Professor

Biography

Prof. Leung has been with the Department of Mathematics at the Hong Kong University of Science and Technology (HKUST) since 2009. Prior to joining HKUST, he was an instructor and postdoc researcher at the University of California, Irvine. He was educated at the HKUST (B.Sc. 99'; M.Phil. 01') and the University of California, Los Angeles (Ph.D. 06', in Mathematics). His research focuses on Eulerian techniques to approximate high frequency asymptotic solutions to wave phenomena and their related inverse problems, numerical methods for interfacial motions, and variational and statistical methods for image processing. Prof. Leung is currently an associate professor of Mathematics and an associate dean of Science.

Research Interests

Numerical methods for partial differential equations and scientific computing

Teaching

• MATH4336  Introduction to Mathematics of Image Processing
• MATH4992  Capstone Project in Applied Mathematics
• MATH6911H  Reading Course: ENO and Weighted ENO Schemes

Selected Publications

  Article

1. Liouville Partial-Differential-Equation Methods for Computing 2-D Complex-Valued Eikonals in the Multivalued Sense in Attenuating Media
   • Author(s): Leung, Shing Yu; Hu, Jiangtao; Qian, Jianliang
   • Source: Geophysics, v. 87, (2), 2022
   • Year: 2021


2. Ray-Illumination Compensation for Adjoint-State First-Arrival Traveltime Tomography
   • Author(s): Hu, Jiangtao; Qian, Jianliang; Cao, Junxing; Wang, Xingjian; Wang, Huazhong; Leung, Shing Yu
   • Source: Geophysics, v. 86, (5), September 2021, p. U109-U119
   • Year: 2021


3. A Level-Set Adjoint-State Method for Transmission Traveltime Tomography in Irregular Domains
   • Author(s): Leung, Shing Yu; Qian, Jianliang; Hu, Jiangtao
   • Source: SIAM Journal on Scientific Computing, v. 43, (3), 2021, p. A2352-A2380
   • Year: 2021


4. Fast Huygens Sweeping Methods for a Class of Nonlocal Schrödinger Equations
   • Author(s): Ho, Ka Ho; Leung, Shing Yu; Qian, Jianliang
   • Source: Journal of Scientific Computing, v. 88, (3), September 2021, article number 54
   • Year: 2021


5. Eulerian algorithms for computing some Lagrangian flow network quantities
   • Author(s): You, Guoqiao; Leung, Shing Yu
   • Source: Journal of Computational Physics, v. 445, 15 November 2021, article number 110620
   • Year: 2021


6. Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media
   • Author(s): Hu, Jiangtao; Qian, Jianliang; Song, Jian; Ouyang, Min; Cao, Junxing; Leung, Shing Yu
   • Source: Geophysics, v. 86, (4), July-August 2021, p. T179-T192
   • Year: 2021


7. A Level Set Method for the Dirichlet k-Partition Problem
   • Author(s): Chu, Kwun Lun; Leung, Shing Yu
   • Source: Journal of Scientific Computing, v. 86, (1), 2 January 2021, article number 11
   • Year: 2021


8. Computing the finite time Lyapunov exponent for flows with uncertainties
   • Author(s): You, Guoqiao; Leung, Shing Yu
   • Source: Journal of Computational Physics, v. 425, 15 January 2021, article number 109905
   • Year: 2021


9. On the numerical solution of nonlinear eigenvalue problems for the Monge-Ampère operator
   • Author(s): Glowinski, Roland; Leung, Shing Yu; Liu, Has; Qian, Jianliang
   • Source: ESAIM - Control, Optimisation and Calculus of Variations, v. 26, 2020, article number 118
   • Year: 2020


10. Efficient algorithms for computing multidimensional integral fractional laplacians via spherical means
    • Author(s): Xu, Boxi; Cheng, Jin; Leung, Shing Yu; Qian, Jianliang
    • Source: SIAM Journal on Scientific Computing, v. 42, (5), September 2020, p. A2910-A2942
    • Year: 2020


11. Fast Construction of Forward Flow Maps using Eulerian Based Interpolation Schemes
    • Author(s): You, Guoqiao; Leung, Shing Yu
    • Source: Journal of Scientific Computing, v. 82, (2), February 2020, article number 32
    • Year: 2020


12. A Simple Semi-Implicit Scheme for Partial Differential Equations with Obstacle Constraints
    • Author(s): Liu, Hao; Leung, Shing Yu
    • Source: Numerical Mathematics Theory Methods and Applications, v. 13, (3), August 2020, p. 620-643
    • Year: 2020


13. Guarantees of riemannian optimization for low rank matrix completion
    • Author(s): Wei, Ke; Cai, Jianfeng; Chan, Tony Fan-cheong; Leung, Shing Yu
    • Source: Inverse Problems and Imaging, v. 14, (2), April 2020, p. 233-265
    • Year: 2020


14. A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge–Ampère Equation
    • Author(s): Liu, Hao; Glowinski, Roland; Leung, Shing Yu; Qian, Jianliang
    • Source: Journal of Scientific Computing, v. 81, (3), December 2019, p. 2271-2302
    • Year: 2019


15. A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge–Ampère Equation
    • Author(s): Glowinski, Roland; Liu, Hao; Leung, Shing Yu; Qian, Jianliang
    • Source: Journal of Scientific Computing, v. 79, (1), April 2019, p. 1-47
    • Year: 2019


16. An alternating direction explicit method for time evolution equations with applications to fractional differential equations
    • Author(s): Liu, Hao; Leung, Shing Yu
    • Source: Methods and applications of analysis, v. 26, (3), 2019, p. 249-268
    • Year: 2019


17. A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge-Ampere Equation
    • Author(s): Liu, Hao; Glowinski, Roland; Leung, Shing Yu; Qian, Jianliang
    • Source: Journal of Scientific Computing, v. 81, (3), December 2019, p. 2271-2302
    • Year: 2019


18. Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories
    • Author(s): Leung, Shing Yu ; Ng, Yu Keung
    • Source: Communications in Computational Physics, v. 26, (4), October 2019, p. 1143-1177
    • Year: 2019


19. Pedagogy and Innovation in Science Education: A Case Study of an Experiential Learning Science Undergraduate Course
    • Author(s): Ng, Yee Fai PHYS; Chan, Kwan Kit; Lei, Huey; Mok, Phoebe; Leung, Shing Yu
    • Source: The European Journal of Social and Behavioural Sciences, 3 January 2019
    • Year: 2019


20. A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampere Equation
    • Author(s): Glowinski, Roland; Liu, Hao ; Leung, Shing Yu ; Qian, Jianliang
    • Source: Journal of Scientific Computing, v.79, (1), April 2019
    • Year: 2019


21. A weak formulation for the multiphase Stokes flow problem without body fitting grids
    • Author(s): Ying, Ningchen ; Hou, Songming; Leung, Shing Yu ; Zhao, Hongkai
    • Source: Pure and Applied Mathematics Quarterly, v. 14, (1), 2018, p. 131-159
    • Year: 2018


22. A Simple Explicit Operator-splitting Method for Effective Hamiltonians
    • Author(s): Glowinski, Roland; Leung, Shing Yu ; Qian, Jianliang
    • Source: SIAM Journal on Scientific Computing. , v. 40, (1), 2018, p. A484-A503
    • Year: 2018


23. Modified Virtual Grid Difference For Discretizing the Laplace-beltrami Operatior on Point Clouds
    • Author(s): Wang, Meng ; Leung, Shing Yu ; Zhaw, Hongkai
    • Source: SIAM Journal on Scientific Computing. , v. 40, (1), 2018, p. A1-A21
    • Year: 2018


24. An Improved Eulerian Approach for the Finite Time Lyapunov Exponent
    • Author(s): You, Guoqiao; Leung, Shing Yu
    • Source: Journal of Scientific Computing. , v. 76, (3), September 2018, p. 1407-1435
    • Year: 2018


25. Eulerian Based Interpolation Schemes for Flow Map Construction and Line Integral Computation with Applications to Lagrangian Coherent Structures Extraction
    • Author(s): You, Guoqiao; Leung, Shingyu
    • Source: Journal of Scientific Computing. , v. 74, (1), January 2018, p. 70-96
    • Year: 2018


26. Eulerian methods for visualizing continuous dynamical systems using Lyapunov exponents
    • Author(s): You, Guoqiao; Wong, Tony; Leung, Shingyu
    • Source: SIAM Journal on Scientific Computing. , v. 39, (2), 2017, p. A415-A437
    • Year: 2017


27. A Level Set Based Variational Principal Flow Method for Nonparametric Dimension Reduction on Riemannian Manifolds
    • Author(s): Liu, Hao; Yao, Zhigang; Leung, Shing Yu; Chan, Tony F.
    • Source: SIAM Journal on Scientific Computing. , v. 39, (4), 2017, p. A1616-A1646
    • Year: 2017


28. A Fast Huygens Sweeping Method for Capturing Paraxial Multi-color Optical Self-focusing in Nematic Liquid Crystals
    • Author(s): Kwan, Wingfai; Leung, Shing Yu; Wang, Xiao Ping; Qian, Jianliang
    • Source: Journal of Computational Physics. , v. 348, November 2017, p. 108-138
    • Year: 2017


29. OPERATOR-SPLITTING BASED FAST SWEEPING METHODS FOR ISOTROPIC WAVE PROPAGATION IN A MOVING FLUID
    • Author(s): Glowinski, Roland; Leung, Shingyu; Qian, Jianliang
    • Source: SIAM Journal on Scientific Computing. , v. 38, (2), 2016, p. A1195-A1223
    • Year: 2016


30. Guarantees of Riemannian Optimization for Low Rank Matrix Recovery
    • Author(s): Wei, Ke; Cai, Jianfeng; Chan, Tony F.; Leung, Shing Yu
    • Source: SIAM Journal on Matrix Analysis and Applications. , v. 37, (3), 2016, p. 1198-1222
    • Year: 2016


31. A Fast Sweeping Method for Eikonal Equations on Implicit Surfaces
    • Author(s): Wong, Ka Wah; Leung, Shing Yu
    • Source: Journal of Scientific Computing. , v. 67, (3), June 2016, p. 837-859
    • Year: 2016


32. A Penalization-Regularization-Operator Splitting Method for Eikonal Based Traveltime Tomography
    • Author(s): Glowinski, Roland; Leung, Shingyu; Qian, Jianliang
    • Source: SIAM Journal on Imaging Sciences. , v. 8, (2), June 2015, article number A017, p. 1263-1292
    • Year: 2015


33. A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems
    • Author(s): You, Guoqiao; Leung, Shingyu
    • Source: Communications in Computational Physics. , v. 18, (1), July 2015, p. 203-229
    • Year: 2015


34. AN IMPROVED FAST LOCAL LEVEL SET METHOD FOR THREE-DIMENSIONAL INVERSE GRAVIMETRY
    • Author(s): Lu, Wangtao; Leung, Shingyu; Qian, Jianliang
    • Source: Inverse Problems and Imaging. , v. 9, (2), 2015, p. 479-509
    • Year: 2015


35. An Eulerian Method for Computing the Coherent Ergodic Partition of Continuous Dynamical Systems
    • Author(s): You, Guoqiao; Leung, Shing Yu
    • Source: Journal of Computational Physics. , v. 264, May 2014, p. 112-132
    • Year: 2014


36. A level-set adjoint-state method for crosswell transmission-reflection traveltime tomography
    • Author(s): Li, Wenbin; Leung, Shingyu; Qian, Jianliang
    • Source: Geophysical Journal International. , v. 199, (1), 2014, article number ggu262, p. 348-367
    • Year: 2014


37. A new continuous max-flow algorithm for multiphase image segmentation using super-level set functions
    • Author(s): Liu, Jun; Tai, Xue-cheng; Leung, Shingyu; Huang, Haiyang
    • Source: Journal of Visual Communication and Image Representation. , v. 25, (6), 2014, p. 1472-1488
    • Year: 2014


38. A Cell Based Particle Method for Modeling Dynamic Interfaces
    • Author(s): Hon, Sean Y.; Leung, Shing Yu; Zhao, Hongkai
    • Source: Journal of Computational Physics. , v. 272, September 2014, p. 279-306
    • Year: 2014


39. Fast Huygens Sweeping Methods for Schrödinger Equations in the Semi-Classical Regime
    • Author(s): Leung, Shing Yu ; Qian, Jianliang; Serna, Susana
    • Source: Methods and Applications of Analysis. , v. 21, (1), March 2014, p. 31-66
    • Year: 2014


40. VIALS: An Eulerian tool based on total variation and the level set method for studying dynamical systems
    • Author(s): You, Guoqiao; Leung, Shing Yu
    • Source: Journal of Computational Physics. , v. 266, June 2014, p. 139-160
    • Year: 2014


41. A Splitting Algorithm for Image Segmentation on Manifolds Represented by the Grid Based Particle Method
    • Author(s): Liu, Jun; Leung, Shingyu
    • Source: Journal of Scientific Computing. , v. 56, (2), August 2013, p. 243-266
    • Year: 2013


42. A THREE-DIMENSIONAL INVERSE GRAVIMETRY PROBLEM FOR ICE WITH SNOW CAPS
    • Author(s): Isakov, Victor; Leung, Shingyu; Qian, Jianliang
    • Source: Inverse Problems and Imaging. , v. 7, (2), May 2013, p. 523-544
    • Year: 2013


43. The backward phase flow method for the Eulerian finite time Lyapunov exponent computations
    • Author(s): Leung, Shingyu
    • Source: Chaos. , v. 23, (4), October 2013, article number 043132
    • Year: 2013


44. A fast local level set adjoint state method for first arrival transmission traveltime tomography with discontinuous slowness
    • Author(s): Li, Wenbin; Leung, Shingyu
    • Source: Geophysical Journal International. , v. 195, (1), October 2013, p. 582-596
    • Year: 2013


45. Expectation-maximization algorithm with total variation regularization for vector-valued image segmentation
    • Author(s): Liu, Jun; Ku, Yin-Bon; Leung, Shingyu
    • Source: Journal of visual communication and image representation. , v. 23, (8), November 2012, p. 1234-1244
    • Year: 2012


46. A fast local level set method for inverse gravimetry
    • Author(s): Isakov, V.; Leung, Shing Yu; Qian, J.
    • Source: Communications in computational physics. , v. 10, (4), 2011, p. 1044-1070
    • Year: 2011


47. An adjoint state method for numerical approximation of continuous traffic congestion equilibria
    • Author(s): Luo, S.; Leung, Shing Yu; Qian, J.
    • Source: Communications in computational physics. , v. 10, (5), 2011, p. 1113-1131
    • Year: 2011


48. An Eulerian approach for computing the finite time Lyapunov exponent
    • Author(s): Leung, Shingyu
    • Source: Journal of computational physics. , v. 230, (9), May 2011, p. 3500-3524
    • Year: 2011


49. A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion
    • Author(s): Leung, Shingyu; Lowengrub, John; Zhao, Hongkai
    • Source: Journal of computational physics. , v. 230, (7), April 2011, p. 2540-2561
    • Year: 2011


50. The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation
    • Author(s): Leung, Shing Yu; Qian, J.
    • Source: Journal of Computational Physics. , v. 229, (23), 2010, NOV, p. 8888-8917
    • Year: 2010


51. Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method
    • Author(s): Leung, Shingyu; Zhao, Hongkai
    • Source: Communications in computational physics. , v. 8, (4), 2010, OCT, p. 758-796
    • Year: 2010


52. Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime
    • Author(s): Leung, Shing Yu; Qian, Jianliang
    • Source: Journal of Computational Physics, v. 228, (8), May 2009, p. 2951-2977
    • Year: 2009


53. A grid based particle method for evolution of open curves and surfaces
    • Author(s): Leung, Shingyu; Zhao, Hongkai
    • Source: Journal of computational physics. , v. 228, (20), 2009, NOV 1, p. 7706-7728
    • Year: 2009


54. Eulerian Gaussian Beams for Semi-Classical Solutions of Schrodinger Equations
    • Author(s): Leung, Shingyu; Qian, Jianliang
    • Source: Journal of Computational Physics. , v. 228, (8), May 1 2009, p. 2951-2977
    • Year: 2009


55. A Grid Based Particle Method for Moving Interface Problems
    • Author(s): Leung, Shingyu; Zhao, Hongkai
    • Source: Journal of Computational Physics. , v. 228, (8), May 1 2009, p. 2993-3024
    • Year: 2009


56. Expectation-Maximization Algorithm with Local Adaptivity
    • Author(s): Leung, Shingyu; Liang, Gang; Solna, Knut; Zhao, Hongkai
    • Source: SIAM journal on imaging sciences. , v. 2, (3), 2009, p. 834-857
    • Year: 2009


57. Eulerian Gaussian Beams for High Frequency Wave Propagation
    • Author(s): Leung, Shingyu; Qian, Jianliang; Burridge, Robert
    • Source: Geophysics. , v. 72, (5), September-October 2007, p. SM61-SM76
    • Year: 2007


58. Transmission Traveltime Tomography Based on Paraxial Liouville Equations and Level Set Formulations
    • Author(s): Leung, Shingyu; Qian, Jianliang
    • Source: Inverse Problems. , v. 23, 2007, p. 799-821
    • Year: 2007


59. A Local Level Set Method for Paraxial Geometrical Optics
    • Author(s): Qian, Jianliang; Leung, Shingyu
    • Source: SIAM J. Sci. Comp.. , v. 28, (1), 2006, p. 206-223
    • Year: 2006


60. An Adjoint State Method for 3D Transmission Traveltime Tomography Using First Arrival
    • Author(s): Leung, Shingyu; Qian, Jianliang
    • Source: Commun. Math. Sci.. , v. 4, (1), March 2006, p. 249-266
    • Year: 2006


61. A Level Set Method for Three-Dimensional Paraxial Geometrical Optics with Multiple Point Sources
    • Author(s): Leung, Shingyu; Qian, Jianliang; Osher, Stanley
    • Source: Communications in Mathematical Sciences, v. 2, (4), December 2004, p. 643-672
    • Year: 2004


62. A Level Set Based Eulerian Method for Paraxial Multivalued Traveltimes
    • Author(s): Qian, Jianliang; Leung, Shingyu
    • Source: Journal of Computational Physics. , v. 197, (2), July 1 2004, p. 711-736
    • Year: 2004


63. A Level Set Method for Three-dimensional Paraxial Geometrical Optics with Multiple Sources
    • Author(s): Leung, Shingyu; Qian, Jianliang; Osher, Stanley
    • Source: Commun. Math. Sci.. , v. 2, (4), December 2004, p. 643-672
    • Year: 2004

  Conference paper

1. An Adjoint State Method for An Schrödinger Inverse Problem
   • Author(s): Wei, Siyang; Leung, Shing Yu
   • Source: Springer Proceedings in Mathematics and Statistics, v. 360, 2021, p. 13-31
   • Year: 2021


2. Recent Developments in Eulerian Approaches for Visualizing Continuous Dynamical System
   • Author(s): Leung, Shing Yu ; You, Guoqiao; Wong, Ka Wah; Ng, Yu Keung
   • Source: Proceedings of the Seventh International Congress of Chinese Mathematicians, Volume II / Editors Lizhen Ji, Lo Yang, Shing-Tung Yau. International Press of Boston, Inc., 2019, p. 579-622, Advanced Lectures in Mathematics, v. 44
   • Year: 2019


3. Primal-dual method for continuous max-flow approaches
   • Author(s): Wei, Ke ; Tai, Xuecheng ; Chan, Tony Fan-cheong ; Leung, Shingyu
   • Source: Computational Vision and Medical Image Processing V - Proceedings of 5th Eccomas Thematic Conference on Computational Vision and Medical Image Processing, VipIMAGE 2015. , 2015, p. 17-24
   • Year: 2015


4. A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation
   • Author(s): Liu, Jun; Tai, Xue-Cheng; Leung, Shing Yu
   • Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). , v. 8081 LNCS, 2013, p. 251-265
   • Year: 2013


5. A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation
   • Author(s): Liu, Jun; Tai, Xue-Cheng; Leung, Shing Yu
   • Source: 9th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, Lund, Sweden. , 19-21 Aug 2013
   • Year: 2012


6. Global Minimization of the Active Contour Model with TV-Inpainting and Two-Phase Denoising
   • Author(s): Leung, Shing Yu; Osher, Stanley
   • Source: Variational, Geometric, and Level Set Methods in Computer Vision: Third International Workshop, VLSM 2005 / Nikos Paragios, Olivier Faugeras, Tony Chan, Christoph Schnörr (Eds.). Berlin : Springer, 2005, p. 149-160, Book series: Lecture Notes in Computer
   • Year: 2005


7. Fast Global Minimization of the Active Contour Model with TV-Inpainting and Two-phase Denoising
   • Author(s): Leung, Shingyu; Osher, Stanley
   • Source: Proceeding of the 3rd IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision. , 2005, p. 149-160
   • Year: 2005


8. A Transmission Tomography Problem Based on Multiple Arrivals from Paraxial Liouville Equations
   • Author(s): Leung, Shingyu; Qian, Jianliang
   • Source: Expanded Abstract for the SEG 75th Annual Meeting, Houston, USA. , 2005
   • Year: 2005

  Other

1. Correction to: A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge–Ampère Equation
   • Author(s): Glowinski, Roland; Liu, Hao; Leung, Shing Yu; Qian, Jianliang
   • Source: Journal of Scientific Computing, v. 79, (1), April 2019, p. 48
   • Year: 2019


2. Correction to: A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampere Equation (vol 79, pg 1, 2019)
   • Author(s): Glowinski, Roland; Liu, Hao; Leung, Shing Yu; Qian, Jianliang
   • Source: Journal of Scientific Computing, v. 79, (1), April 2019, p. 48
   • Year: 2019