Applied Mathematics Seminar: New optimized Robin-Robin domain decomposition methods using Krylov solvers for the Stokes-Darcy system


10:00 AM - 11:30 AM



  • Time: 10.00 am-11.30 am
  • Date: Monday, January 8, 2024
  • Venue: MB441
  • Speaker: Prof. Xiaoming He (Missouri University of Science and Technology)


In this presentation, we design optimized Schwarz domain decomposition algorithms to accelerate the Krylov type solution for the Stokes-Darcy system. We use particular solutions of this system on a circular geometry to analyze the iteration operator mode by mode. We introduce a new optimization strategy of the so-called Robin parameters based on a specific linear relation between these parameters, using the min-max and the expectation minimization approaches. Moreover, we use a Krylov solver to deal with the iteration operator and accelerate this new optimized domain decomposition algorithm. Several numerical experiments are provided to validate the effectiveness of this new method.


Dr. Xiaoming He received his B. S. in Computational Mathematics from Sichuan University in 2002, his M.S. Computational Mathematics from Sichuan University in 2005, and his Ph.D. in Mathematics from Virginia Tech in 2009. After that, he joined Department of Scientific Computing at Florida State University as a postdoctoral research associate. In 2010 he joined Department of Mathematics and Statistics at Missouri University of Science and Technology as a tenure-track assistant professor. He was promoted to tenured associate professor in 2016 and full professor in 2021. His research interests include interface problems, computational fluid dynamics, computational plasma physics, finite element methods, various decoupling methods, data assimilation, stochastic PDEs, control problems, etc. Interdisciplinary collaboration with various engineering areas plays a key role in his research. In 2018 he was awarded Humboldt Research Fellowship for Experienced Researchers. He is a managing editor of International Journal of Numerical Analysis & Modeling. He is also the founding president of SIAM Central States Section and the organizing committee chair of the first two annual meetings of SIAM Central States Section. Since 2019, he has been on the steering committee of Midwest Numerical Analysis Day. Since 2021, he has been on the SIAM Committee on Programs and Conferences and a Faculty Fellow to Vice Chancellor of Research at Missouri S&T.
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