- PhD, Applied Mathematics, University ofWashington (1994)
- MA, Applied Mathematics, University ofWashington (1991)
- MA, Mathematics, Nanjing Normal University (1988)
- BA, Mathematics, Nanjing Normal University(1982)
- 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.
- On convergence of the immersed boundary method for elliptic interface problems, Zhilin Li, Math. Of Comp.,84 (2015), 1169-1188
- 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
- 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.
- 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.
- 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
- A fast iterative algorithm for elliptic interface problems. SIAM J. Numer. Anal. 35:230--254, 1998.
- New Cartesian grid methods for interface problems using the finite element formulation, NumerischeMathematik, 96:61-98, 2003, with T. Lin, and X. Wu.
- An Augmented Cartesian Grid Method for Stokes-Darcy Fluid Structure Interactions, Volume 106, Issue 7, Pages 556–575, 2016
- 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.
- 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
- Junior Faculty Enhancement Award, 1997. Oak Ridge Associated Universities, USA
- Boeing Excellence Award. 1991. University of Washington, Seattle,
- Endowed Professor from Jiangsu Province, 2011-2014, China.
Advisor to Confucius’s Institute at NCSU/NNU