勷勤数学•专家报告

题      目：A robust preconditioner for Darcy flow in high contrast porous media

报  告  人：Eric Chung (钟子信)   教授  (邀请人：钟柳强 )

                                    香港中文大学

时      间：6月20日  11：00-12：00

地     点：数学院西楼二楼会议室

报告人简介:

       钟子信 (Eric T. Chung) , 香港中文大学教授, 数学系副主任。在加州大学洛杉矶分校获得博士学位，2017年获得香港数学学会青年学者奖, 2022 年获得ICCM数学银奖。研究兴趣为间断Galerkin方法、计算波传播问题、多尺度模型约化、区域分解方法和反问题等，已在SIAM系列刊物，JCP，CMAME, JSC等国际知名刊物上发表百余篇学术论文，目前担任Journal of Computational and Applied Mathematics, Computers & Mathematics with Applications, Mathematics and Computers in Simulation等多个国际学术期刊的编委。

摘      要：

       In this talk, we present a two-level overlapping domain decomposition preconditioner for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite element method for discretizing the partial differential equation by Darcy’s law with the no-flux boundary condition and is then followed by a velocity elimination technique to yield a linear algebraic system with only unknowns of pressure. Then, our main objective is to design a robust and efficient domain decomposition preconditioner for this system, which is accomplished by engineering a multiscale coarse space that is capable of characterizing high-contrast features of the permeability field. A generalized eigenvalue problem is solved in each non-overlapping coarse element in a communication-free manner to form the global solver, which are accompanied by local solvers originated from additive Schwarz methods but with a non-Galerkin discretization to derive the two-level preconditioner. We provide a rigorous analysis indicating that the condition number of the preconditioned system could be bounded above with several assumptions. Extensive numerical experiments with various types of three-dimensional high-contrast models are exhibited.

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