Article 
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Liouville Partial-Differential-Equation Methods for Computing 2-D Complex-Valued Eikonals in the Multivalued Sense in Attenuating Media
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Author(s): Leung, Shing Yu; Hu, Jiangtao; Qian, Jianliang
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Source: Geophysics, v. 87, (2), 2022
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Ray-Illumination Compensation for Adjoint-State First-Arrival Traveltime Tomography
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Author(s): Hu, Jiangtao; Qian, Jianliang; Cao, Junxing; Wang, Xingjian; Wang, Huazhong; Leung, Shing Yu
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Source: Geophysics, v. 86, (5), September 2021, p. U109-U119
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A Level-Set Adjoint-State Method for Transmission Traveltime Tomography in Irregular Domains
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Author(s): Leung, Shing Yu; Qian, Jianliang; Hu, Jiangtao
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Source: SIAM Journal on Scientific Computing, v. 43, (3), 2021, p. A2352-A2380
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Fast Huygens Sweeping Methods for a Class of Nonlocal Schrödinger Equations
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Author(s): Ho, Ka Ho; Leung, Shing Yu; Qian, Jianliang
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Source: Journal of Scientific Computing, v. 88, (3), September 2021, article number 54
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Eulerian algorithms for computing some Lagrangian flow network quantities
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Author(s): You, Guoqiao; Leung, Shing Yu
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Source: Journal of Computational Physics, v. 445, 15 November 2021, article number 110620
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Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media
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Author(s): Hu, Jiangtao; Qian, Jianliang; Song, Jian; Ouyang, Min; Cao, Junxing; Leung, Shing Yu
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Source: Geophysics, v. 86, (4), July-August 2021, p. T179-T192
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A Level Set Method for the Dirichlet k-Partition Problem
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Author(s): Chu, Kwun Lun; Leung, Shing Yu
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Source: Journal of Scientific Computing, v. 86, (1), 2 January 2021, article number 11
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Computing the finite time Lyapunov exponent for flows with uncertainties
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Author(s): You, Guoqiao; Leung, Shing Yu
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Source: Journal of Computational Physics, v. 425, 15 January 2021, article number 109905
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On the numerical solution of nonlinear eigenvalue problems for the Monge-Ampère operator
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Author(s): Glowinski, Roland; Leung, Shing Yu; Liu, Has; Qian, Jianliang
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Source: ESAIM - Control, Optimisation and Calculus of Variations, v. 26, 2020, article number 118
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Efficient algorithms for computing multidimensional integral fractional laplacians via spherical means
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Author(s): Xu, Boxi; Cheng, Jin; Leung, Shing Yu; Qian, Jianliang
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Source: SIAM Journal on Scientific Computing, v. 42, (5), September 2020, p. A2910-A2942
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Fast Construction of Forward Flow Maps using Eulerian Based Interpolation Schemes
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Author(s): You, Guoqiao; Leung, Shing Yu
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Source: Journal of Scientific Computing, v. 82, (2), February 2020, article number 32
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A Simple Semi-Implicit Scheme for Partial Differential Equations with Obstacle Constraints
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Author(s): Liu, Hao; Leung, Shing Yu
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Source: Numerical Mathematics Theory Methods and Applications, v. 13, (3), August 2020, p. 620-643
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Guarantees of riemannian optimization for low rank matrix completion
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Author(s): Wei, Ke; Cai, Jianfeng; Chan, Tony Fan-cheong; Leung, Shing Yu
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Source: Inverse Problems and Imaging, v. 14, (2), April 2020, p. 233-265
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A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge–Ampère Equation
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Author(s): Liu, Hao; Glowinski, Roland; Leung, Shing Yu; Qian, Jianliang
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Source: Journal of Scientific Computing, v. 81, (3), December 2019, p. 2271-2302
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A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge–Ampère Equation
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Author(s): Glowinski, Roland; Liu, Hao; Leung, Shing Yu; Qian, Jianliang
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Source: Journal of Scientific Computing, v. 79, (1), April 2019, p. 1-47
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An alternating direction explicit method for time evolution equations with applications to fractional differential equations
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Author(s): Liu, Hao; Leung, Shing Yu
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Source: Methods and applications of analysis, v. 26, (3), 2019, p. 249-268
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A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge-Ampere Equation
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Author(s): Liu, Hao; Glowinski, Roland; Leung, Shing Yu; Qian, Jianliang
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Source: Journal of Scientific Computing, v. 81, (3), December 2019, p. 2271-2302
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Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories
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Author(s): Leung, Shing Yu ; Ng, Yu Keung
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Source: Communications in Computational Physics, v. 26, (4), October 2019, p. 1143-1177
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Pedagogy and Innovation in Science Education: A Case Study of an Experiential Learning Science Undergraduate Course
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Author(s): Ng, Yee Fai PHYS; Chan, Kwan Kit; Lei, Huey; Mok, Phoebe; Leung, Shing Yu
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Source: The European Journal of Social and Behavioural Sciences, 3 January 2019
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A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampere Equation
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Author(s): Glowinski, Roland; Liu, Hao ; Leung, Shing Yu ; Qian, Jianliang
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Source: Journal of Scientific Computing, v.79, (1), April 2019
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A weak formulation for the multiphase Stokes flow problem without body fitting grids
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Author(s): Ying, Ningchen ; Hou, Songming; Leung, Shing Yu ; Zhao, Hongkai
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Source: Pure and Applied Mathematics Quarterly, v. 14, (1), 2018, p. 131-159
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A Simple Explicit Operator-splitting Method for Effective Hamiltonians
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Author(s): Glowinski, Roland; Leung, Shing Yu ; Qian, Jianliang
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Source: SIAM Journal on Scientific Computing. , v. 40, (1), 2018, p. A484-A503
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Modified Virtual Grid Difference For Discretizing the Laplace-beltrami Operatior on Point Clouds
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Author(s): Wang, Meng ; Leung, Shing Yu ; Zhaw, Hongkai
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Source: SIAM Journal on Scientific Computing. , v. 40, (1), 2018, p. A1-A21
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An Improved Eulerian Approach for the Finite Time Lyapunov Exponent
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Author(s): You, Guoqiao; Leung, Shing Yu
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Source: Journal of Scientific Computing. , v. 76, (3), September 2018, p. 1407-1435
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Eulerian Based Interpolation Schemes for Flow Map Construction and Line Integral Computation with Applications to Lagrangian Coherent Structures Extraction
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Author(s): You, Guoqiao; Leung, Shingyu
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Source: Journal of Scientific Computing. , v. 74, (1), January 2018, p. 70-96
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Eulerian methods for visualizing continuous dynamical systems using Lyapunov exponents
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Author(s): You, Guoqiao; Wong, Tony; Leung, Shingyu
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Source: SIAM Journal on Scientific Computing. , v. 39, (2), 2017, p. A415-A437
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A Level Set Based Variational Principal Flow Method for Nonparametric Dimension Reduction on Riemannian Manifolds
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Author(s): Liu, Hao; Yao, Zhigang; Leung, Shing Yu; Chan, Tony F.
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Source: SIAM Journal on Scientific Computing. , v. 39, (4), 2017, p. A1616-A1646
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A Fast Huygens Sweeping Method for Capturing Paraxial Multi-color Optical Self-focusing in Nematic Liquid Crystals
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Author(s): Kwan, Wingfai; Leung, Shing Yu; Wang, Xiao Ping; Qian, Jianliang
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Source: Journal of Computational Physics. , v. 348, November 2017, p. 108-138
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OPERATOR-SPLITTING BASED FAST SWEEPING METHODS FOR ISOTROPIC WAVE PROPAGATION IN A MOVING FLUID
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Author(s): Glowinski, Roland; Leung, Shingyu; Qian, Jianliang
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Source: SIAM Journal on Scientific Computing. , v. 38, (2), 2016, p. A1195-A1223
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Guarantees of Riemannian Optimization for Low Rank Matrix Recovery
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Author(s): Wei, Ke; Cai, Jianfeng; Chan, Tony F.; Leung, Shing Yu
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Source: SIAM Journal on Matrix Analysis and Applications. , v. 37, (3), 2016, p. 1198-1222
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A Fast Sweeping Method for Eikonal Equations on Implicit Surfaces
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Author(s): Wong, Ka Wah; Leung, Shing Yu
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Source: Journal of Scientific Computing. , v. 67, (3), June 2016, p. 837-859
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A Penalization-Regularization-Operator Splitting Method for Eikonal Based Traveltime Tomography
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Author(s): Glowinski, Roland; Leung, Shingyu; Qian, Jianliang
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Source: SIAM Journal on Imaging Sciences. , v. 8, (2), June 2015, article number A017, p. 1263-1292
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A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems
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Author(s): You, Guoqiao; Leung, Shingyu
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Source: Communications in Computational Physics. , v. 18, (1), July 2015, p. 203-229
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AN IMPROVED FAST LOCAL LEVEL SET METHOD FOR THREE-DIMENSIONAL INVERSE GRAVIMETRY
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Author(s): Lu, Wangtao; Leung, Shingyu; Qian, Jianliang
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Source: Inverse Problems and Imaging. , v. 9, (2), 2015, p. 479-509
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An Eulerian Method for Computing the Coherent Ergodic Partition of Continuous Dynamical Systems
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Author(s): You, Guoqiao; Leung, Shing Yu
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Source: Journal of Computational Physics. , v. 264, May 2014, p. 112-132
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A level-set adjoint-state method for crosswell transmission-reflection traveltime tomography
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Author(s): Li, Wenbin; Leung, Shingyu; Qian, Jianliang
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Source: Geophysical Journal International. , v. 199, (1), 2014, article number ggu262, p. 348-367
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A new continuous max-flow algorithm for multiphase image segmentation using super-level set functions
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Author(s): Liu, Jun; Tai, Xue-cheng; Leung, Shingyu; Huang, Haiyang
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Source: Journal of Visual Communication and Image Representation. , v. 25, (6), 2014, p. 1472-1488
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A Cell Based Particle Method for Modeling Dynamic Interfaces
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Author(s): Hon, Sean Y.; Leung, Shing Yu; Zhao, Hongkai
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Source: Journal of Computational Physics. , v. 272, September 2014, p. 279-306
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Fast Huygens Sweeping Methods for Schrödinger Equations in the Semi-Classical Regime
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Author(s): Leung, Shing Yu ; Qian, Jianliang; Serna, Susana
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Source: Methods and Applications of Analysis. , v. 21, (1), March 2014, p. 31-66
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VIALS: An Eulerian tool based on total variation and the level set method for studying dynamical systems
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Author(s): You, Guoqiao; Leung, Shing Yu
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Source: Journal of Computational Physics. , v. 266, June 2014, p. 139-160
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A Splitting Algorithm for Image Segmentation on Manifolds Represented by the Grid Based Particle Method
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Author(s): Liu, Jun; Leung, Shingyu
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Source: Journal of Scientific Computing. , v. 56, (2), August 2013, p. 243-266
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A THREE-DIMENSIONAL INVERSE GRAVIMETRY PROBLEM FOR ICE WITH SNOW CAPS
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Author(s): Isakov, Victor; Leung, Shingyu; Qian, Jianliang
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Source: Inverse Problems and Imaging. , v. 7, (2), May 2013, p. 523-544
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The backward phase flow method for the Eulerian finite time Lyapunov exponent computations
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Author(s): Leung, Shingyu
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Source: Chaos. , v. 23, (4), October 2013, article number 043132
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A fast local level set adjoint state method for first arrival transmission traveltime tomography with discontinuous slowness
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Author(s): Li, Wenbin; Leung, Shingyu
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Source: Geophysical Journal International. , v. 195, (1), October 2013, p. 582-596
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Expectation-maximization algorithm with total variation regularization for vector-valued image segmentation
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Author(s): Liu, Jun; Ku, Yin-Bon; Leung, Shingyu
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Source: Journal of visual communication and image representation. , v. 23, (8), November 2012, p. 1234-1244
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A fast local level set method for inverse gravimetry
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Author(s): Isakov, V.; Leung, Shing Yu; Qian, J.
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Source: Communications in computational physics. , v. 10, (4), 2011, p. 1044-1070
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An adjoint state method for numerical approximation of continuous traffic congestion equilibria
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Author(s): Luo, S.; Leung, Shing Yu; Qian, J.
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Source: Communications in computational physics. , v. 10, (5), 2011, p. 1113-1131
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An Eulerian approach for computing the finite time Lyapunov exponent
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Author(s): Leung, Shingyu
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Source: Journal of computational physics. , v. 230, (9), May 2011, p. 3500-3524
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A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion
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Author(s): Leung, Shingyu; Lowengrub, John; Zhao, Hongkai
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Source: Journal of computational physics. , v. 230, (7), April 2011, p. 2540-2561
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The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation
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Author(s): Leung, Shing Yu; Qian, J.
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Source: Journal of Computational Physics. , v. 229, (23), 2010, NOV, p. 8888-8917
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Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method
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Author(s): Leung, Shingyu; Zhao, Hongkai
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Source: Communications in computational physics. , v. 8, (4), 2010, OCT, p. 758-796
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Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime
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Author(s): Leung, Shing Yu; Qian, Jianliang
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Source: Journal of Computational Physics, v. 228, (8), May 2009, p. 2951-2977
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A grid based particle method for evolution of open curves and surfaces
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Author(s): Leung, Shingyu; Zhao, Hongkai
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Source: Journal of computational physics. , v. 228, (20), 2009, NOV 1, p. 7706-7728
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Eulerian Gaussian Beams for Semi-Classical Solutions of Schrodinger Equations
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Author(s): Leung, Shingyu; Qian, Jianliang
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Source: Journal of Computational Physics. , v. 228, (8), May 1 2009, p. 2951-2977
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A Grid Based Particle Method for Moving Interface Problems
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Author(s): Leung, Shingyu; Zhao, Hongkai
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Source: Journal of Computational Physics. , v. 228, (8), May 1 2009, p. 2993-3024
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Expectation-Maximization Algorithm with Local Adaptivity
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Author(s): Leung, Shingyu; Liang, Gang; Solna, Knut; Zhao, Hongkai
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Source: SIAM journal on imaging sciences. , v. 2, (3), 2009, p. 834-857
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Eulerian Gaussian Beams for High Frequency Wave Propagation
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Author(s): Leung, Shingyu; Qian, Jianliang; Burridge, Robert
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Source: Geophysics. , v. 72, (5), September-October 2007, p. SM61-SM76
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Transmission Traveltime Tomography Based on Paraxial Liouville Equations and Level Set Formulations
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Author(s): Leung, Shingyu; Qian, Jianliang
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Source: Inverse Problems. , v. 23, 2007, p. 799-821
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A Local Level Set Method for Paraxial Geometrical Optics
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Author(s): Qian, Jianliang; Leung, Shingyu
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Source: SIAM J. Sci. Comp.. , v. 28, (1), 2006, p. 206-223
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An Adjoint State Method for 3D Transmission Traveltime Tomography Using First Arrival
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Author(s): Leung, Shingyu; Qian, Jianliang
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Source: Commun. Math. Sci.. , v. 4, (1), March 2006, p. 249-266
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A Level Set Method for Three-Dimensional Paraxial Geometrical Optics with Multiple Point Sources
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Author(s): Leung, Shingyu; Qian, Jianliang; Osher, Stanley
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Source: Communications in Mathematical Sciences, v. 2, (4), December 2004, p. 643-672
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A Level Set Based Eulerian Method for Paraxial Multivalued Traveltimes
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Author(s): Qian, Jianliang; Leung, Shingyu
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Source: Journal of Computational Physics. , v. 197, (2), July 1 2004, p. 711-736
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A Level Set Method for Three-dimensional Paraxial Geometrical Optics with Multiple Sources
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Author(s): Leung, Shingyu; Qian, Jianliang; Osher, Stanley
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Source: Commun. Math. Sci.. , v. 2, (4), December 2004, p. 643-672
Conference paper 
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An Adjoint State Method for An Schrödinger Inverse Problem
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Author(s): Wei, Siyang; Leung, Shing Yu
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Source: Springer Proceedings in Mathematics and Statistics, v. 360, 2021, p. 13-31
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Recent Developments in Eulerian Approaches for Visualizing Continuous Dynamical System
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Author(s): Leung, Shing Yu ; You, Guoqiao; Wong, Ka Wah; Ng, Yu Keung
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Source: Proceedings of the Seventh International Congress of Chinese Mathematicians, Volume II / Editors Lizhen Ji, Lo Yang, Shing-Tung Yau. International Press of Boston, Inc., 2019, p. 579-622, Advanced Lectures in Mathematics, v. 44
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Primal-dual method for continuous max-flow approaches
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Author(s): Wei, Ke ; Tai, Xuecheng ; Chan, Tony Fan-cheong ; Leung, Shingyu
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Source: Computational Vision and Medical Image Processing V - Proceedings of 5th Eccomas Thematic Conference on Computational Vision and Medical Image Processing, VipIMAGE 2015. , 2015, p. 17-24
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A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation
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Author(s): Liu, Jun; Tai, Xue-Cheng; Leung, Shing Yu
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Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). , v. 8081 LNCS, 2013, p. 251-265
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A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation
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Author(s): Liu, Jun; Tai, Xue-Cheng; Leung, Shing Yu
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Source: 9th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, Lund, Sweden. , 19-21 Aug 2013
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Global Minimization of the Active Contour Model with TV-Inpainting and Two-Phase Denoising
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Author(s): Leung, Shing Yu; Osher, Stanley
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Source: Variational, Geometric, and Level Set Methods in Computer Vision: Third International Workshop, VLSM 2005 / Nikos Paragios, Olivier Faugeras, Tony Chan, Christoph Schnörr (Eds.). Berlin : Springer, 2005, p. 149-160, Book series: Lecture Notes in Computer
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Fast Global Minimization of the Active Contour Model with TV-Inpainting and Two-phase Denoising
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Author(s): Leung, Shingyu; Osher, Stanley
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Source: Proceeding of the 3rd IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision. , 2005, p. 149-160
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A Transmission Tomography Problem Based on Multiple Arrivals from Paraxial Liouville Equations
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Author(s): Leung, Shingyu; Qian, Jianliang
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Source: Expanded Abstract for the SEG 75th Annual Meeting, Houston, USA. , 2005
Other 
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Correction to: A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge–Ampère Equation
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Author(s): Glowinski, Roland; Liu, Hao; Leung, Shing Yu; Qian, Jianliang
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Source: Journal of Scientific Computing, v. 79, (1), April 2019, p. 48
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Correction to: A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampere Equation (vol 79, pg 1, 2019)
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Author(s): Glowinski, Roland; Liu, Hao; Leung, Shing Yu; Qian, Jianliang
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Source: Journal of Scientific Computing, v. 79, (1), April 2019, p. 48
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