Siu-Long LEI 李兆隆
Associate Professor
Coordinator of Student Exchange Programs

Academic Qualification

  • Ph.D. in Mathematics, Hong Kong University of Science and Technology, Hong Kong (2009)
  • M.Sc. in Mathematics, University of Macau, Macau (2000)
  • B.Ed. in Mathematics, University of Macau, Macau (1997)

Working Experiences

  • 2016 – present: Associate Professor, University of Macau, Macau
  • 2010 – 2016: Assistant Professor, University of Macau, Macau
  • 2000 – 2010: Lecturer, University of Macau, Macau
  • 1997 – 2000: Teaching Assistant, University of Macau, Macau

Teaching

B.Sc. Courses

  1. Discrete Mathematics (MATH1000)
  2. Numerical Analysis (MATH2007)
  3. Numerical Method and Computation (CISC2002/ECEN2006)

Awards

  1. Macau Science Award, Second Prize in Natural Science, FDCT Macau, 2018 (with Prof. Haiwei Sun).
  2. Teaching Award, University of Macau, 2004.
  3. The Most Famous Teacher, FST Student Association, University of Macau, 2003.
  4. My Favorite F. S. T. Staff, FST Student Association, University of Macau, 2000.

Research

Research Interests

  • Numerical Linear Algebra
  • Numerical Methods for Differential Equations

Recent Research Projects

  1. PI: Lei Siu Long, “Fast numerical solution algorithms for solving space-fractional partial differential equations on non-uniform grid ”. University of Macau. Grant No.: MYRG-GRG2023-00181-FST-UMDF. 
  2. PI: Lei Siu Long, Co-PI: Chou Lot Kei, “Multivariate fractional partial differential equations with compression format numerical solutions”. Science and Technology Development Fund (FDCT) of Macau SAR. Grant No.: 0032/APD/2021.
  3. PI: Lei Siu Long, “Numerical solution methods for solving space-fractional diffusion equation of order less than one”. University of Macau. Grant No.: MYRG2022-00262-FST
  4. PI: Lei Siu Long, “Tensor-train format solution of fractional PDEs and its applications in options pricing”. University of Macau. Grant No.: MYRG2020-00208-FST
  5. PI: Lei Siu Long, “Fast algorithms for high-dimensional time-space fractional diffusion equations”. University of Macau. Grant No.: MYRG2018-00025-FST
  6. PI: Lei Siu Long, Co-PI: Chou Lot Kei, “A tensor train based fast algorithm for solving high-dimensional fractional partial differential equations”. Science and Technology Development Fund (FDCT) of Macau SAR. Grant No.: 048/2017/A.
  7. PI: Lei Siu Long, “Preconditioning Techniques for High-Dimensional Nonlocal Diffusion Problems”. University of Macau. Grant No.: MYRG2016-00202-FST.
  8. PI: Lei Siu Long, “Splitting Schemes for Fractional Diffusion Equations and Their Fast Algorithms”. Science and Technology Development Fund (FDCT) of Macau SAR. Grant No.: 115/2013/A3.
  9. PI: Lei Siu Long, “Second-order Accurate Numerical Methods for Anomalous Diffusion Problems and Their Fast Algorithms”. University of Macau. Grant No.: MYRG071(Y1-L2)-FST13-LSL.
  10. PI: Lei Siu Long, “Circulant Precoditioners for Fractional Diffusion Equations”. University of Macau. Grant No.: MYRG038(Y1-L1)-FST12-LSL.
  11. PI: Lei Siu Long, “Numerical Methods for Phase-Field Simulation of Two-Phase Flows”. University of Macau. Grant No.: SRG012-FST11-12T-LSL.

Selected Publications

Journal Papers (Name of students is underlined)

  1. W. Qu, Y. Y. Huang, and S. L. Lei, A fast preconditioning strategy for QSC-CN scheme of space fractional diffusion equations and its spectral analysis, Advances in Applied Mathematics and Mechanics, (2024) Accepted. 
  2. Y. Xu, S. L. Lei, and H. W. Sun, An efficient red–black skewed extrapolation cascadic multigrid method for two-dimensional Poisson equation, Computational and Applied Mathematics, 43:3 (2024). (link)
  3. S. Wu, L. K. Chou, X. Chen, and S. L. Lei, A preconditioned iterative method for coupled fractional partial differential equation in European option pricing, Open Mathematics, 21 (2023), 20230169. (link)
  4. L. Y. Sun, S. L. Lei, and H. W. Sun, Efficient finite difference scheme for a hidden-memory variable-order time-fractional diffusion equation. Computational and Applied Mathematics, 42:362 (2023). (link)
  5. Y. Y. Huang, W. Qu, and S. L. Lei, On τ-preconditioner for a novel fourth-order difference scheme of two-dimensional Riesz space-fractional diffusion equations. Computers & Mathematics with Applications, 145 (2023), pp. 124-140. (link).
  6. X. Chen, X. X. Gong, S. L. Lei, and Y. F. Sun, A preconditioned iterative method for a multi-state time-fractional linear complementary problem in option pricing. Fractal & Fractional, 7, 4, 334 (2023). (link)
  7. Y. C. Huang, L. K. Chou, and S. L. Lei, Divide-and-conquer solver in Tensor-Train format for d-dimensional time-space fractional diffusion equations, Journal of Scientific Computing, 96, 29 (2023). (link) (Matlab code for generating the TT of the initial data can be downloaded here.)
  8. Y. Y. Huang and S. L. Lei, A mixed-type circulant preconditioner for a nonlocal elastic model, East Asian Journal on Applied Mathematics, 13 (2023), pp. 791-812. (link)
  9. L. Y. Sun, S. L. Lei, H. W. Sun, and J. L. Zhang, An $\alpha$-robust fast algorithm for distributed-order time-space fractional diffusion equation with weakly singular solution, Mathematics and Computers in Simulation, 207 (2023), pp. 437-452. (link)
  10. Y. Xu, S. L. Lei, and H. W. Sun, An efficient multigrid method with preconditioned smoother for two-dimensional anisotropic space-fractional diffusion equations, Computers & Mathematics with Applications, 124 (2022), pp. 218-226. (link)
  11. L. Y. Sun, Z. W. Fang, S. L. Lei, H. W. Sun, and J. L. Zhang, A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations, Applied Mathematics and Computation, 425 (2022), 127095. (link)
  12. L. K. Chou and S. L. Lei, High dimensional Riesz space distributed-order advection-dispersion equations with ADI scheme in compression format, Electronic Research Archive, 30 (2022), pp. 1463-1476. (link)
  13. X. M. Gu, S. L. Lei, K. Zhang, Z. L. Shen, C. Wen, and B. Carpentieri, A Hessenberg-type algorithm for computing PageRank Problems, Numerical Algorithms, 89 (2022), pp. 1845-1863. (link)
  14. L. K. Chou and S.L. Lei, Finite volume approximation with ADI scheme and low-rank solver for high dimensional spatial distributed-order fractional diffusion equations, Computers and Mathematics with Applications, 89 (2021), pp. 116-126. (link).
  15. X. Chen, D. Ding, S. L. Lei, and W. F. Wang, An implicit-explicit preconditioned direct method for pricing options under regime-switching tempered fractional partial differential models, Numerical Algorithms, 87 (2021), pp. 939–965. (link).
  16. S. W. Ng, S. L. Lei, J. Lu, and Z. G. Gong, Speeding up SimRank computations by polynomial preconditioners, Applied Numerical Mathematics, 153 (2020), pp. 147-163. (link)
  17. L. K. Chou and S. L. Lei, Tensor-train format solution with preconditioned iterative method for high dimensional time-dependent space-fractional diffusion equations with error analysis, Journal of Scientific Computing, 80 (2019), pp. 1731-1763. (link)
  18. X. Chen, S. W. Deng and S. L. Lei, A robust preconditioner for two-dimensional conservative space-fractional diffusion equations on convex domains, Journal of Scientific Computing, 80 (2019), pp. 1033-1057. (link)
  19. Y. C. Huang and S. L. Lei, Fast solvers for finite difference scheme of two-dimensional time-space fractional differential equations, Numerical Algorithms, 84 (2019), pp. 37-62. (link)
  20. X. Chen, D. Ding, S. L. Lei and W. F. Wang, A fast preconditioned iterative method for two-dimensional options pricing under fractional differential models, Computers and Mathematics with Applications, 79 (2020), pp. 440-456. (link)
  21. S. L. Lei, D. Y. Fan and X. Chen, Fast solution algorithms for exponentially tempered fractional diffusion equations, Numerical Methods for Partial Differential Equations, 34 (2018), pp. 1301-1323. (link)
  22. S. L. Lei, W. F. Wang, X. Chen and D. Ding, A Fast Preconditioned Penalty Method for American Options Pricing Under Regime-Switching Tempered Fractional Diffusion Models, Journal of Scientific Computing, 75 (2018), pp. 1633-1655. (link)
  23. X. Chen, W. F. Wang, D. Ding and S. L. Lei, A fast preconditioned policy iteration method for solving the tempered fractional HJB equation governing American options valuation, Computers and Mathematics with Applications, 73 (2017), pp. 1932-1944. (link)
  24. Y. C. Huang and S. L. Lei, A fast numerical method for block lower triangular Toeplitz with dense Teoplitz blocks system with applications to time-space fractional diffusion equations, Numerical Algorithms, 76 (2017), pp. 605-616. (link)
  25. L. K. Chou and S. L. Lei, Fast ADI method for high dimensional fractional diffusion equations in conservative form with preconditioned strategy, Computers and Mathematics with Applications, 73 (2017), pp. 385-403. (link)
  26. W. Qu and S. L. Lei, On CSCS-based iteration method for tempered fractional diffusion equations, Japan Journal of Industrial and Applied Mathematics, 33 (2016), pp. 583-597. (link)
  27. S. L. Lei and Y. C. Huang, Fast algorithms for high-order numerical methods for space fractional diffusion equations, International Journal of Computer Mathematics, 94 (2017), pp. 1062-1078. (link)
  28. S. L. Lei, X. Chen and X. H. Zhang, Multilevel circulant preconditioner for high-dimensional fractional diffusion equations, East Asian Journal of Applied Mathematics, 6 (2016), pp. 109-130. (link)
  29. S. W. Vong, P. Lyu, X. Chen and S. L. Lei, High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives, Numerical Algorithms, 72 (2016), pp. 195-210. (link)
  30. Z. B. Wang, S. W. Vong and S. L. Lei, Finite difference schemes for two-dimensional time-space fractional differential equations, International Journal of Computer Mathematics, 93 (2016), pp. 578-595. (link)
  31. W. F. Wang, X. Chen, D. Ding and S. L. Lei, Circulant preconditioning technique for barrier options pricing under fractional diffusion models, International Journal of Computer Mathematics, 92 (2015), pp. 2596-2614. (link)
  32. W. Qu, S. L. Lei and S. W. Vong, A note on the stability of a second order finite difference scheme for space fractional diffusion equations, Numerical Algebra, Control and Optimization, 4 (2014), pp. 317-325. (link)
  33. W. Qu, S. L. Lei and S. W. Vong, Circulant and skew-circulant splitting iteration for fractional advection-diffusion equations, International Journal of Computer Mathematics, 91 (2014), pp. 2232-2242. (link)
  34. S. L. Lei and H. W. Sun, A circulant preconditioner for fractional diffusion equations, Journal of Computational Physics, 242 (2013), pp. 715-725. (link)
  35. S. W. Vong, Q. J. Meng, and S. L. Lei, On a discrete-time collocation method for the nonlinear Schrodinger equation with wave operator, Numerical Methods for Partial Differential Equations, 29 (2013), pp. 693-705. (link)
  36. S. L. Lei and X. P. Wang, Dripping and jetting in coflowing liquid streams, Advances in Adaptive Data Analysis, 3 (2011), pp. 269-290. (link)
  37. S. L. Lei, Adaptive method for spike solutions of Gierer-Meinhardt system on irregular domain, Discrete and Continuous Dynamical Systems – Series B, 15 (2011), pp. 651-668. (link)
  38. C. M. Wu, S. L. Lei, T. Z. Qian and X. P. Wang, Stick-slip motion of moving contact line on chemically patterned surfaces, Communications in Computational Physics, 7 (2010), pp. 403-422. (link)
  39. T. Z. Qian, C. M. Wu, S. L. Lei, X. P. Wang and P. Sheng, Modeling and simulations for molecular scale hydrodynamics of moving contact line in immiscible two-phase flows, Journal of Physics: Condensed Matter, 21 (2009), pp. 464119. (link)
  40. X. Q. Jin, S. L. Lei and Y. M. Wei, Circulant preconditioners for solving singular perturbation delay differential equations, Numerical Linear Algebra with Applications, 12 (2005), pp. 327-336. (link)
  41. X. Q. Jin, S. L. Lei and Y. M. Wei, Circulant preconditioners for solving differential equations with multi-delays, Computers and Mathematics with Applications, 47 (2004), pp. 1429-1436. (link)
  42. S. L. Lei and X. Q. Jin, BCCB preconditioners for systems of BVM-based numerical integrators, Numerical Linear Algebra with Applications, 11 (2004), pp. 25-40. (link)
  43. X. Q. Jin and S. L. Lei, Sine transform based preconditioners for solving constant-coefficient first-order PDEs, Linear Algebra and its Applications, 366 (2003), pp. 283-294. (link)
  44. F. R. Lin, X. Q. Jin and S. L. Lei, Strang-type preconditioners for solving linear systems from delay differential equations, BIT, 43 (2003), pp. 136-149. (link)
  45. S. L. Lei, K. I. Kou and X. Q. Jin, Preconditioners for ill-conditioned block Toeplitz systems with application in image restoration, East-West Journal of Numerical Mathematics, 7 (1999), pp. 175-185. (The journal now is named as Journal of Numerical Mathematics.)

Invited Editor of Special Issue

  1. D. Ding and S. L. Lei, Special issue “Application of Fractional Partial Differential Equations in Computational Finance”, Fractal and Fractional (SCIE, IF 3.577), Submission deadline: 25 February 2023.
  2. G. H. Hu, S. L. Lei, and S. W. Vong, Special issue for the 2017 workshop on computational mathematics and scientific computing, Numerical Mathematics: Theory, Methods and Applications, vol. 11 no. 4 (2018).
  3. G. H. Hu, S. L. Lei, and S. W. Vong, Special issue for the EASIAM annual conference 2016, East Asian Journal on Applied Mathematics, vol. 7 no. 4 (2017)
  4. G. H. Hu, S. L. Lei, and S. W. Vong, Special issue for the fourth workshop on numerical algebra and high performance computation, East Asian Journal on Applied Mathematics, vol. 4 no. 1 (2014).

Conference Papers

  1. S. L. Lei, M. Lao and I. Chan, Simulation on vortex effect for superconducting devices, Computational Methods in Engineering and Science – Proceedings of EPMESC X (2006), pp. 313-318. Eds: Z. Yao, M. Yuan and Y. Chen, Tsinghua University Press and Springer, 2006.
  2. S. L. Lei and X. Q. Jin, Strang-type preconditioners for solving differential-algebraic equations, NAA (2000), Lecture Notes in Computer Science, Vol. 1988, pp. 505-512, Eds.: L. Vulkov, J. Wasniewski and P. Yalamov, Springer, 2001.

Services

Professional Services

Reviewer for journals:

Journal of the Franklin Institute, SIAM Journal of Scientific Computing, BIT, Numerische Mathematik, Journal of Scientific Computing, Applied Mathematics and Computation, Journal of Applied Mathematics and Computing, East Asian Journal of Applied Mathematics, Numerical Mathematics: Theory, Methods and Applications, Journal of Computational and Applied Mathematics, Numerical Methods for Partial Differential Equations, Computer Mathematics with Applications, Mathematics and Computers in Simulation, International Journal of Computer Mathematics, Numerical Algebra, Control and Optimization, Mathematics, Japan Journal of Industrial and Applied Mathematics, Fractal and Fractional, Networks and Heterogeneous Media, Electronics, Electronic Research Archive, Photonics, Journal of Applied Analysis, Computer Modeling in Engineering & Sciences, ANZIAM, Advances in Applied Mathematics and Mechanics, Expert System, IEEE Transactions on Computer Aided Design of IC and Systems, Neurocomputing, Physica D Nonlinear Phenomena, Algorithms.

University Services

  • Affiliate Member of Chao Kuang Piu College
  • Coordinator of FST Student Exchange Program 
  • Advisor, Student Advisory Program for FST Undergraduate Students 

Community Services

  • General affairs for Macau Mathematics Society (2014 – present)
  • Member of the referee panel for the Contemporary Undergraduate Mathematical Contest of Modelling (Macau region), organized by China Society for Industrial and Applied Mathematics (2014 – present)

Professional Affiliations

  • Executive Member of East Asia Society for Industrial and Applied Mathematics (EASIAM)

Students

Master Students

  • Wei Qu (2013)
  • Xinhe Zhang (2015)
  • Xu Chen (2015)
  • Yunchi Huang (2017)
  • Ricky Lot Kei Chou (2016)
  • Daoying Fan (2016)
  • Siwen Deng (2018)
  • YuanyuanHuang (2020)
  • Xiaoxiao Cai (2021)
  • Wanna Deng (2022)
  • Shuang Wu (2022)
  • Liangshu Lin (2023)
  • Zhaotong Shi (2023)
  • Hongliang Huang (on-going)
  • Yuefan Chang (on-going)
  • Xiaolong Hu (on-going)
  • Jinghao Xi (on-going)
  • Yutong Xu (on-going)

Please contact me if you want to be my master student.

PhD Student

  • Xu Chen (2018)
  • Ricky, Lot Kei Chou (2019)
  • Yunchi Huang (2020)
  • Yuanyuan Huang (2023)
  • Yuan Xu (on-going)
  • Luyao Sun (on-going)
  • Shuang Wu (on-going)

Please contact me if you want to be my Ph.D. student.

Contact Details

Faculty of Science and Technology
University of Macau, E11
Avenida da Universidade, Taipa,
Macau, China

Room: E11-3066
Telephone: (853) 8822-4449
Fax: (853) 8822-2426
Email: sllei