Long Lee

Department of Mathematics
Ross Hall 212
University of Wyoming
Dept 3036, 1000 E. University Ave.
Laramie, WY 82071-3036

office phone:(307) 766-4368
fax number: (307) 766-6838
email: llee-at-uwyo-dot-edu


Ph.D. Applied Mathematics, University of Washington, Seattle, 2002

Research Interests:

Numerical analysis and mathematical modeling for fluid problems, nonlinear waves, template matching, and pattern recognition.

Publication: Google Scholar Profile ; Researchgate

* == graduate student
** == undergraduate student
  1. G. A. Braga, F. C. Fertado, Vincenzo Isaia, and L. Lee, Numerical renormalization group algorithms for self-similar solutions of partial differential equations. pre-print Download
  2. Man-Chung Yeung, Craig C. Douglas, and L. Lee, A spectral projection preconditioner for solving ill-conditioned linear systems. Journal of Computational Science, Vol 20, May 2017, pp 177-186. arXiv
  3. S. Huzurbazar, D. Kuang*, and L. Lee, Landmark-based algorithms for group average and pattern recognition. Pattern Recognition, Minior revision, Download
  4. R. Camassa, D. Kuang*, and L. Lee, A geodesic landmark shooting algorithm for template matching and its applications. SIAM Journal on Image Sciences (SIIMS), Vol. 10(1), 2017, pp 303-334. Download
  5. Y.-H. Kuo*, L. Lee, and G. Lyng, Analysis and development of compact finite difference schemes with optimized numerical dispersion relations. arXiv
  6. R. Camassa and L. Lee, A connection between the shallow-water equations and the Euler-Poincaré equations.
  7. R. Camassa, D. Kuang*, and L. Lee, Solitary waves and N-particle algorithms for a class of Euler-Poincaré equations. Studies in Applied Mathematics, Vol.137, (2016), pp 502-546. Selected in the journal's "Highlights of the Year 2016 Virtual Issue" Link Download
  8. Craig C. Douglas, L. Lee, and Man-Chung Yeung, On solving ill-conditioned linear systems. Procedia Computer Science Vol. 80, (2016) pp 1-10. arXiv
  9. D. Kuang* and L. Lee, A conservative formulation and a numerical algorithm for the double-gyre nonlinear shallow-water model, Numer. Math. Theor. Meth. Appl. Vol 8, No. 4, (2015) pp 634-650; arXiv
  10. Y. Kim**, L. Lee, and G. Lyng, The WKB approximation of semiclassical eigenvalues of the Zakharov-Shabat problem, J. Math. Phys. 55(8) (2014), 083516, arXiv
  11. L. Lee and G. Lyng, A second look at the Gaussian semiclassical soliton ensemble for the focusing nonlinear Schrödinger equation, Phys. Lett. A, 377 (2013), 1179-1188. Download
  12. R. Camassa, M. G. Forest, L. Lee, H. R. Ogrosky*, and J. Olander*, Ring-wave as a mass transport mechanism in air-driven core-annular flows, Physical Review E, v8 (6), Dec. (2012), 066305. Download
  13. L. Lee, G. Lyng, and I. Vankova**, The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schrödinger equation, Physica D, 241 (2012), 1767-1781. Download
  14. L. Lee and I. Vankova**, A class of Cartesian grid embedded boundary algorithms for incompressible flow with time-varying complex geometries, Physica D, 240 (2011), 1583-1592. Download
  15. R. Camassa, P. H. Chiu*, L. Lee, and T. W. H. Sheu, A particle method and numerical investigation of a quasi-linear partial differential equation, Commun. Pure and Appl. Analysis, 10 (2011), 1503-1512. Download
  16. R. Camassa, P. H. Chiu*, L. Lee, and T. W. H. Sheu, Viscous and inviscid regularizations in a class of evolutionary partial differential equations, J. Comp. Phys., 229, (2010), 6676-6687. Download
  17. L. Lee, A class of high-resolution methods for incompressible flows, Computers & Fluids, 39, (2010) 1022- 1032. Download
  18. P. H. Chiu*, L. Lee, and T. W. H. Sheu, A sixth-order dual preserving algorithm for the Camassa-Holm equation, J. Comput. Appl. Math. 223, (2010), 2767-2778. Download
  19. P. H. Chiu*, L. Lee, and T. W. H. Sheu, A dispersion-relation-preserving algorithm for a nonlinear
  20. shallow-water wave equation, J. Comput. Phys. 228, (2009), 8034-8052. Download
  21. R. Camassa and L. Lee, Complete integrable particle methods and the recurrence of initial states for a nonlinear shallow-water wave equation, J. Comput. Phys., 227, (2008), 7206-7221. Download
  22. R. Camassa and L. Lee, A completely integrable particle method for a nonlinear shallow-water wave equation in periodic domains, Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis, 14(S2), (2007), 1-5. Download
  23. R. Camassa, J. Huang, L. Lee, Integral and integrable algorithm for a nonlinear shallow-water wave equation, J. Comput. Phys. 216, (2006), 547-572.
  24. R. Camassa and L. Lee, Thin film dynamics in a liquid lined circular pipe, Advances in Engineering Mechanics - Reflections and Outlooks, edited by A. T. Chwang, M. H. Teng and D. T. Valentine, World Scientific Publishing, March (2006), 222-238.
  25. R. Camassa, J. Huang, and L. Lee, On a completely integrable numerical scheme for a nonlinear shallow-water wave equation, Journal of Nonlinear Mathematical Physics, 12, (2005), 146-162.
  26. L. Lee and R.J. LeVeque. An immersed interface method for the incompressible Navier-Stokes equations, SIAM Sci. Comp. 25, (2003), 832-856.
  27. H-C. Chiu, S-D. Ni, Y. T. Yeh, L. Lee, W. S. Liu, C. F. Wen, and C.C. Liu. A new strong-motion array in Taiwan: SMART-2, Terr. Atm. Ocean. Sci., 5, (1994), 463-475.