Publications

Fast Operator-Splitting Methods for Nonlinear Elliptic Equations

Jingyu Yang, Shingyu Leung, Jianliang Qian, Hao Liu (corresponding author)

SIAM J. Sci. Comput.

• Numerical Partial Differential Equations

Operator-splitting methods for L2 optimal-transport using a convexity-preserving formulation of the Monge–Ampère equation

Jingyu Yang, Shingyu Leung, Jianliang Qian, Hao Liu (corresponding author)

J. Comput. Phys., 565, 115237

• Numerical Partial Differential Equations

High-Order Spherical Runge-Kutta Schemes Based on Spherical Linear Extrapolation

Young Kyu Lee (corresponding author), Shingyu Leung

Journal of Scientific Computing, vol. 107, article 103

• Numerical Partial Differential Equations

A Multilayer Level-set Method for Eikonal-based Traveltime Tomography

Wenbin Li, Ken K.T. Hung, Shingyu Leung (corresponding author)

J. Comput. Phys., 560, 114941

• Inverse Problems

Efficient Hadamard Integrators for Time-Dependent Wave Equations in Bounded Domains: Forward and Backward Propagation

Yuxiao Wei, Shingyu Leung, Robert Burridge, Jianliang Qian (corresponding author)

SIAM J. Multiscale Model. Simul., 24 (1), 32-67

• Numerical Partial Differential Equations

Energy-Stable Alternating Direction Explicit Schemes on Adaptive Meshes

Shingyu Leung

• Human AI Co-creation

High-Order Alternating Direction Explicit Schemes for Linear Dissipative Systems

Shingyu Leung

• Human AI Co-creation

Energy-Stable Alternating Direction Explicit Schemes for Nonlinear Diffusion

Shingyu Leung

• Human AI Co-creation

A Moment-Based Eulerian Method for Variance-Based Finite-Time Lyapunov Exponent Computation in Stochastic Flows

Shingyu Leung

• Human AI Co-creation

Level-Set Implicit Retraction Interpolation on General Implicit Hypersurfaces

Shingyu Leung

• Human AI Co-creation

Geodesic Interpolation on the Grassmann Manifold: GLERP and Recursive GIDER Interpolants

Shingyu Leung

• Human AI Co-creation

Analytic First Derivatives of SIDER Interpolation

Shingyu Leung

• Human AI Co-creation

A Quaternion-BCH Framework for the Local Accuracy of SIDER Interpolation

Shingyu Leung

• Human AI Co-creation

Local Consistency and Higher-Order Structure of Spherical Interpolation

Shingyu Leung

• Human AI Co-creation

A Uniformly Accurate Diffeomorphic Embedding Method for Solving Eikonal Equations on Implicit Surfaces

Yuxiao Wei, Jianliang Qian, Shingyu Leung (corresponding author)

SIAM J. Sci. Comput., 47(6), A3413-A3440

• Numerical Partial Differential Equations

An Eulerian variance-based finite-time Lyapunov exponent (vFTLE) approach for flows with uncertainties

Guoqiao You (corresponding author), Wai Ming Chau, Shingyu Leung

J. Comput. Phys., 541, 114353

• Computational Dynamical Systems

An Adaptive Ray-Tracing Method for Eikonal Equations on Spheres Using STVDRK Integrators and SENO Interpolations

Wai Ming Chau, Shingyu Leung (corresponding author)

J. Comput. Phys., 537, 114100

• Numerical Partial Differential Equations

A Spherical Crank-Nicolson Integrator Based on the Exponential Map and the Spherical Linear Interpolation

Shingyu Leung

• Numerical Partial Differential Equations

A Semi-lagrangian Spherical Essentially Non-oscillatory (SENO) Scheme for Advection Equations of S2-Valued Functions

Shingyu Leung

Spectral and High-Order Methods for Partial Differential Equations ICOSAHOM 2023, Lecture Notes in Computational Science and Engineering, vol. 142, Springer, Cham

• Numerical Partial Differential Equations

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

Shingyu Leung, Wai Ming Chau, Young Kyu Lee

J. Sci. Comput., 101(63)

• Numerical Partial Differential Equations

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

Yuxiao Wei, Jin Cheng, Shingyu Leung, Robert Burridge, Jianliang Qian

J. Sci. Comput., 100(79)

• Numerical Partial Differential Equations

Solving Partial Differential Equations on Evolving Surfaces via the Constrained Least-Squares (CLS) and Grid-Based Particle Method

Ningchen Ying, Shingyu Leung

• Numerical Partial Differential Equations
• Interfaces Problems

A Constrained Least-Squares Ghost Sample Points (CLS-GSP) Method for Differential Operators on Point Clouds

Ningchen Ying, Kwunlun Chu, Shingyu Leung

• Numerical Partial Differential Equations
• Interfaces Problems

Local Trajectory Variation Exponent (LTVE) for Visualizing Dynamical Systems

Yun Chen Tsai (corresponding author), Shingyu Leung

Commun. Comput. Phys., 36(5), 1411-1439

• Computational Dynamical Systems

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

Young Kyu Lee, Shingyu Leung (corresponding author)

Communications on Applied Mathematics and Computation, 6(2), 1189-1216

• Interfaces Problems

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

Chun Kit Hung, Shingyu Leung (corresponding author)

SIAM J. Sci. Comput., 45(6), A2813-A2835

• Interfaces Problems

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

Wai Ming Chau, Shingyu Leung (corresponding author)

Commun. Comput. Phys., 33(3), 824-848

• Computational Dynamical Systems

Sparse Subsampling of Flow Measurements for Finite-Time Lyapunov Exponent in Domains with Obstacles

Yu-Keung Ng, Guoqiao You (corresponding author), Shingyu Leung

Journal of Computational and Applied Mathematics, 431, 115255

• Computational Dynamical Systems

Spherical Essentially Non-Oscillatory (SENO) Interpolation

Ki Wai Fong, Shingyu Leung (corresponding author)

J. Sci. Comput., 94:28

• Numerical Partial Differential Equations

An Efficient Operator–Splitting Method for the Eigenvalue Problem of the Monge-Ampere Equation

Hao Liu, Shingyu Leung (corresponding author), Jianliang Qian

Commun. Optim. Theory, 2022, 7

• Numerical Partial Differential Equations

Liouville partial-differential-equation methods for computing 2D complex multivalued eikonals in attenuating media

Shingyu Leung, Jiangtao Hu, Jianliang Qian (corresponding author)

Geophysics, 87(2), T71-T84

• Inverse Problems

Ray Illumination Compensation for Adjoint-State First-Arrival Traveltime Tomography

Jiangtao Hu (corresponding author), Jianliang Qian, Junxing Cao, Xingjian Wang, Huazhong Wang, Shingyu Leung

Geophysics, 86(5)

• Inverse Problems

Eulerian algorithms for computing some Lagrangian flow network quantities

Guoqiao You (corresponding author), Shingyu Leung

J. Comput. Phys., 445, 110620

• Computational Dynamical Systems

An Adjoint State Method for an Inverse Problem for the Schrodinger Equation

Siyang Wei, Shingyu Leung (corresponding author)

Mathematical Methods in Image Processing and Inverse Problems

• Inverse Problems

Fast Huygens Sweeping Methods for a Class of Nonlocal Schrodinger Equations

Kaho Ho, Shingyu Leung (corresponding author), Jianliang Qian

J. Sci. Comput., 88:54

• Numerical Partial Differential Equations

A Level-Set Adjoint-State Method for Transmission Traveltime Tomography in Irregular Domains

Shingyu Leung, Jianliang Qian (corresponding author), Jiangtao Hu

SIAM J. Sci. Comput., 43(3), A2352-A2380

• Inverse Problems

Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media

Jiangtao Hu, Jianliang Qian (corresponding author), Jian Song, Min Ouyang, Junxing Cao, Shingyu Leung

Geophysics, 86(4), T179-T192

• Numerical Partial Differential Equations
• Inverse Problems

A Level Set Method for the Dirichlet k-Partition Problem

Kwunlun Chu, Shingyu Leung (corresponding author)

J. Sci. Comput., 86:11

• Numerical Partial Differential Equations

Computing the Finite Time Lyapunov Exponent for Flows with Uncertainties

Guoqiao You (corresponding author), Shingyu Leung

J. Comput. Phys., 425, 109905

• Computational Dynamical Systems

On the Numerical Solution of Nonlinear Eigenvalue Problems for the Monge-Ampere Operator

Roland Glowinski, Shingyu Leung, Hao Liu (corresponding author), Jianliang Qian

ESAIM: Control, Optimization and Calculus of Variations, 26, 118

• Numerical Partial Differential Equations

Efficient algorithms for computing multi-dimensional fractional Laplacians via spherical means

Boxi Xu (corresponding author), Jin Cheng, Shingyu Leung, Jianliang Qian

SIAM J. Sci. Comput., 42(5), A2910-A2942

• Numerical Partial Differential Equations

A Simple Semi-Implicit Scheme for Partial Differential Equations with Obstacle Constraints

Hao Liu (corresponding author), Shingyu Leung

Numer. Math. Theor. Meth. Appl., 13(3), 620-643

• Numerical Partial Differential Equations

Fast Construction of Forward Flow Maps using Eulerian Based Interpolation Schemes

Guoqiao You (corresponding author), Shingyu Leung

J. Sci. Comput., 82, 32

• Computational Dynamical Systems

Guarantees of Riemannian Optimization for Low Rank Matrix Completion

Ke Wei (corresponding author), Jian-Feng Cai, T.F. Chan, Shingyu Leung

Inverse Problems and Imaging, 14(2), 233-265

• Image Processing and Data Sciences

An Alternating Direction Explicit Method for Time Evolution Equations with Applications to Fractional Differential Equations

Hao Liu (corresponding author), Shingyu Leung

Methods and Applications of Analysis, 26(3), 249-268

• Numerical Partial Differential Equations

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three dimensional Monge-Ampere Equation

Hao Liu (corresponding author), Roland Glowinski, Shingyu Leung, Jianliang Qian

J. Sci. Comput., 81(3), 2271-2302

• Numerical Partial Differential Equations

Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories

Yu-Keung Ng, Shingyu Leung (corresponding author)

Commun. Comput. Phys., 26(4), 1143-1177

• Computational Dynamical Systems

Recent Developments in Eulerian Approaches for Visualizing Continuous Dynamical Systems

Shingyu Leung (corresponding author), Guoqiao You, Tony Wong, Yu Keung Ng

Proceedings of the Seventh International Congress of Chinese Mathematicians, 2, 579-622

• Computational Dynamical Systems

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation

Roland Glowinski, Hao Liu (corresponding author), Shingyu Leung, Jianliang Qian

J. Sci. Comput., 79(1), 1-47

• Numerical Partial Differential Equations

An Improved Eulerian Approach for the Finite Time Lyapunov Exponent

Guoqiao You (corresponding author), Shingyu Leung

J. Sci. Comput., 76(3), 1407-1435

• Computational Dynamical Systems

A Weak Formulation for the Multiphase Stokes Flow Problem without Body Fitting Grids

Ningchen Ying (corresponding author), Songming Hou, Shingyu Leung, Hongkai Zhao

Pure and Applied Mathematics Quarterly, 14(1), 131-159

• Interfaces Problems

A Simple Explicit Operator-Splitting Method for Effective Hamiltonians

Roland Glowinski, Shingyu Leung (corresponding author), Jianliang Qian

SIAM J. Sci. Comput., 40(1), A484-A503

• Numerical Partial Differential Equations

Modified Virtual Grid Difference for Discretizing the Laplace-Beltrami Operator on Point Clouds

Meng Wang, Shingyu Leung (corresponding author), Hongkai Zhao

SIAM J. Sci. Comput., 40(1), A1-A21

• Interfaces Problems

Eulerian Based Interpolation Schemes for Flow Map Construction and Line Integral Computation with Applications to Coherent Structures Extraction

Guoqiao You, Shingyu Leung (corresponding author)

J. Sci. Comput., 74(1), 70-96

• Computational Dynamical Systems

A Fast Huygens Sweeping Method for Capturing Paraxial Multi-color Optical Self-focusing in Nematic Liquid Crystals

Wingfai Kwan, Shingyu Leung (corresponding author), Xiao-Ping Wang, Jianliang Qian

J. Comput. Phys., 348, 108-138

• Numerical Partial Differential Equations

A Level Set Based Variational Principal Flow Method for Nonparametric Dimension Reduction on Riemannian Manifolds

Hao Liu, Zhigang Yao, Shingyu Leung (corresponding author), Tony F. Chan

SIAM J. Sci. Comput., 39(4), A1616-A1646

• Image Processing and Data Sciences

Eulerian Methods for Visualizing Continuous Dynamical Systems using Lyapunov Exponents

Guoqiao You, Tony Wong, Shingyu Leung (corresponding author)

SIAM J. Sci. Comput., 39(2), A415-A437

• Computational Dynamical Systems

A Fast Sweeping Method for Eikonal Equations on Implicit Surfaces

Tony Wong, Shingyu Leung (corresponding author)

J. Sci. Comput., 67, 837, pp. 837-859

• Interfaces Problems

Operator-Splitting Based Fast Sweeping Methods for Isotropic Wave Propagation in a Moving Fluid

Roland Glowinski, Shingyu Leung (corresponding author), Jianliang Qian

SIAM J. Sci. Comput., 38(2), A1195-A1223

• Numerical Partial Differential Equations

Guarantees of Riemannian Optimization for Low Rank Matrix Recovery

Ke Wei (corresponding author), Jian-Feng Cai, T.F. Chan, Shingyu Leung

SIAM J. Matrix Anal. Appl., 37(3), 1198-1222

• Image Processing and Data Sciences

A Penalization-Regularization-Operator Splitting Method for Eikonal-based Traveltime Tomography

Roland Glowinski, Shingyu Leung, Jianliang Qian (corresponding author)

SIAM J. Imaging Sciences, 8(2), 1263-1292

• Inverse Problems

An Improved Fast Local Level Set Method for Three-Dimensional Inverse Gravimetry

Wangtao Lu, Shingyu Leung, Jianliang Qian (corresponding author)

Inverse Problems and Imaging, 9(2), 479-509

• Inverse Problems

Primal-Dual Method for Continuous Max-Flow Approaches

Ke Wei (corresponding author), X.C. Tai, T.F. Chan, Shingyu Leung

Proceedings of the 5th Eccomas Thematic Conference on Computational Vision and Medical Image Processing (VipIMAGE 2015)

• Image Processing and Data Sciences

A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems

Guoqiao You, Shingyu Leung (corresponding author)

Commun. Comput. Phys., 18(1), 203-229

• Computational Dynamical Systems

Fast Huygen Sweeping Methods for Schrodinger Equations in the Semi-Classical Regime

Shingyu Leung, Jianliang Qian, Susana Serna

Methods and Applications of Analysis, 21(1), 31-66

• Numerical Partial Differential Equations

A Level-Set Adjoint-State Method for Crosswell Transmission-Reflection Traveltime Tomography

Wenbin Li, Shingyu Leung, Jianliang Qian

Geophysical J. Int., 199(1), 348-367

• Inverse Problems

A New Continuous Max-flow Algorithm for Multiphase Image Segmentation using Super-level Set Functions

Jun Liu, Xue-cheng Tai, Shingyu Leung, Haiyang Huang

Journal of Visual Communication and Image Representation, 25(6), 1472-1488

• Image Processing and Data Sciences

A Cell Based Particle Method for Modeling Dynamic Interfaces

Sean Y. Hon, Shingyu Leung, Hongkai Zhao

J. Comput. Phys., 272, 279-306

• Interfaces Problems

VIALS: An Eulerian Tool Based on Total Variation and the Level Set Method for Studying Dynamical Systems

Guoqiao You, Shingyu Leung

J. Comput. Phys., 266, 139-160

• Computational Dynamical Systems

An Eulerian Method for Computing the Coherent Ergodic Partition of Continuous Dynamical Systems

Guoqiao You, Shingyu Leung

J. Comput. Phys., 264, 112-132

• Computational Dynamical Systems

A fast local level set adjoint state method for first arrival transmission traveltime tomography with discontinuous slowness

Wenbin Li, Shingyu Leung

Geophysical J. Int., 195(1), 582-596

• Inverse Problems

A Three-Dimensional Inverse Gravimetry Problem for Ice With Snow Caps

Victor Isakov, Shingyu Leung, Jianliang Qian

Inverse Problems and Imaging, 7(2)

• Inverse Problems

A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation

Jun Liu, Xue-Cheng Tai, Shingyu Leung

EMMCVPR Lecture Notes in Computer Science, 8081, 251-265

• Image Processing and Data Sciences

A Splitting Algorithm for Image Segmentation on Manifolds Represented by the Grid based Particle Method

Jun Liu, Shingyu Leung

J. Sci. Comput., 56, 243-266

• Image Processing and Data Sciences

The Backward Phase Flow Method for the Eulerian Finite Time Lyapunov Exponent Computations

Shingyu Leung

Chaos, 23, 043132

• Computational Dynamical Systems

Expectation-Maximization Algorithm with Total Variation Regularization for Vector-Valued Image Segmentation

Jun Liu, Yin Bon Ku, Shingyu Leung

Journal of Visual Communication and Image Representation, 23(8), 1234-1244

• Image Processing and Data Sciences

An Eulerian Approach for Computing the Finite Time Lyapunov Exponent

Shingyu Leung

J. Comput. Phys., 230(29), 3500-3524

• Computational Dynamical Systems

An Adjoint State Method for Numerical Approximation of Continuous Traffic Congestion Equilibria

Songting Luo, Shingyu Leung, Jianliang Qian

Commun. Comput. Phys., 10(5), 1113-1131

• Inverse Problems

Mathematical Restoration Techniques to Improve Micro-CT Images of Implant Osseointegration

J.H. Ha, A. Hokugo, C.M. Mengatto, S. Leung, S. Osher, I. Nishimura

IADR/AADR/CADR 89th General Session, Journal of Dental Research - Spec Issue A, 90

• Image Processing and Data Sciences

A Fast Local Level Set Method for Inverse Gravimetry

Victor Isakov, Shingyu Leung, Jianliang Qian

Commun. Comput. Phys., 10(4), 1044-1070

• Inverse Problems

A Grid Based Particle Method for Solving Partial Differential Equations on Evolving Surfaces and Modeling High Order Geometrical Motion

Shingyu Leung, John Lowengrub, Hongkai Zhao

J. Comput. Phys., 230(7), 2540-2561

• Interfaces Problems

The Backward Phase Flow and FBI-Transform-Based Eulerian Gaussian Beams for the Schrodinger Equation

Shingyu Leung, Jianliang Qian

J. Comput. Phys., 229(23), 8888-8917

• Numerical Partial Differential Equations

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

Shingyu Leung, Hongkai Zhao

Commun. Comput. Phys., 8(4), 758-796

• Numerical Partial Differential Equations
• Interfaces Problems

A Grid Based Particle Method for Evolution of Open Curves and Surfaces

Shingyu Leung, Hongkai Zhao

J. Comput. Phys., 228(20), 7706-7728

• Interfaces Problems

Expectation-Maximization Algorithm with Local Adaptivity

Shingyu Leung, Gang Liang, Knut Solna, Hongkai Zhao

SIAM J. Imaging Sci., 2(3), 834-857

• Image Processing and Data Sciences

A Grid Based Particle Method for Moving Interface Problems

Shingyu Leung, Hongkai Zhao

J. Comput. Phys., 228(8), 2993-3024

• Interfaces Problems

Eulerian Gaussian Beams for Semi-Classical Solutions of Schrodinger Equations

Shingyu Leung, Jianliang Qian

J. Comput. Phys., 228(8), 2951-2977

• Numerical Partial Differential Equations

Eulerian Gaussian Beams for High Frequency Wave Propagation

Shingyu Leung, Jianliang Qian, Robert Burridge

Geophysics, 72(5), SM61-SM76

• Numerical Partial Differential Equations

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

Shingyu Leung, Jianliang Qian

Inverse Problems, 23, 799-821

• Inverse Problems

An Adjoint State Method for 3D Transmission Traveltime Tomography Using First Arrival

Shingyu Leung, Jianliang Qian

Commun. Math. Sci., 4(1), 249-266

• Inverse Problems

A Local Level Set Method for Paraxial Geometrical Optics

Jianliang Qian, Shingyu Leung

SIAM J. Sci. Comput., 28(1), 206-223

• Numerical Partial Differential Equations

A Transmission Tomography Problem Based on Multiple Arrivals from Paraxial Liouville Equations

Shingyu Leung, Jianliang Qian

Expanded Abstract for the SEG 75th Annual Meeting, Houston, USA

• Inverse Problems

Fast Global Minimization of the Active Contour Model with TV-Inpainting and Two-phase Denoising

Shingyu Leung, Stanley Osher

Proceedings of the 3rd IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, 149-160

• Image Processing and Data Sciences

A Level Set Method for Three-dimensional Paraxial Geometrical Optics with Multiple Sources

Shingyu Leung, Jianliang Qian, Stanley Osher

Commun. Math. Sci., 2(4), 643-672

• Numerical Partial Differential Equations

A Level Set Based Eulerian Method for Paraxial Multivalued Traveltimes

Jianliang Qian, Shingyu Leung

J. Comput. Phys., 197(2), 711-736

• Numerical Partial Differential Equations