计算与应用讨论班

报告题目：Robust Preconditioners for Multiphysics Problems in Brain Mechanics

报告人：Xiaozhe Hu（Tufts University）

时间：2026年04月15日（星期三），15:00-17:00

地点：海纳苑2幢205

摘要：We aim to develop reliable simulations of biophysical processes in the brain, such as blood flow and metabolic waste clearance, which involve interface-driven multiphysics problems coupled across dimensions. However, the complexity of interface coupling often degrades the performance of standard numerical methods. To address this, we design parameter-robust preconditioners within the operator preconditioning framework, specifically tailored for these multiphysics problems. Our approach integrates rational approximations for fractional operators, deflation techniques to handle near-kernel spaces, and specialized multigrid methods to enforce interface constraints. We establish theoretical guarantees for the parameter-robustness of these preconditioners and validate their effectiveness through numerical experiments. The results demonstrate the scalability and practical applicability of our methods in complex, real-world scenarios.

报告人简介：Xiaozhe Hu is a Professor in the Department of Mathematics at Tufts University. He received his Ph.D. in Computational Mathematics from Zhejiang University in 2009. He conducted a year of postdoctoral research at the Beijing International Center for Mathematical Research and then became a postdoctoral fellow in the Department of Mathematics at Pennsylvania State University in 2010. He served as a Research Assistant Professor at Penn State before joining Tufts in 2014.

Hu's primary research interests are in numerical analysis and scientific computing, with an emphasis on the development, analysis, and implementation of numerical algorithms for solving partial differential equations and graph problems arising from different applications, such as multiphase flow in porous media, magnetohydrodynamics, bioinformatics, and quantum computing. He has published nearly 100 articles in top-tier journals and serves as an Associate Editor for the SIAM Journal on Scientific Computing.  

His algorithms have been used by commercial companies such as NVIDIA, China National Offshore Oil Company, and PetroChina. In 2016, his work received the Riemann-Liouville Award at the International Conference on Fractional Differentiation and Its Applications, and his algorithm was named a Best Performer in the Disease Module Identification DREAM Challenges. He was a plenary speaker at the 24th International Conference on Domain Decomposition Methods in 2017 and the 13th International Conference on Large-Scale Scientific Computations in 2021. His research has been supported by the U.S. Department of Energy and the National Science Foundation.

联系人：李雨文（liyuwen@zju.edu.cn）