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Zhilin Li Professor


Educational Background

  • PhD, Applied Mathematics, University ofWashington (1994)
  • MA, Applied Mathematics, University ofWashington (1991)
  • MA, Mathematics, Nanjing Normal University (1988)
  • BA, Mathematics, Nanjing Normal University(1982)


Professional Experiences

  • 8/2006--present, Professor, Department of Mathematics, North Carolina State University, USA
  • 8/1997--8/2006, Assistant, Associate Professor, Department of Mathematics, North Carolina State University, USA
  • 8/1996-8/1997, Associate Professor, Department of Mathematics and Statistics, Mississippi State University, USA
  • 9/1994--8/1996, Hendrick/CAM (Computational and Applied Mathematics) Assistant
  • Professor,University of California at Los Angeles (UCLA), USA
  • 3/1982-8/1989, AssistantProfessor, Lecturer, Nanjing Normal University, China



Research Interests: Numerical analysis and scientific computing; numerical methods for partial differential equations involving free boundary and moving interface problems, and problems on irregular domains, finite difference and finite element methods; Immersed Interface Method (IIM), Immersed Finite Element Methods (IFEM), Augmented IIM and IFEM, computational fluid dynamics (CFD), and biological flows.


Research Projects: Some new novel ideas and analysis for interface, fluid structure interactions, US-NSF, 2015-2018, $250,000.


Journal Articles(selected

  1. On convergence of the immersed boundary method for elliptic interface problems, Zhilin Li, Math. Of Comp.,84 (2015), 1169-1188
  2. A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions, Z. Li, L. Xiao, Q. Cai, H. Zhao, R. Luo, Journal of Computational Physics  (2015), pp. 182-193
  3. Immersed finite elements for optimal control problems of elliptic PDEs with interfaces, Q. Zhang, K. Ito,  Z. Li, Z. Zhang,  Journal of Computational Physics, 298, 305-319, 2015.
  4. An augmented method for free boundary problems with moving contact lines. Computers and Fluids, Li, Z. L., Lai, M. C., He, G. W., and Zhao, H. K. , 39(6), 1033-1040.
  5. Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Non-homogeneous Jump Conditions, SIAM J. Numer. Anal., Vol. 46, 472-495, 2008, Y. Gong, B. Li, and Z. Li
  6. A fast iterative algorithm for elliptic interface problems.  SIAM J. Numer. Anal.  35:230--254, 1998.
  7. New Cartesian grid methods for interface problems using the finite element formulation, NumerischeMathematik, 96:61-98, 2003,  with T. Lin,  and X. Wu.
  8. An Augmented Cartesian Grid Method for Stokes-Darcy Fluid Structure Interactions, Volume 106, Issue 7, Pages 556–575, 2016
  9. Adaptive mesh refinement techniques for the immersed interface method applied to flow problems, Li, Z. L., and Song, P. (2013), Computers and Structures, 122, 249-258.
  10. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources,  SIAM J. Numer. Anal. 31:1019--1044, 1994, with R. J. LeVeque, cited by 1071.



  • The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains, SIAM Frontiers in Applied Mathematics 33, 2006, ISBN-10: 0-89871-609-8 / ISBN-13: 978-0-898716-09-2, Zhilin Li and Kazufumi Ito.  
  • Layton, A., Stockie, J., Li, Z. L., and Huang, H. X. (2012). Special issue on fluid motion driven by immersed structures preface. Communications in Computational Physics, 12(2), I-III.
  • T. Witelski, D. Ambrose, A. Bertozzi, A. Layton, Z. Li, M. Minion, Special Issue of Discrete and continuous dynamical systems. Series B, 2012; 17(4).  Fluid dynamics, Analysis, and Numerics (FAN), A conference in honor of J. Thomas Beale,
  • Moving Interface Problems and Application in Fluid Dynamics, AMS Contemporary Mathematics, Vol. 466, 2008, B-C. Khoo, Z. Li, and P. Ling, Editors.
  • Special issue of Applied Numerical Mathematics for the International Conference on Scientific Computing, Nanjing, China, June 4 -- June 8, 2005, Vol. 57, issues 5-7, 2007, Z. Li, Y. Song, and T. Tang editors.
  • Interface Problems and Methods in Biological and Physical Flows, Lecture Notes Series, Vol. 17, IMS, Singapore, World Scientific, 2008, B-C. Khoo, Z. Li, and P. Ling, Editors.
  • 1. Industrial Mathematics, SIAM Publisher, Philadelphia, ISBN O-89871-467-2, 2000, P. Gremaud, Z. Li, R. Smith, and H. Tran.
  • Numerical Analysis and Applications, Lecture Notes in Computer Sciences, LNCS 3401, Springer, 2005, Z. Li, L. Vulkov, J.Wasniewski, Editors.


Patents: Immersed Interface Method, Cubic spline interface package.


Honors and Awards

  1. Junior Faculty Enhancement Award, 1997. Oak Ridge Associated Universities, USA
  2. Boeing Excellence Award. 1991. University of Washington, Seattle,
    Washington, USA
  3. Endowed Professor from Jiangsu Province, 2011-2014, China.


Academic Title

Advisor to Confucius’s Institute at NCSU/NNU