Shing Yu LEUNG
梁承裕
PhD in Mathematics
University of California, Los Angeles, 2006

Associate Dean of Science (Student Recruitment)

Professor
Department of Mathematics



(852) 2358 7414
masyleung@ust.hk
Room 3434
Personal Web

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Google Scholar
rXnFQQQAAAAJ

ORCID
0000-0002-4549-2761

ResearcherID
E-3100-2013

Scopus ID
7202044873




Research Interest Publications Projects Teaching Assignment RPG Supervision Space used




Research Interest

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Applied mathematics
Computational mathematics
Nonlinear partial differential equations
Scientific computation



Publications

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All Years 65 2022 0 2021 8 2020 5 2019 6 2018 5 2017 3 2016 38

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2021 8

A Level Set Method for the Dirichlet k-Partition Problem
Journal of Scientific Computing, v. 86, (1), January 2021, article number 11
Chu, Kwun Lun; Leung, Shing Yu Article
A Level-Set Adjoint-State Method for Transmission Traveltime Tomography in Irregular Domains
SIAM Journal on Scientific Computing, v. 43, (3), 2021, p. A2352-A2380
Leung, Shing Yu; Qian, Jianliang; Hu, Jiangtao Article
Computing the finite time Lyapunov exponent for flows with uncertainties
Journal of Computational Physics, v. 425, 15 January 2021, article number 109905
You, Guoqiao; Leung, Shing Yu Article
Eulerian Algorithms for Computing Some Lagrangian Flow Network Quantities
Journal of Computational Physics, v. 445, 15 November 2021, article number 110620
You, Guoqiao; Leung, Shing Yu Article
Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media
Geophysics, v. 86, (4), July-August 2021, p. T179-T192
Hu, Jiangtao; Qian, Jianliang; Song, Jian; Ouyang, Min; Cao, Junxing; Leung, Shing Yu Article
Fast Huygens Sweeping Methods for a Class of Nonlocal Schr?dinger Equations
Journal of Scientific Computing, v. 88, (3), September 2021, article number 54
Ho, Ka Ho; Leung, Shing Yu; Qian, Jianliang Article
Ray-Illumination Compensation for Adjoint-State First-Arrival Traveltime Tomography
Geophysics, v. 86, (5), September 2021, p. U109-U119
Hu, Jiangtao; Qian, Jianliang; Cao, Junxing; Wang, Xingjian; Wang, Huazhong; Leung, Shing Yu Article
An Adjoint State Method for An Schr?dinger Inverse Problem
Springer Proceedings in Mathematics and Statistics, v. 360, 2021, p. 13-31
Wei, Siyang; Leung, Shing Yu Conference paper

2020 5

A Simple Semi-Implicit Scheme for Partial Differential Equations with Obstacle Constraints
Numerical Mathematics: Theory Methods and Applications, v. 13, (3), August 2020, p. 620-643
Liu, Hao; Leung, Shing Yu Article
Efficient algorithms for computing multidimensional integral fractional laplacians via spherical means
SIAM Journal on Scientific Computing, v. 42, (5), September 2020, p. A2910-A2942
Xu, Boxi; Cheng, Jin; Leung, Shing Yu; Qian, Jianliang Article
Fast Construction of Forward Flow Maps using Eulerian Based Interpolation Schemes
Journal of Scientific Computing, v. 82, (2), February 2020, article number 32
You, Guoqiao; Leung, Shing Yu Article
Guarantees of riemannian optimization for low rank matrix completion
Inverse Problems and Imaging, v. 14, (2), April 2020, p. 233-265
Wei, Ke; Cai, Jianfeng; Chan, Tony Fan-cheong; Leung, Shing Yu Article
On the numerical solution of nonlinear eigenvalue problems for the Monge-Ampère operator
ESAIM - Control, Optimisation and Calculus of Variations, v. 26, December 2020, article number 118
Glowinski, Roland; Leung, Shing Yu; Liu, Hao; Qian, Jianliang Article

2019 6

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge–Ampère Equation
Journal of Scientific Computing, v. 81, (3), December 2019, p. 2271-2302
Liu, Hao; Glowinski, Roland; Leung, Shing Yu; Qian, Jianliang Article
A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge–Ampère Equation
Journal of Scientific Computing, v. 79, (1), April 2019, p. 1-47
Glowinski, Roland; Liu, Hao; Leung, Shing Yu; Qian, Jianliang Article
An alternating direction explicit method for time evolution equations with applications to fractional differential equations
Methods and Applications of Analysis, v. 26, (3), April 2019, p. 249-268
Liu, Hao; Leung, Shing Yu Article
Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories
Communications in Computational Physics, v. 26, (4), October 2019, p. 1143-1177
Leung, Shing Yu; Ng, Yu Keung Article
Pedagogy and Innovation in Science Education: A Case Study of an Experiential Learning Science Undergraduate Course
The European Journal of Social and Behavioural Sciences, v. 25, (2), 3 January 2019, p. 2910-2926
Ng, Yee Fai; Chan, Kwan Kit; Lei, Huey; Mok, Phoebe; Leung, Shing Yu Article
Recent Developments in Eulerian Approaches for Visualizing Continuous Dynamical System
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
Leung, Shing Yu; You, Guoqiao; Wong, Ka Wah; Ng, Yu Keung Conference paper

2018 5

A Simple Explicit Operator-splitting Method for Effective Hamiltonians
SIAM Journal on Scientific Computing, v. 40, (1), July 2018, p. A484-A503
Glowinski, Roland; Leung, Shing Yu; Qian, Jianliang Article
A weak formulation for the multiphase Stokes flow problem without body fitting grids
Pure and Applied Mathematics Quarterly, v. 14, (1), 2018, p. 131-159
Ying, Ningchen; Hou, Songming; Leung, Shing Yu; Zhao, Hongkai Article
An Improved Eulerian Approach for the Finite Time Lyapunov Exponent
Journal of Scientific Computing, v. 76, (3), September 2018, p. 1407-1435
You, Guoqiao; Leung, Shing Yu Article
Eulerian Based Interpolation Schemes for Flow Map Construction and Line Integral Computation with Applications to Lagrangian Coherent Structures Extraction
Journal of Scientific Computing, v. 74, (1), January 2018, p. 70-96
You, Guoqiao; Leung, Shingyu Article
Modified Virtual Grid Difference For Discretizing the Laplace-beltrami Operatior on Point Clouds
SIAM Journal on Scientific Computing, v. 40, (1), 2018, p. A1-A21
Wang, Meng; Leung, Shing Yu; Zhaw, Hongkai Article

2017 3

A Fast Huygens Sweeping Method for Capturing Paraxial Multi-color Optical Self-focusing in Nematic Liquid Crystals
Journal of Computational Physics, v. 348, November 2017, p. 108-138
Kwan, Wingfai; Leung, Shing Yu; Wang, Xiao Ping; Qian, Jianliang Article
A Level Set Based Variational Principal Flow Method for Nonparametric Dimension Reduction on Riemannian Manifolds
SIAM Journal on Scientific Computing, v. 39, (4), 2017, p. A1616-A1646
Liu, Hao; Yao, Zhigang; Leung, Shing Yu; Chan, Tony F. Article
Eulerian methods for visualizing continuous dynamical systems using Lyapunov exponents
SIAM Journal on Scientific Computing, v. 39, (2), 2017, p. A415-A437
You, Guoqiao; Wong, Tony; Leung, Shingyu Article

2016 3

A Fast Sweeping Method for Eikonal Equations on Implicit Surfaces
Journal of Scientific Computing, v. 67, (3), June 2016, p. 837-859
Wong, Ka Wah; Leung, Shing Yu Article
Guarantees of Riemannian Optimization for Low Rank Matrix Recovery
SIAM Journal on Matrix Analysis and Applications, v. 37, (3), 2016, p. 1198-1222
Wei, Ke; Cai, Jianfeng; Chan, Tony F.; Leung, Shing Yu Article
Operator-Splitting Based Fast Sweeping Methods for Isotropic Wave Propagation in a Moving Fluid
SIAM Journal on Scientific Computing, v. 38, (2), 2016, p. A1195-A1223
Glowinski, Roland; Leung, Shingyu; Qian, Jianliang Article

2015 4

A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems
Communications in Computational Physics, v. 18, (1), July 2015, p. 203-229
You, Guoqiao; Leung, Shingyu Article
A Penalization-Regularization-Operator Splitting Method for Eikonal Based Traveltime Tomography
SIAM Journal on Imaging Sciences, v. 8, (2), June 2015, article number A017, p. 1263-1292
Glowinski, Roland; Leung, Shingyu; Qian, Jianliang Article
An improved fast local level set method for three-dimensional inverse gravimetry
Inverse Problems and Imaging, v. 9, (2), May 2015, p. 479-509
Lu, Wangtao; Leung, Shingyu; Qian, Jianliang Article
Primal-dual method for continuous max-flow approaches
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
Wei, Ke; Tai, Xuecheng; Chan, Tony Fan-cheong; Leung, Shingyu Conference paper

2014 6

A Cell Based Particle Method for Modeling Dynamic Interfaces
Journal of Computational Physics, v. 272, September 2014, p. 279-306
Hon, Sean Y.; Leung, Shing Yu; Zhao, Hongkai Article
A level-set adjoint-state method for crosswell transmission-reflection traveltime tomography
Geophysical Journal International, v. 199, (1), October 2014, p. 348-367
Li, Wenbin; Leung, Shingyu; Qian, Jianliang Article
A new continuous max-flow algorithm for multiphase image segmentation using super-level set functions
Journal of Visual Communication and Image Representation, v. 25, (6), August 2014, p. 1472-1488
Liu, Jun; Tai, Xue-cheng; Leung, Shingyu; Huang, Haiyang Article
An Eulerian Method for Computing the Coherent Ergodic Partition of Continuous Dynamical Systems
Journal of Computational Physics, v. 264, May 2014, p. 112-132
You, Guoqiao; Leung, Shing Yu Article
Fast Huygens Sweeping Methods for Schr?dinger Equations in the Semi-Classical Regime
Methods and Applications of Analysis, v. 21, (1), March 2014, p. 31-66
Leung, Shing Yu; Qian, Jianliang; Serna, Susana Article
VIALS: An Eulerian tool based on total variation and the level set method for studying dynamical systems
Journal of Computational Physics, v. 266, June 2014, p. 139-160
You, Guoqiao; Leung, Shing Yu Article

2013 5

A fast local level set adjoint state method for first arrival transmission traveltime tomography with discontinuous slowness
Geophysical Journal International, v. 195, (1), October 2013, p. 582-596
Li, Wenbin; Leung, Shingyu Article
A Splitting Algorithm for Image Segmentation on Manifolds Represented by the Grid Based Particle Method
Journal of Scientific Computing, v. 56, (2), August 2013, p. 243-266
Liu, Jun; Leung, Shingyu Article
A three-dimensional inverse gravimetry problem for ice with snow caps
Inverse Problems and Imaging, v. 7, (2), May 2013, p. 523-544
Isakov, Victor; Leung, Shingyu; Qian, Jianliang Article
The backward phase flow method for the Eulerian finite time Lyapunov exponent computations
Chaos, v. 23, (4), October 2013, article number 043132
Leung, Shingyu Article
A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation
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
Liu, Jun; Tai, Xue-Cheng; Leung, Shing Yu Conference paper

2012 2

Expectation-maximization algorithm with total variation regularization for vector-valued image segmentation
Journal of Visual Communication and Image Representation, v. 23, (8), November 2012, p. 1234-1244
Liu, Jun; Ku, Yin-Bon; Leung, Shingyu Article
A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation
9th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, Lund, Sweden, 19-21 Aug 2013
Liu, Jun; Tai, Xue-Cheng; Leung, Shing Yu Conference paper

2011 4

A Fast Local Level Set Method for Inverse Gravimetry
Communications in Computational Physics, v. 10, (4), October 2011, p. 1044-1070
Isakov, Victor; Leung, Shing Yu; Qian, Jianliang Article
A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion
Journal of Computational Physics, v. 230, (7), April 2011, p. 2540-2561
Leung, Shingyu; Lowengrub, John; Zhao, Hongkai Article
An adjoint state method for numerical approximation of continuous traffic congestion equilibria
Communications in Computational Physics, v. 10, (5), October 2011, p. 1113-1131
Luo, Songting; Leung, Shing Yu; Qian, Jianliang Article
An Eulerian approach for computing the finite time Lyapunov exponent
Journal of Computational Physics, v. 230, (9), May 2011, p. 3500-3524
Leung, Shingyu Article

2010 2

Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method
Communications in Computational Physics, v. 8, (4), October 2010, p. 758-796
Leung, Shingyu; Zhao, Hongkai Article
The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schr?dinger equation
Journal of Computational Physics, v. 229, (23), November 2010, p. 8888-8917
Leung, Shing Yu; Qian, Jianliang Article

2009 4

A grid based particle method for evolution of open curves and surfaces
Journal of Computational Physics, v. 228, (20), November 2009, p. 7706-7728
Leung, Shingyu; Zhao, Hongkai Article
A Grid Based Particle Method for Moving Interface Problems
Journal of Computational Physics, v. 228, (8), May 2009, p. 2993-3024
Leung, Shingyu; Zhao, Hongkai Article
Eulerian Gaussian beams for Schr?dinger equations in the semi-classical regime
Journal of Computational Physics, v. 228, (8), May 2009, p. 2951-2977
Leung, Shing Yu; Qian, Jianliang Article
Expectation-Maximization Algorithm with Local Adaptivity
SIAM Journal on Imaging Sciences, v. 2, (3), January 2009, p. 834-857
Leung, Shingyu; Liang, Gang; Solna, Knut; Zhao, Hongkai Article

2007 2

Eulerian Gaussian Beams for High Frequency Wave Propagation
Geophysics, v. 72, (5), September-October 2007, p. SM61-SM72
Leung, Shingyu; Qian, Jianliang; Burridge, Robert Article
Transmission Traveltime Tomography Based on Paraxial Liouville Equations and Level Set Formulations
Inverse Problems, v. 23, (2), April 2007, article number 019, p. 799-821
Leung, Shingyu; Qian, Jianliang Article

2006 2

A Local Level Set Method for Paraxial Geometrical Optics
SIAM Journal on Scientific Computing, v. 28, (1), 2006, p. 206-223
Qian, Jianliang; Leung, Shingyu Article
An Adjoint State Method for 3D Transmission Traveltime Tomography Using First Arrival
Commun. Math. Sci., v. 4, (1), March 2006, p. 249-266
Leung, Shingyu; Qian, Jianliang Article

2005 2

A Transmission Tomography Problem Based on Multiple Arrivals from Paraxial Liouville Equations
Expanded Abstract for the SEG 75th Annual Meeting, Houston, USA, 2005
Leung, Shingyu; Qian, Jianliang Conference paper
Global Minimization of the Active Contour Model with TV-Inpainting and Two-Phase Denoising
Variational, Geometric, and Level Set Methods in Computer Vision: Third International Workshop, VLSM 2005 / Nikos Paragios, Olivier Faugeras, Tony Chan, Christoph Schn?rr (Eds.). Berlin : Springer, 2005, p. 149-160, Book series: Lecture Notes in Computer Science book series, v. 3752
Leung, Shing Yu; Osher, Stanley Conference paper

2004 2

A Level Set Based Eulerian Method for Paraxial Multivalued Traveltimes
Journal of Computational Physics, v. 197, (2), July 2004, p. 711-736
Qian, Jianliang; Leung, Shingyu Article
A Level Set Method for Three-Dimensional Paraxial Geometrical Optics with Multiple Point Sources
Communications in Mathematical Sciences, v. 2, (4), December 2004, p. 643-672
Leung, Shingyu; Qian, Jianliang; Osher, Stanley Article


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Article 7

A Level Set Method for the Dirichlet k-Partition Problem
Journal of Scientific Computing, v. 86, (1), January 2021, article number 11
Chu, Kwun Lun; Leung, Shing Yu
A Level-Set Adjoint-State Method for Transmission Traveltime Tomography in Irregular Domains
SIAM Journal on Scientific Computing, v. 43, (3), 2021, p. A2352-A2380
Leung, Shing Yu; Qian, Jianliang; Hu, Jiangtao
Computing the finite time Lyapunov exponent for flows with uncertainties
Journal of Computational Physics, v. 425, 15 January 2021, article number 109905
You, Guoqiao; Leung, Shing Yu
Eulerian Algorithms for Computing Some Lagrangian Flow Network Quantities
Journal of Computational Physics, v. 445, 15 November 2021, article number 110620
You, Guoqiao; Leung, Shing Yu
Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media
Geophysics, v. 86, (4), July-August 2021, p. T179-T192
Hu, Jiangtao; Qian, Jianliang; Song, Jian; Ouyang, Min; Cao, Junxing; Leung, Shing Yu
Fast Huygens Sweeping Methods for a Class of Nonlocal Schr?dinger Equations
Journal of Scientific Computing, v. 88, (3), September 2021, article number 54
Ho, Ka Ho; Leung, Shing Yu; Qian, Jianliang
Ray-Illumination Compensation for Adjoint-State First-Arrival Traveltime Tomography
Geophysics, v. 86, (5), September 2021, p. U109-U119
Hu, Jiangtao; Qian, Jianliang; Cao, Junxing; Wang, Xingjian; Wang, Huazhong; Leung, Shing Yu

Conference paper 1

An Adjoint State Method for An Schr?dinger Inverse Problem
Springer Proceedings in Mathematics and Statistics, v. 360, 2021, p. 13-31
Wei, Siyang; Leung, Shing Yu


Expand All Collapse All


Article 5

A Simple Semi-Implicit Scheme for Partial Differential Equations with Obstacle Constraints
Numerical Mathematics: Theory Methods and Applications, v. 13, (3), August 2020, p. 620-643
Liu, Hao; Leung, Shing Yu
Efficient algorithms for computing multidimensional integral fractional laplacians via spherical means
SIAM Journal on Scientific Computing, v. 42, (5), September 2020, p. A2910-A2942
Xu, Boxi; Cheng, Jin; Leung, Shing Yu; Qian, Jianliang
Fast Construction of Forward Flow Maps using Eulerian Based Interpolation Schemes
Journal of Scientific Computing, v. 82, (2), February 2020, article number 32
You, Guoqiao; Leung, Shing Yu
Guarantees of riemannian optimization for low rank matrix completion
Inverse Problems and Imaging, v. 14, (2), April 2020, p. 233-265
Wei, Ke; Cai, Jianfeng; Chan, Tony Fan-cheong; Leung, Shing Yu
On the numerical solution of nonlinear eigenvalue problems for the Monge-Ampère operator
ESAIM - Control, Optimisation and Calculus of Variations, v. 26, December 2020, article number 118
Glowinski, Roland; Leung, Shing Yu; Liu, Hao; Qian, Jianliang


Expand All Collapse All


Article 5

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge–Ampère Equation
Journal of Scientific Computing, v. 81, (3), December 2019, p. 2271-2302
Liu, Hao; Glowinski, Roland; Leung, Shing Yu; Qian, Jianliang
A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge–Ampère Equation
Journal of Scientific Computing, v. 79, (1), April 2019, p. 1-47
Glowinski, Roland; Liu, Hao; Leung, Shing Yu; Qian, Jianliang
An alternating direction explicit method for time evolution equations with applications to fractional differential equations
Methods and Applications of Analysis, v. 26, (3), April 2019, p. 249-268
Liu, Hao; Leung, Shing Yu
Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories
Communications in Computational Physics, v. 26, (4), October 2019, p. 1143-1177
Leung, Shing Yu; Ng, Yu Keung
Pedagogy and Innovation in Science Education: A Case Study of an Experiential Learning Science Undergraduate Course
The European Journal of Social and Behavioural Sciences, v. 25, (2), 3 January 2019, p. 2910-2926
Ng, Yee Fai; Chan, Kwan Kit; Lei, Huey; Mok, Phoebe; Leung, Shing Yu

Conference paper 1

Recent Developments in Eulerian Approaches for Visualizing Continuous Dynamical System
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
Leung, Shing Yu; You, Guoqiao; Wong, Ka Wah; Ng, Yu Keung


Expand All Collapse All


Article 5

A Simple Explicit Operator-splitting Method for Effective Hamiltonians
SIAM Journal on Scientific Computing, v. 40, (1), July 2018, p. A484-A503
Glowinski, Roland; Leung, Shing Yu; Qian, Jianliang
A weak formulation for the multiphase Stokes flow problem without body fitting grids
Pure and Applied Mathematics Quarterly, v. 14, (1), 2018, p. 131-159
Ying, Ningchen; Hou, Songming; Leung, Shing Yu; Zhao, Hongkai
An Improved Eulerian Approach for the Finite Time Lyapunov Exponent
Journal of Scientific Computing, v. 76, (3), September 2018, p. 1407-1435
You, Guoqiao; Leung, Shing Yu
Eulerian Based Interpolation Schemes for Flow Map Construction and Line Integral Computation with Applications to Lagrangian Coherent Structures Extraction
Journal of Scientific Computing, v. 74, (1), January 2018, p. 70-96
You, Guoqiao; Leung, Shingyu
Modified Virtual Grid Difference For Discretizing the Laplace-beltrami Operatior on Point Clouds
SIAM Journal on Scientific Computing, v. 40, (1), 2018, p. A1-A21
Wang, Meng; Leung, Shing Yu; Zhaw, Hongkai


Expand All Collapse All


Article 3

A Fast Huygens Sweeping Method for Capturing Paraxial Multi-color Optical Self-focusing in Nematic Liquid Crystals
Journal of Computational Physics, v. 348, November 2017, p. 108-138
Kwan, Wingfai; Leung, Shing Yu; Wang, Xiao Ping; Qian, Jianliang
A Level Set Based Variational Principal Flow Method for Nonparametric Dimension Reduction on Riemannian Manifolds
SIAM Journal on Scientific Computing, v. 39, (4), 2017, p. A1616-A1646
Liu, Hao; Yao, Zhigang; Leung, Shing Yu; Chan, Tony F.
Eulerian methods for visualizing continuous dynamical systems using Lyapunov exponents
SIAM Journal on Scientific Computing, v. 39, (2), 2017, p. A415-A437
You, Guoqiao; Wong, Tony; Leung, Shingyu


Expand All Collapse All


Article 3

A Fast Sweeping Method for Eikonal Equations on Implicit Surfaces
Journal of Scientific Computing, v. 67, (3), June 2016, p. 837-859
Wong, Ka Wah; Leung, Shing Yu
Guarantees of Riemannian Optimization for Low Rank Matrix Recovery
SIAM Journal on Matrix Analysis and Applications, v. 37, (3), 2016, p. 1198-1222
Wei, Ke; Cai, Jianfeng; Chan, Tony F.; Leung, Shing Yu
Operator-Splitting Based Fast Sweeping Methods for Isotropic Wave Propagation in a Moving Fluid
SIAM Journal on Scientific Computing, v. 38, (2), 2016, p. A1195-A1223
Glowinski, Roland; Leung, Shingyu; Qian, Jianliang


Expand All Collapse All


Article 3

A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems
Communications in Computational Physics, v. 18, (1), July 2015, p. 203-229
You, Guoqiao; Leung, Shingyu
A Penalization-Regularization-Operator Splitting Method for Eikonal Based Traveltime Tomography
SIAM Journal on Imaging Sciences, v. 8, (2), June 2015, article number A017, p. 1263-1292
Glowinski, Roland; Leung, Shingyu; Qian, Jianliang
An improved fast local level set method for three-dimensional inverse gravimetry
Inverse Problems and Imaging, v. 9, (2), May 2015, p. 479-509
Lu, Wangtao; Leung, Shingyu; Qian, Jianliang

Conference paper 1

Primal-dual method for continuous max-flow approaches
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
Wei, Ke; Tai, Xuecheng; Chan, Tony Fan-cheong; Leung, Shingyu


Expand All Collapse All


Article 6

A Cell Based Particle Method for Modeling Dynamic Interfaces
Journal of Computational Physics, v. 272, September 2014, p. 279-306
Hon, Sean Y.; Leung, Shing Yu; Zhao, Hongkai
A level-set adjoint-state method for crosswell transmission-reflection traveltime tomography
Geophysical Journal International, v. 199, (1), October 2014, p. 348-367
Li, Wenbin; Leung, Shingyu; Qian, Jianliang
A new continuous max-flow algorithm for multiphase image segmentation using super-level set functions
Journal of Visual Communication and Image Representation, v. 25, (6), August 2014, p. 1472-1488
Liu, Jun; Tai, Xue-cheng; Leung, Shingyu; Huang, Haiyang
An Eulerian Method for Computing the Coherent Ergodic Partition of Continuous Dynamical Systems
Journal of Computational Physics, v. 264, May 2014, p. 112-132
You, Guoqiao; Leung, Shing Yu
Fast Huygens Sweeping Methods for Schr?dinger Equations in the Semi-Classical Regime
Methods and Applications of Analysis, v. 21, (1), March 2014, p. 31-66
Leung, Shing Yu; Qian, Jianliang; Serna, Susana
VIALS: An Eulerian tool based on total variation and the level set method for studying dynamical systems
Journal of Computational Physics, v. 266, June 2014, p. 139-160
You, Guoqiao; Leung, Shing Yu


Expand All Collapse All


Article 4

A fast local level set adjoint state method for first arrival transmission traveltime tomography with discontinuous slowness
Geophysical Journal International, v. 195, (1), October 2013, p. 582-596
Li, Wenbin; Leung, Shingyu
A Splitting Algorithm for Image Segmentation on Manifolds Represented by the Grid Based Particle Method
Journal of Scientific Computing, v. 56, (2), August 2013, p. 243-266
Liu, Jun; Leung, Shingyu
A three-dimensional inverse gravimetry problem for ice with snow caps
Inverse Problems and Imaging, v. 7, (2), May 2013, p. 523-544
Isakov, Victor; Leung, Shingyu; Qian, Jianliang
The backward phase flow method for the Eulerian finite time Lyapunov exponent computations
Chaos, v. 23, (4), October 2013, article number 043132
Leung, Shingyu

Conference paper 1

A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation
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
Liu, Jun; Tai, Xue-Cheng; Leung, Shing Yu


Expand All Collapse All


Article 1

Expectation-maximization algorithm with total variation regularization for vector-valued image segmentation
Journal of Visual Communication and Image Representation, v. 23, (8), November 2012, p. 1234-1244
Liu, Jun; Ku, Yin-Bon; Leung, Shingyu

Conference paper 1

A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation
9th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, Lund, Sweden, 19-21 Aug 2013
Liu, Jun; Tai, Xue-Cheng; Leung, Shing Yu


Expand All Collapse All


Article 4

A Fast Local Level Set Method for Inverse Gravimetry
Communications in Computational Physics, v. 10, (4), October 2011, p. 1044-1070
Isakov, Victor; Leung, Shing Yu; Qian, Jianliang
A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion
Journal of Computational Physics, v. 230, (7), April 2011, p. 2540-2561
Leung, Shingyu; Lowengrub, John; Zhao, Hongkai
An adjoint state method for numerical approximation of continuous traffic congestion equilibria
Communications in Computational Physics, v. 10, (5), October 2011, p. 1113-1131
Luo, Songting; Leung, Shing Yu; Qian, Jianliang
An Eulerian approach for computing the finite time Lyapunov exponent
Journal of Computational Physics, v. 230, (9), May 2011, p. 3500-3524
Leung, Shingyu


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Article 2

Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method
Communications in Computational Physics, v. 8, (4), October 2010, p. 758-796
Leung, Shingyu; Zhao, Hongkai
The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schr?dinger equation
Journal of Computational Physics, v. 229, (23), November 2010, p. 8888-8917
Leung, Shing Yu; Qian, Jianliang


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Article 4

A grid based particle method for evolution of open curves and surfaces
Journal of Computational Physics, v. 228, (20), November 2009, p. 7706-7728
Leung, Shingyu; Zhao, Hongkai
A Grid Based Particle Method for Moving Interface Problems
Journal of Computational Physics, v. 228, (8), May 2009, p. 2993-3024
Leung, Shingyu; Zhao, Hongkai
Eulerian Gaussian beams for Schr?dinger equations in the semi-classical regime
Journal of Computational Physics, v. 228, (8), May 2009, p. 2951-2977
Leung, Shing Yu; Qian, Jianliang
Expectation-Maximization Algorithm with Local Adaptivity
SIAM Journal on Imaging Sciences, v. 2, (3), January 2009, p. 834-857
Leung, Shingyu; Liang, Gang; Solna, Knut; Zhao, Hongkai


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Article 2

Eulerian Gaussian Beams for High Frequency Wave Propagation
Geophysics, v. 72, (5), September-October 2007, p. SM61-SM72
Leung, Shingyu; Qian, Jianliang; Burridge, Robert
Transmission Traveltime Tomography Based on Paraxial Liouville Equations and Level Set Formulations
Inverse Problems, v. 23, (2), April 2007, article number 019, p. 799-821
Leung, Shingyu; Qian, Jianliang


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Article 2

A Local Level Set Method for Paraxial Geometrical Optics
SIAM Journal on Scientific Computing, v. 28, (1), 2006, p. 206-223
Qian, Jianliang; Leung, Shingyu
An Adjoint State Method for 3D Transmission Traveltime Tomography Using First Arrival
Commun. Math. Sci., v. 4, (1), March 2006, p. 249-266
Leung, Shingyu; Qian, Jianliang


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Conference paper 2

A Transmission Tomography Problem Based on Multiple Arrivals from Paraxial Liouville Equations
Expanded Abstract for the SEG 75th Annual Meeting, Houston, USA, 2005
Leung, Shingyu; Qian, Jianliang
Global Minimization of the Active Contour Model with TV-Inpainting and Two-Phase Denoising
Variational, Geometric, and Level Set Methods in Computer Vision: Third International Workshop, VLSM 2005 / Nikos Paragios, Olivier Faugeras, Tony Chan, Christoph Schn?rr (Eds.). Berlin : Springer, 2005, p. 149-160, Book series: Lecture Notes in Computer Science book series, v. 3752
Leung, Shing Yu; Osher, Stanley


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Article 2

A Level Set Based Eulerian Method for Paraxial Multivalued Traveltimes
Journal of Computational Physics, v. 197, (2), July 2004, p. 711-736
Qian, Jianliang; Leung, Shingyu
A Level Set Method for Three-Dimensional Paraxial Geometrical Optics with Multiple Point Sources
Communications in Mathematical Sciences, v. 2, (4), December 2004, p. 643-672
Leung, Shingyu; Qian, Jianliang; Osher, Stanley


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2016 3

A Fast Sweeping Method for Eikonal Equations on Implicit Surfaces
Journal of Scientific Computing, v. 67, (3), June 2016, p. 837-859
Wong, Ka Wah; Leung, Shing Yu Article
Guarantees of Riemannian Optimization for Low Rank Matrix Recovery
SIAM Journal on Matrix Analysis and Applications, v. 37, (3), 2016, p. 1198-1222
Wei, Ke; Cai, Jianfeng; Chan, Tony F.; Leung, Shing Yu Article
Operator-Splitting Based Fast Sweeping Methods for Isotropic Wave Propagation in a Moving Fluid
SIAM Journal on Scientific Computing, v. 38, (2), 2016, p. A1195-A1223
Glowinski, Roland; Leung, Shingyu; Qian, Jianliang Article

2015 4

A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems
Communications in Computational Physics, v. 18, (1), July 2015, p. 203-229
You, Guoqiao; Leung, Shingyu Article
A Penalization-Regularization-Operator Splitting Method for Eikonal Based Traveltime Tomography
SIAM Journal on Imaging Sciences, v. 8, (2), June 2015, article number A017, p. 1263-1292
Glowinski, Roland; Leung, Shingyu; Qian, Jianliang Article
An improved fast local level set method for three-dimensional inverse gravimetry
Inverse Problems and Imaging, v. 9, (2), May 2015, p. 479-509
Lu, Wangtao; Leung, Shingyu; Qian, Jianliang Article
Primal-dual method for continuous max-flow approaches
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
Wei, Ke; Tai, Xuecheng; Chan, Tony Fan-cheong; Leung, Shingyu Conference paper

2014 6

A Cell Based Particle Method for Modeling Dynamic Interfaces
Journal of Computational Physics, v. 272, September 2014, p. 279-306
Hon, Sean Y.; Leung, Shing Yu; Zhao, Hongkai Article
A level-set adjoint-state method for crosswell transmission-reflection traveltime tomography
Geophysical Journal International, v. 199, (1), October 2014, p. 348-367
Li, Wenbin; Leung, Shingyu; Qian, Jianliang Article
A new continuous max-flow algorithm for multiphase image segmentation using super-level set functions
Journal of Visual Communication and Image Representation, v. 25, (6), August 2014, p. 1472-1488
Liu, Jun; Tai, Xue-cheng; Leung, Shingyu; Huang, Haiyang Article
An Eulerian Method for Computing the Coherent Ergodic Partition of Continuous Dynamical Systems
Journal of Computational Physics, v. 264, May 2014, p. 112-132
You, Guoqiao; Leung, Shing Yu Article
Fast Huygens Sweeping Methods for Schr?dinger Equations in the Semi-Classical Regime
Methods and Applications of Analysis, v. 21, (1), March 2014, p. 31-66
Leung, Shing Yu; Qian, Jianliang; Serna, Susana Article
VIALS: An Eulerian tool based on total variation and the level set method for studying dynamical systems
Journal of Computational Physics, v. 266, June 2014, p. 139-160
You, Guoqiao; Leung, Shing Yu Article

2013 5

A fast local level set adjoint state method for first arrival transmission traveltime tomography with discontinuous slowness
Geophysical Journal International, v. 195, (1), October 2013, p. 582-596
Li, Wenbin; Leung, Shingyu Article
A Splitting Algorithm for Image Segmentation on Manifolds Represented by the Grid Based Particle Method
Journal of Scientific Computing, v. 56, (2), August 2013, p. 243-266
Liu, Jun; Leung, Shingyu Article
A three-dimensional inverse gravimetry problem for ice with snow caps
Inverse Problems and Imaging, v. 7, (2), May 2013, p. 523-544
Isakov, Victor; Leung, Shingyu; Qian, Jianliang Article
The backward phase flow method for the Eulerian finite time Lyapunov exponent computations
Chaos, v. 23, (4), October 2013, article number 043132
Leung, Shingyu Article
A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation
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
Liu, Jun; Tai, Xue-Cheng; Leung, Shing Yu Conference paper

2012 2

Expectation-maximization algorithm with total variation regularization for vector-valued image segmentation
Journal of Visual Communication and Image Representation, v. 23, (8), November 2012, p. 1234-1244
Liu, Jun; Ku, Yin-Bon; Leung, Shingyu Article
A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation
9th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, Lund, Sweden, 19-21 Aug 2013
Liu, Jun; Tai, Xue-Cheng; Leung, Shing Yu Conference paper

2011 4

A Fast Local Level Set Method for Inverse Gravimetry
Communications in Computational Physics, v. 10, (4), October 2011, p. 1044-1070
Isakov, Victor; Leung, Shing Yu; Qian, Jianliang Article
A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion
Journal of Computational Physics, v. 230, (7), April 2011, p. 2540-2561
Leung, Shingyu; Lowengrub, John; Zhao, Hongkai Article
An adjoint state method for numerical approximation of continuous traffic congestion equilibria
Communications in Computational Physics, v. 10, (5), October 2011, p. 1113-1131
Luo, Songting; Leung, Shing Yu; Qian, Jianliang Article
An Eulerian approach for computing the finite time Lyapunov exponent
Journal of Computational Physics, v. 230, (9), May 2011, p. 3500-3524
Leung, Shingyu Article

2010 2

Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method
Communications in Computational Physics, v. 8, (4), October 2010, p. 758-796
Leung, Shingyu; Zhao, Hongkai Article
The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schr?dinger equation
Journal of Computational Physics, v. 229, (23), November 2010, p. 8888-8917
Leung, Shing Yu; Qian, Jianliang Article

2009 4

A grid based particle method for evolution of open curves and surfaces
Journal of Computational Physics, v. 228, (20), November 2009, p. 7706-7728
Leung, Shingyu; Zhao, Hongkai Article
A Grid Based Particle Method for Moving Interface Problems
Journal of Computational Physics, v. 228, (8), May 2009, p. 2993-3024
Leung, Shingyu; Zhao, Hongkai Article
Eulerian Gaussian beams for Schr?dinger equations in the semi-classical regime
Journal of Computational Physics, v. 228, (8), May 2009, p. 2951-2977
Leung, Shing Yu; Qian, Jianliang Article
Expectation-Maximization Algorithm with Local Adaptivity
SIAM Journal on Imaging Sciences, v. 2, (3), January 2009, p. 834-857
Leung, Shingyu; Liang, Gang; Solna, Knut; Zhao, Hongkai Article

2007 2

Eulerian Gaussian Beams for High Frequency Wave Propagation
Geophysics, v. 72, (5), September-October 2007, p. SM61-SM72
Leung, Shingyu; Qian, Jianliang; Burridge, Robert Article
Transmission Traveltime Tomography Based on Paraxial Liouville Equations and Level Set Formulations
Inverse Problems, v. 23, (2), April 2007, article number 019, p. 799-821
Leung, Shingyu; Qian, Jianliang Article

2006 2

A Local Level Set Method for Paraxial Geometrical Optics
SIAM Journal on Scientific Computing, v. 28, (1), 2006, p. 206-223
Qian, Jianliang; Leung, Shingyu Article
An Adjoint State Method for 3D Transmission Traveltime Tomography Using First Arrival
Commun. Math. Sci., v. 4, (1), March 2006, p. 249-266
Leung, Shingyu; Qian, Jianliang Article

2005 2

A Transmission Tomography Problem Based on Multiple Arrivals from Paraxial Liouville Equations
Expanded Abstract for the SEG 75th Annual Meeting, Houston, USA, 2005
Leung, Shingyu; Qian, Jianliang Conference paper
Global Minimization of the Active Contour Model with TV-Inpainting and Two-Phase Denoising
Variational, Geometric, and Level Set Methods in Computer Vision: Third International Workshop, VLSM 2005 / Nikos Paragios, Olivier Faugeras, Tony Chan, Christoph Schn?rr (Eds.). Berlin : Springer, 2005, p. 149-160, Book series: Lecture Notes in Computer Science book series, v. 3752
Leung, Shing Yu; Osher, Stanley Conference paper

2004 2

A Level Set Based Eulerian Method for Paraxial Multivalued Traveltimes
Journal of Computational Physics, v. 197, (2), July 2004, p. 711-736
Qian, Jianliang; Leung, Shingyu Article
A Level Set Method for Three-Dimensional Paraxial Geometrical Optics with Multiple Point Sources
Communications in Mathematical Sciences, v. 2, (4), December 2004, p. 643-672
Leung, Shingyu; Qian, Jianliang; Osher, Stanley Article


No Publications






Teaching Assignment

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2021-22 Winter 0 2021-22 Fall 6 2020-21 Summer 2 2020-21 Spring 6 2020-21 Winter 0 2020-21 Fall 2

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MATH4992 Capstone Project in Applied Mathematics
MATH5311 Advanced Numerical Methods I
MATH6913M Reading Course: Level Set Methods
MFIT5006 Mathematical Foundation of FinTech
UROP1100E Undergraduate Research Opportunities Series 1
UROP2100E Undergraduate Research Opportunities Series 2


MAED6980 MSc Project
UROP1100D Undergraduate Research Opportunities Series 1


MAED5851 Scientific Computation
MAED6980 MSc Project
MATH4336 Introduction to Mathematics of Image Processing
MATH4900 Academic and Professional Development
SCIE1500 Guided Study on Research I
SCIE3110 Teaching Science Using Innovative Teaching Tools


MATH4992 Capstone Project in Applied Mathematics
MFIT5006 Mathematical Foundation of FinTech


No Teaching Assignments


No Teaching Assignments






Research Postgraduate (RPG) Supervision From January 2019 to December 2022 (As of 30 January 2022)

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All Supervisions Current RPGs Graduated RPGs

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Current RPGs

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Doctor of Philosophy FAN, Ganghua (co-supervision)
Mathematics( 2021 - )

HUNG, Chun Kit
Mathematics( 2021 - )

LIU, Xinyu
Mathematics( 2021 - )

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Master of Philosophy HUNG, Kin Ting Ken
Mathematics( 2021 - )

FONG, Ki Wai
Mathematics( 2020 - )

LEE, Young Kyu
Mathematics( 2020 - )

HO, Ka Ho
Mathematics( 2019 - )

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Graduated RPGs

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Doctor of Philosophy CHU, Kwun Lun
Mathematics( Completed in 2020 )

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Master of Philosophy HUNG, Chun Kit
Mathematics( Completed in 2021 )

TAN, Haiyi
Mathematics( Completed in 2019 )

WEI, Siyang
Mathematics( Completed in 2019 )









ProjectsFrom January 2020 to December 2022

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All Projects 1

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No Projects.
Numerical Methods for Hyperbolic Partial Differential Equations on Surfaces


曲面上双曲型偏微分方程的数值方法 Leading


RGC - General Research Fund


Project Team (HKUST)
LEUNG Shing Yu (Lead)


2020 -