Professor

Biography

Shingyu Leung has been a faculty member in the Department of Mathematics at the Hong Kong University of Science and Technology (HKUST) since 2009. Before joining HKUST, he served as an instructor and postdoctoral researcher at the University of California, Irvine. He holds a B.Sc. (1999) and an M.Phil. (2001) in Mathematics from HKUST, as well as a Ph.D. (2006) in Mathematics from the University of California, Los Angeles. Prof. Leung's research interests include Eulerian techniques for approximating high-frequency asymptotic solutions to wave phenomena and related inverse problems, numerical methods for modeling interfacial motions, and variational and statistical methods for image processing. Currently, he is a Professor of Mathematics and the Associate Dean of Science at HKUST.

Research Interests

Numerical methods for partial differential equations and scientific computing

Selected Publications

  Article

1. Local Trajectory Variation Exponent (LTVE) for Visualizing Dynamical Systems
   • Author(s): Tsai, Yun Chen; Leung, Shing Yu
   • Source: Communications in Computational Physics, v. 36, (5), 2024, p. 1411-1439
   • Year: 2024


2. SLERP-TVDRK (STVDRK) Methods for Ordinary Differential Equations on Spheres
   • Author(s): Leung, Shing Yu; Chau, Wai Ming; Lee, Young Kyu
   • Source: Journal of Scientific Computing, v. 101, (3), December 2024, article number 63
   • Year: 2024


3. Hadamard Integrators for Wave Equations in Time and Frequency Domain: Eulerian Formulations via Butterfly Algorithms
   • Author(s): Wei, Yuxiao; Cheng, Jin; Leung, Shing Yu; Burridge, Robert; Qian, Jianliang
   • Source: Journal of scientific computing, v. 100, (3), September 2024, article number 79
   • Year: 2024


4. Operator-Splitting/Finite Element Methods for the Minkowski Problem
   • Author(s): Liu, Hao; Leung, Shing Yu; Qian, Jianliang
   • Source: SIAM Journal on Scientific Computing, v. 46, (5), October 2024, p. A3230-A3257
   • Year: 2024


5. A Simple Embedding Method for Scalar Hyperbolic Conservation Laws on Implicit Surfaces
   • Author(s): Hung, Chun Kit; Leung, Shingyu
   • Source: SIAM Journal on Scientific Computing, v. 45, (6), December 2023, p. A2813-A2835
   • Year: 2023


6. Spherical Essentially Non-oscillatory (SENO) Interpolation
   • Author(s): Fong, Ki Wai; Leung, Shing Yu
   • Source: Journal of Scientific Computing, v. 94, (1), January 2023, article number 28
   • Year: 2023


7. Sparse subsampling of flow measurements for finite-time Lyapunov exponent in domains with obstacles
   • Author(s): Ng, Yu Keung; You, Guoqiao; Leung, Shingyu
   • Source: Journal of Computational and Applied Mathematics, v. 431, October 2023, article number 115255
   • Year: 2023


8. Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems
   • Author(s): Chau, Wai Ming; Leung, Shingyu
   • Source: Communications in Computational Physics, v. 33, (3), March 2023, p. 824-848
   • Year: 2023


9. A Simple Embedding Method for the Laplace-Beltrami Eigenvalue Problem on Implicit Surfaces
   • Author(s): Lee, Young Kyu; Leung, Shing Yu
   • Source: Communications on Applied Mathematics and Computation, October 2023
   • Year: 2023


10. Liouville Partial-Differential-Equation Methods for Computing 2D Complex Multivalued Eikonals in Attenuating Media
    • Author(s): Leung, Shing Yu; Hu, Jiangtao; Qian, Jianliang
    • Source: Geophysics, v. 87, (2), March 2022, p. T71-T84
    • Year: 2022


11. 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


12. 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), July 2021, article number 54
    • Year: 2021


13. 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


14. 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


15. 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


16. 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


17. 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), January 2021, article number 11
    • Year: 2021


18. 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


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


20. 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


21. 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


22. 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), April 2019, p. 249-268
    • Year: 2019


23. 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


24. 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


25. 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


26. Pedagogy and Innovation in Science Education: A Case Study of an Experiential Learning Science Undergraduate Course
    • Author(s): Ng, Yee Fai; Chan, Kwan Kit; Lei, Huey; Mok, Phoebe; Leung, Shing Yu
    • Source: The European Journal of Social and Behavioural Sciences, v. 25, (2), 3 January 2019, p. 156-173
    • Year: 2019


27. 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


28. 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


29. 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), July 2018, p. A484-A503
    • Year: 2018


30. 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


31. 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


32. 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


33. 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


34. 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


35. 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


36. 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


37. 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


38. 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


39. 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), May 2015, p. 479-509
    • Year: 2015


40. 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


41. 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


42. 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


43. 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), October 2014, p. 348-367
    • Year: 2014


44. 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


45. 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), August 2014, p. 1472-1488
    • Year: 2014


46. 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


47. 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


48. 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


49. 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


50. 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


51. 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


52. 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


53. An adjoint state method for numerical approximation of continuous traffic congestion equilibria
    • Author(s): Luo, Songting; Leung, Shing Yu; Qian, Jianliang
    • Source: Communications in Computational Physics, v. 10, (5), October 2011, p. 1113-1131
    • Year: 2011


54. A Fast Local Level Set Method for Inverse Gravimetry
    • Author(s): Isakov, Victor; Leung, Shing Yu; Qian, Jianliang
    • Source: Communications in Computational Physics, v. 10, (4), October 2011, p. 1044-1070
    • Year: 2011


55. 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


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


57. 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), October 2010, p. 758-796
    • Year: 2010


58. 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


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


60. 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), January 2009, p. 834-857
    • Year: 2009


61. 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), November 2009, p. 7706-7728
    • Year: 2009


62. 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-SM72
    • Year: 2007


63. Transmission Traveltime Tomography Based on Paraxial Liouville Equations and Level Set Formulations
    • Author(s): Leung, Shingyu; Qian, Jianliang
    • Source: Inverse Problems, v. 23, (2), April 2007, article number 019, p. 799-821
    • Year: 2007


64. 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


65. A Local Level Set Method for Paraxial Geometrical Optics
    • Author(s): Qian, Jianliang; Leung, Shingyu
    • Source: SIAM Journal on Scientific Computing, v. 28, (1), 2006, p. 206-223
    • Year: 2006


66. 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 2004, p. 711-736
    • Year: 2004


67. 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

  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: Energy Minimization Methods in Computer Vision and Pattern Recognition / Anders Heyden, Fredrik Kahl, Carl Olsson, Magnus Oskarsson, Xue-Cheng Tai, editors. Berlin : Springer, 2013, p. 251-265, Book series: Lecture Notes in Computer Science, v. 8081
   • 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 Science book series, v. 3752
   • Year: 2005


7. 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