illustrate how the theory can provide instructions on choosing Robin parameters, and show the features of the proposed model and domain decomposition methods.

报告人简介：侯江勇，西北大学数学学院副教授，研究生导师。2016年在西安交通大学数学与统计学院获理学博士学位。2022年担任陕西省流体力学数学理论与计算重点实验室副主任。2021年担任陕西省计算数学学会第十届理事会常务理事。主要研究方向为油藏数值模拟、偏微分方程数值计算等。主持一项国家自然科学青年基金，一项重点项目子项目，两项省基金，参与一项国家自然科学重点项目。在SIAM J.Sci.Comput.，Comput.Methods Appl.Mech.Engrg., J. Sci.Comput., Adv. Comput. Math.等国际权威计算数学杂志发表论文。获得陕西省工业与应用数学学会第六届青年优秀论文奖一等奖和第四届青年优秀论文奖二等奖，陕西省数学会青年教师优秀论文二等奖，陕西省自然科学优秀学术论文奖三等奖。荣获西北大学2021-2022教学年度优秀教师称号。