Department of Mathematics, HKUST  

  LEUNG, Shing-Yu   梁承裕

  PhD Univ of California, Los Angeles

Office: Room 3434  

Telephone: 7414  

Email: masyleung@ust.hk  

URL:
https://www.math.hkust.edu.hk/~masyleung  
  Professor

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

       Selected Publications

Full Publication List [HKUST Scholarly Publications]  

Article   

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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

  36. 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

  37. 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

  38. 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

  39. 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

  40. 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

  41. 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

  42. 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

  43. 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

  44. 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

  45. 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

  46. 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

  47. 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

  48. 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

  49. 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

  50. 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

  51. 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

  52. 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

  53. 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

  54. 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. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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-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