主题：Preconditioning Techniques for Numerical Solution of Incompressible Navier-Stokes Equations不可压缩Navier-Stokes方程数值解的预处理技巧

主讲人：西交利物浦大学 牛强 副教授

主持人：555000jc赌船 林一丁 讲师

时间：2023年6月24日（周六）10:00

地点：柳林校区通博楼B412会议室

主办单位：555000jc赌船科研处

主讲人简介：

Qiang Niu received the Ph.D. degree from Xiamen University, in 2008. He is currently a Senior Associate Professor with the Department of Applied Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Suzhou, China. His research interests are Numerical Linear Algebra and scientific computing. He has authored or coauthored more than 30 papers in well recognized international journals, Numerische Mathematik, Journal of Computational Physics, BIT, Applied Numerical Mathematics, etc.牛强，西交利物浦大学应用数学系副教授，2008年厦门大学数学博士毕业,研究方向：数值代数，科学计算。发表论文30多篇，包括Numerische Mathematik, Journal of Computational Physics, BIT, Applied Numerical Mathematics等。

内容提要：

Abstract: In recent years, considerable effort has been placed on developing efficient and robust methods for the incompressible Navier–Stokes equations. In this talk, we give a brief review of preconditioning methods in combination with Krylov subspace methods for solving the incompressible NS equations and present a dimensional wise splitting iteration methods and related preconditioners. The convergence of preconditioned iterative methods will be given, and the optimal choice of the relaxation parameter that leads to the best performance of the iterative method will be analyzed by Fourier Analysis. Finally, the influence of boundary conditions on the optimal choice of the parameter, the use of inner and outer iterations will be studied numerically.近年来，人们在对不可压缩 Navier-Stokes 方程的有效、稳定算法方面付出了相当大的努力。在报告中，我们简要回顾了使用预处理的 Krylov 子空间方法求解不可压缩 Navier-Stokes 方程的算法，并提出了一种按空间分裂的迭代方法和相关的预处理方法。我们证明了预处理算法的收敛性，并通过傅立叶方法分析了迭代方法最佳性能时的最佳松弛参数的选取问题。最后，我们使用数值方法研究了边界条件对最优参数选择的影响，以及内外迭代的使用策略。