Preconditioning Techniques for Numerical Solution of Incompressible Navier-Stokes Equations



题目:Preconditioning Techniques for Numerical Solution of Incompressible Navier-Stokes Equations

报告人:牛强 教授 单位:西交利物浦大学数学系


地点:数学院 A302     


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.


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.