Shing Yu LEUNG
梁承裕

PhD in Mathematics
University of California, Los Angeles, 2006

Associate Dean of Science (Undergraduate Studies & Student Affairs)

Professor
Department of Mathematics

Google Scholar
rXnFQQQAAAAJ
ORCID
0000-0002-4549-2761
ResearcherID
E-3100-2013
Scopus ID
7202044873

Research Interest

  • Applied mathematics
  • Computational mathematics
  • Nonlinear partial differential equations
  • Scientific computation

Publications

2024 3

Hadamard Integrators for Wave Equations in Time and Frequency Domain: Eulerian Formulations via Butterfly Algorithms

Journal of Scientific Computing, v. 100, (3), September 2024, article number 79
Wei, Yuxiao; Cheng, Jin; Leung, Shing Yu; Burridge, Robert; Qian, Jianliang
Article

Operator-Splitting/Finite Element Methods for the Minkowski Problem

SIAM Journal on Scientific Computing, v. 46, (5), November 2024, p. A3230-A3257
Liu, Hao; Leung, Shing Yu; Qian, Jianliang
Article

SLERP-TVDRK (STVDRK) Methods for Ordinary Differential Equations on Spheres

Journal of Scientific Computing, v. 101, (3), October 2024, article number 63
Leung, Shing Yu; Chau, Wai Ming; Lee, Young Kyu
Article
2023 5

A Simple Embedding Method for Scalar Hyperbolic Conservation Laws on Implicit Surfaces

SIAM Journal on Scientific Computing, v. 45, (6), December 2023, p. A2813-A2835
Hung, Chun Kit; Leung, Shingyu
Article

A Simple Embedding Method for the Laplace-Beltrami Eigenvalue Problem on Implicit Surfaces

Communications on Applied Mathematics and Computation, October 2023
Lee, Young Kyu; Leung, Shing Yu
Article

Sparse subsampling of flow measurements for finite-time Lyapunov exponent in domains with obstacles

Journal of Computational and Applied Mathematics, v. 431, October 2023, article number 115255
Ng, Yu Keung; You, Guoqiao; Leung, Shingyu
Article

Spherical Essentially Non-oscillatory (SENO) Interpolation

Journal of Scientific Computing, v. 94, (1), January 2023, article number 28
Fong, Ki Wai; Leung, Shing Yu
Article

Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems

Communications in Computational Physics, v. 33, (3), March 2023, p. 824-848
Chau, Wai Ming; Leung, Shingyu
Article
2022 1

Liouville Partial-Differential-Equation Methods for Computing 2D Complex Multivalued Eikonals in Attenuating Media

Geophysics, v. 87, (2), March 2022, p. T71-T84
Leung, Shing Yu; Hu, Jiangtao; Qian, Jianliang
Article
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 Schrödinger Equations

Journal of Scientific Computing, v. 88, (3), July 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 Schrödinger 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. 156-173
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 Schrödinger 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 Schrödinger 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 Schrödinger 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 Schnörr (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
Article 3

Hadamard Integrators for Wave Equations in Time and Frequency Domain: Eulerian Formulations via Butterfly Algorithms

Journal of Scientific Computing, v. 100, (3), September 2024, article number 79
Wei, Yuxiao; Cheng, Jin; Leung, Shing Yu; Burridge, Robert; Qian, Jianliang

Operator-Splitting/Finite Element Methods for the Minkowski Problem

SIAM Journal on Scientific Computing, v. 46, (5), November 2024, p. A3230-A3257
Liu, Hao; Leung, Shing Yu; Qian, Jianliang

SLERP-TVDRK (STVDRK) Methods for Ordinary Differential Equations on Spheres

Journal of Scientific Computing, v. 101, (3), October 2024, article number 63
Leung, Shing Yu; Chau, Wai Ming; Lee, Young Kyu
Article 5

A Simple Embedding Method for Scalar Hyperbolic Conservation Laws on Implicit Surfaces

SIAM Journal on Scientific Computing, v. 45, (6), December 2023, p. A2813-A2835
Hung, Chun Kit; Leung, Shingyu

A Simple Embedding Method for the Laplace-Beltrami Eigenvalue Problem on Implicit Surfaces

Communications on Applied Mathematics and Computation, October 2023
Lee, Young Kyu; Leung, Shing Yu

Sparse subsampling of flow measurements for finite-time Lyapunov exponent in domains with obstacles

Journal of Computational and Applied Mathematics, v. 431, October 2023, article number 115255
Ng, Yu Keung; You, Guoqiao; Leung, Shingyu

Spherical Essentially Non-oscillatory (SENO) Interpolation

Journal of Scientific Computing, v. 94, (1), January 2023, article number 28
Fong, Ki Wai; Leung, Shing Yu

Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems

Communications in Computational Physics, v. 33, (3), March 2023, p. 824-848
Chau, Wai Ming; Leung, Shingyu
Article 1

Liouville Partial-Differential-Equation Methods for Computing 2D Complex Multivalued Eikonals in Attenuating Media

Geophysics, v. 87, (2), March 2022, p. T71-T84
Leung, Shing Yu; Hu, Jiangtao; Qian, Jianliang
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 Schrödinger Equations

Journal of Scientific Computing, v. 88, (3), July 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 Schrödinger Inverse Problem

Springer Proceedings in Mathematics and Statistics, v. 360, 2021, p. 13-31
Wei, Siyang; Leung, Shing Yu
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
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. 156-173
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
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
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
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
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
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 Schrödinger 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
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
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
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
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 Schrödinger equation

Journal of Computational Physics, v. 229, (23), November 2010, p. 8888-8917
Leung, Shing Yu; Qian, Jianliang
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 Schrödinger 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
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
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
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 Schnörr (Eds.). Berlin : Springer, 2005, p. 149-160, Book series: Lecture Notes in Computer Science book series, v. 3752
Leung, Shing Yu; Osher, Stanley
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
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. 156-173
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 Schrödinger 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 Schrödinger 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 Schrödinger 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 Schnörr (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

MATH4900 Academic and Professional Development
MATH4999 Independent Capstone Project
SCIE1090D Community Services Project: Underwater Robot Community Engagement Project
SCIE1500 Guided Study on Research I
SCIE2500 Guided Study on Research II
SCIE3500 IRE Research Project I
SCIE3900 International Research Experience
SCIE4500 IRE Research Project II
UROP1100O Undergraduate Research Opportunities Series 1
UROP2100O Undergraduate Research Opportunities Series 2
SCIE3900 International Research Experience
DASC2010 Calculus for Data Analytics in Science
MAED5851 Scientific Computation
MATH4992 Capstone Project in Applied Mathematics
MATH4999 Independent Capstone Project
MATH6912G Reading Course: Computer Methods for DAEs
SCIE1090C Community Services Project: Developing Leadership Through Service Learning
UROP1100N Undergraduate Research Opportunities Series 1
No Teaching Assignments
No Teaching Assignments
No Teaching Assignments

Research Postgraduate (RPG) Supervision

From January 2022 to December 2025 (As of 07 April 2025)
Current RPGs
Doctor of Philosophy

  • SHI, Xiao (co-supervision)
    Mathematics

  • HUNG, Kin Ting Ken
    Mathematics

  • LEE, Young Kyu
    Mathematics

Master of Philosophy

  • LEUNG, Ka Lun
    Mathematics

  • CHAU, Wai Ming
    Mathematics

  • GURUNG, Nishan
    Mathematics

Graduated RPGs
Doctor of Philosophy

  • HUNG, Chun Kit
    Mathematics( Completed in 2024 )

  • FAN, Ganghua (co-supervision)
    Mathematics( Completed in 2023 )

Master of Philosophy

  • HO, Ka Ho
    Mathematics( Completed in 2024 )

  • HUNG, Kin Ting Ken
    Mathematics( Completed in 2023 )

  • FONG, Ki Wai
    Mathematics( Completed in 2022 )

  • LEE, Young Kyu
    Mathematics( Completed in 2022 )

Projects

From January 2023 to December 2025 (As of 07 April 2025)
  • Spherical Total Variation Diminishing Runge-Kutta (STVDRK) Schemes
    球面總變差收斂龍格-庫塔(STVDRK)方案 Leading
    RGC - General Research Fund
    Project Team (HKUST)
    • LEUNG Shing Yu (Lead)
    2025 -
  • Essentially Non-Oscillatory (ENO) Scheme for Spherical Data Interpolation
    球面資料內插的本質非振盪（ENO）方案 Leading
    RGC - General Research Fund
    Project Team (HKUST)
    • LEUNG Shing Yu (Lead)
    2023 -
  • Numerical Methods for Hyperbolic Partial Differential Equations on Surfaces
    曲面上雙曲型偏微分方程的數值方法 Leading
    RGC - General Research Fund
    Project Team (HKUST)
    • LEUNG Shing Yu (Lead)
    2020 - 2023
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