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Professor
Biography
Prof. Leung has been with the Department of Mathematics at the Hong Kong University of Science and Technology (HKUST) since 2009. Prior to joining HKUST, he was an instructor and postdoc researcher at the University of California, Irvine. He was educated at the HKUST (B.Sc. 99'; M.Phil. 01') and the University of California, Los Angeles (Ph.D. 06', in Mathematics). His research focuses on Eulerian techniques to approximate high frequency asymptotic solutions to wave phenomena and their related inverse problems, numerical methods for interfacial motions, and variational and statistical methods for image processing. Prof. Leung is currently an associate professor of Mathematics and an associate dean of Science.Research Interests
Numerical methods for partial differential equations and scientific computingTeaching
 MAED5851 Scientific Computation
 MATH4992 Capstone Project in Applied Mathematics
 MATH4999 Independent Capstone Project
Selected Publications
Article

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. A2813A2835
 Year: 2023

Spherical Essentially Nonoscillatory (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

Sparse subsampling of flow measurements for finitetime 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

WithinCluster 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. 824848
 Year: 2023

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

Liouville PartialDifferentialEquation 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. T71T84
 Year: 2022

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

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

RayIllumination Compensation for AdjointState FirstArrival 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. U109U119
 Year: 2021

Eulerian partialdifferentialequation methods for complexvalued eikonals in attenuating media
 Author(s): Hu, Jiangtao; Qian, Jianliang; Song, Jian; Ouyang, Min; Cao, Junxing; Leung, Shing Yu
 Source: Geophysics, v. 86, (4), JulyAugust 2021, p. T179T192
 Year: 2021

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

A LevelSet AdjointState 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. A2352A2380
 Year: 2021

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

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

On the numerical solution of nonlinear eigenvalue problems for the MongeAmpère 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

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. A2910A2942
 Year: 2020

A Simple SemiImplicit 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. 620643
 Year: 2020

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. 249268
 Year: 2019

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. 11431177
 Year: 2019

A Finite Element/OperatorSplitting 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. 147
 Year: 2019

A Finite Element/OperatorSplitting 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. 22712302
 Year: 2019

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. 156173
 Year: 2019

Modified Virtual Grid Difference For Discretizing the Laplacebeltrami Operatior on Point Clouds
 Author(s): Wang, Meng; Leung, Shing Yu; Zhaw, Hongkai
 Source: SIAM Journal on Scientific Computing, v. 40, (1), 2018, p. A1A21
 Year: 2018

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. 14071435
 Year: 2018

A Simple Explicit Operatorsplitting 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. A484A503
 Year: 2018

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. 7096
 Year: 2018

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. 131159
 Year: 2018

A Fast Huygens Sweeping Method for Capturing Paraxial Multicolor Optical Selffocusing 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. 108138
 Year: 2017

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. A415A437
 Year: 2017

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. A1616A1646
 Year: 2017

OperatorSplitting 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. A1195A1223
 Year: 2016

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. 11981222
 Year: 2016

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. 837859
 Year: 2016

A PenalizationRegularizationOperator 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. 12631292
 Year: 2015

An improved fast local level set method for threedimensional inverse gravimetry
 Author(s): Lu, Wangtao; Leung, Shingyu; Qian, Jianliang
 Source: Inverse Problems and Imaging, v. 9, (2), May 2015, p. 479509
 Year: 2015

A Fast SemiImplicit 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. 203229
 Year: 2015

Fast Huygens Sweeping Methods for Schrödinger Equations in the SemiClassical Regime
 Author(s): Leung, Shing Yu; Qian, Jianliang; Serna, Susana
 Source: Methods and Applications of Analysis, v. 21, (1), March 2014, p. 3166
 Year: 2014

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. 279306
 Year: 2014

A levelset adjointstate method for crosswell transmissionreflection traveltime tomography
 Author(s): Li, Wenbin; Leung, Shingyu; Qian, Jianliang
 Source: Geophysical Journal International, v. 199, (1), October 2014, p. 348367
 Year: 2014

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. 112132
 Year: 2014

A new continuous maxflow algorithm for multiphase image segmentation using superlevel set functions
 Author(s): Liu, Jun; Tai, Xuecheng; Leung, Shingyu; Huang, Haiyang
 Source: Journal of Visual Communication and Image Representation, v. 25, (6), August 2014, p. 14721488
 Year: 2014

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. 139160
 Year: 2014

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

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. 582596
 Year: 2013

A threedimensional 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. 523544
 Year: 2013

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. 243266
 Year: 2013

Expectationmaximization algorithm with total variation regularization for vectorvalued image segmentation
 Author(s): Liu, Jun; Ku, YinBon; Leung, Shingyu
 Source: Journal of Visual Communication and Image Representation, v. 23, (8), November 2012, p. 12341244
 Year: 2012

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. 35003524
 Year: 2011

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. 11131131
 Year: 2011

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. 10441070
 Year: 2011

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. 25402561
 Year: 2011

The backward phase flow and FBItransformbased 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. 88888917
 Year: 2010

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. 758796
 Year: 2010

Eulerian Gaussian beams for Schrödinger equations in the semiclassical regime
 Author(s): Leung, Shing Yu; Qian, Jianliang
 Source: Journal of Computational Physics, v. 228, (8), May 2009, p. 29512977
 Year: 2009

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. 29933024
 Year: 2009

ExpectationMaximization 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. 834857
 Year: 2009

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. 77067728
 Year: 2009

Eulerian Gaussian Beams for High Frequency Wave Propagation
 Author(s): Leung, Shingyu; Qian, Jianliang; Burridge, Robert
 Source: Geophysics, v. 72, (5), SeptemberOctober 2007, p. SM61SM72
 Year: 2007

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. 799821
 Year: 2007

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. 249266
 Year: 2006

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. 206223
 Year: 2006

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. 711736
 Year: 2004

A Level Set Method for ThreeDimensional 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. 643672
 Year: 2004
Conference paper

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. 1331
 Year: 2021

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, ShingTung Yau. International Press of Boston, Inc., 2019, p. 579622, Advanced Lectures in Mathematics, v. 44
 Year: 2019

Primaldual method for continuous maxflow approaches
 Author(s): Wei, Ke; Tai, Xuecheng; Chan, Tony Fancheong; 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. 1724
 Year: 2015

A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation
 Author(s): Liu, Jun; Tai, XueCheng; Leung, Shing Yu
 Source: Energy Minimization Methods in Computer Vision and Pattern Recognition / Anders Heyden, Fredrik Kahl, Carl Olsson, Magnus Oskarsson, XueCheng Tai, editors. Berlin : Springer, 2013, p. 251265, Book series: Lecture Notes in Computer Science, v. 8081
 Year: 2013

A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation
 Author(s): Liu, Jun; Tai, XueCheng; Leung, Shing Yu
 Source: 9th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, Lund, Sweden, 1921 Aug 2013
 Year: 2012

Global Minimization of the Active Contour Model with TVInpainting and TwoPhase 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. 149160, Book series: Lecture Notes in Computer Science book series, v. 3752
 Year: 2005

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