Article

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), 2 January 2021, article number 11

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

On the numerical solution of nonlinear eigenvalue problems for the MongeAmpère operator

Author(s): Glowinski, Roland; Leung, Shing Yu; Liu, Has; Qian, Jianliang

Source: ESAIM  Control, Optimisation and Calculus of Variations, v. 26, 2020, article number 118

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

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

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

Guarantees of riemannian optimization for low rank matrix completion

Author(s): Wei, Ke; Cai, Jianfeng; Chan, Tony Fancheong; Leung, Shing Yu

Source: Inverse Problems and Imaging, v. 14, (2), April 2020, p. 233265

An alternating direction explicit method for time evolution equations with applications to fractional differential equations

Author(s): Liu, Hao; Leung, Shing Yu

Source: Methods and applications of analysis, v. 26, (3), 2019, p. 249268

A Finite Element/OperatorSplitting Method for the Numerical Solution of the Three Dimensional MongeAmpere Equation

Author(s): Liu, Hao; Glowinski, Roland; Leung, Shing Yu; Qian, Jianliang

Source: Journal of Scientific Computing, v. 81, (3), December 2019, p. 22712302

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

Pedagogy and Innovation in Science Education: A Case Study of an Experiential Learning Science Undergraduate Course

Author(s): Ng, Yee Fai PHYS; Chan, Kwan Kit; Lei, Huey; Mok, Phoebe; Leung, Shing Yu

Source: The European Journal of Social and Behavioural Sciences, 3 January 2019

A Finite Element/OperatorSplitting Method for the Numerical Solution of the Two Dimensional Elliptic MongeAmpere Equation

Author(s): Glowinski, Roland; Liu, Hao ; Leung, Shing Yu ; Qian, Jianliang

Source: Journal of Scientific Computing, v.79, (1), April 2019

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

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), 2018, p. A484A503

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

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

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

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

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

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

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

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

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

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

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

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), 2015, p. 479509

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

A levelset adjointstate method for crosswell transmissionreflection traveltime tomography

Author(s): Li, Wenbin; Leung, Shingyu; Qian, Jianliang

Source: Geophysical Journal International. , v. 199, (1), 2014, article number ggu262, p. 348367

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), 2014, p. 14721488

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

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

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

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

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

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

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

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

A fast local level set method for inverse gravimetry

Author(s): Isakov, V.; Leung, Shing Yu; Qian, J.

Source: Communications in computational physics. , v. 10, (4), 2011, p. 10441070

An adjoint state method for numerical approximation of continuous traffic congestion equilibria

Author(s): Luo, S.; Leung, Shing Yu; Qian, J.

Source: Communications in computational physics. , v. 10, (5), 2011, p. 11131131

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

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

The backward phase flow and FBItransformbased Eulerian Gaussian beams for the Schrödinger equation

Author(s): Leung, Shing Yu; Qian, J.

Source: Journal of Computational Physics. , v. 229, (23), 2010, NOV, p. 88888917

Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method

Author(s): Leung, Shingyu; Zhao, Hongkai

Source: Communications in computational physics. , v. 8, (4), 2010, OCT, p. 758796

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

A grid based particle method for evolution of open curves and surfaces

Author(s): Leung, Shingyu; Zhao, Hongkai

Source: Journal of computational physics. , v. 228, (20), 2009, NOV 1, p. 77067728

Eulerian Gaussian Beams for SemiClassical Solutions of Schrodinger Equations

Author(s): Leung, Shingyu; Qian, Jianliang

Source: Journal of Computational Physics. , v. 228, (8), May 1 2009, p. 29512977

A Grid Based Particle Method for Moving Interface Problems

Author(s): Leung, Shingyu; Zhao, Hongkai

Source: Journal of Computational Physics. , v. 228, (8), May 1 2009, p. 29933024

ExpectationMaximization Algorithm with Local Adaptivity

Author(s): Leung, Shingyu; Liang, Gang; Solna, Knut; Zhao, Hongkai

Source: SIAM journal on imaging sciences. , v. 2, (3), 2009, p. 834857

Eulerian Gaussian Beams for High Frequency Wave Propagation

Author(s): Leung, Shingyu; Qian, Jianliang; Burridge, Robert

Source: Geophysics. , v. 72, (5), SeptemberOctober 2007, p. SM61SM76

Transmission Traveltime Tomography Based on Paraxial Liouville Equations and Level Set Formulations

Author(s): Leung, Shingyu; Qian, Jianliang

Source: Inverse Problems. , v. 23, 2007, p. 799821

A Local Level Set Method for Paraxial Geometrical Optics

Author(s): Qian, Jianliang; Leung, Shingyu

Source: SIAM J. Sci. Comp.. , v. 28, (1), 2006, p. 206223

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

A Level Set Based Eulerian Method for Paraxial Multivalued Traveltimes

Author(s): Qian, Jianliang; Leung, Shingyu

Source: Journal of Computational Physics. , v. 197, (2), July 1 2004, p. 711736

A Level Set Method for Threedimensional Paraxial Geometrical Optics with Multiple Sources

Author(s): Leung, Shingyu; Qian, Jianliang; Osher, Stanley

Source: Commun. Math. Sci.. , v. 2, (4), December 2004, p. 643672
Conference paper

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

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

A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation

Author(s): Liu, Jun; Tai, XueCheng; Leung, Shing Yu

Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). , v. 8081 LNCS, 2013, p. 251265

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

Fast Global Minimization of the Active Contour Model with TVInpainting and Twophase Denoising

Author(s): Leung, Shingyu; Osher, Stanley

Source: Proceeding of the 3rd IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision. , 2005, p. 149160

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
Other

Correction to: A Finite Element/OperatorSplitting Method for the Numerical Solution of the Two Dimensional Elliptic MongeAmpere Equation (vol 79, pg 1, 2019)

Author(s): Glowinski, Roland; Liu, Hao; Leung, Shing Yu; Qian, Jianliang

Source: Journal of Scientific Computing, v. 79, (1), April 2019, p. 48

