数学与统计学院学术报告[2020] 031号

(高水平大学建设系列报告384号)

报告题目: Some Algorithms for Biot Model with Applications in Brain Swelling Simulation

报告人：　 蔡明超 教授（ Morgan State University, Maryland ）

报告时间：2020年7月6日

直播平台及链接： 腾讯会议 https://meeting.tencent.com/s/hbzFDmqF7N9g 会议 ID：992 746 568

报告内容：Biot’s model has been widely used in Biomechanics, for example, brain swelling simulation and perfusion in cardiac modeling. In this talk, we present some algorithms for Biot’s model. In the first algorithm, a stabilized Finite Element discretization is applied. To solve the resulting saddle point linear systems, some preconditioners and iterative methods are proposed. In the preconditioners, the Schur complement approximation is derived by using a Fourier analysis approach. We show that these preconditioners are robust with respect to physical parameters. We also discuss a multiphysics reformulation of the Biot model. From the reformulation, the Biot model can be viewed as a generalized Stokes subproblem combining with a reaction-diffusion subproblem. A coupled algorithm and a decoupled algorithm are then devised. The approximation properties of these algorithms are investigated. As applications of these algorithms, we study brain edema under different configurations. Specifically, based on a 2D MRI data, elaborate numerical experiments are conducted to study the effects of physical parameters on brain swelling.

报告人简历：Prof. Mingchao Cai received his Phd in computational and applied math from HongKong University of Science and Technology (HKUST). Before joining Morgan State University, Maryland, he worked in several universities including TU-Dortmund and Courant Institute at Newyork University. His main interests are modeling and numerical simulations of fluid/structure problems with multiphysics, fast iterative solvers, and parallel computing.

欢迎感兴趣的师生参加！

　　　　　　　　　　　　　　　　　　　　　　　　　 数学与统计学院

　　　　　　　　　　　　　　　　　　　　　　 2020年7月2日