PUBLICATIONS

(BY TOPIC)

• Ki Wai Fong and Shingyu Leung*. Spherical Essentially Non-Oscillatory (SENO) Interpolation. J. Sci. Comput., (2023) 94:28. [ArXiv]
• Hao Liu, Shingyu Leung*, and Jianliang Qian. An Efficient Operator–Splitting Method for the Eigenvalue Problem of the Monge-Ampere Equation. Commun. Optim. Theory, 2022 (2022) 7.
  
• Kaho Ho, Shingyu Leung*, and Jianliang Qian. Fast Huygens Sweeping Methods for a Class of Nonlocal Schrodinger Equations. J. Sci. Comput. 88:54, 2021.
• Jiangtao Hu, Jianliang Qian, Jian Song, Min Ouyang, Junxing Cao, and Shingyu Leung. Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media. Geophysics, 86(4):T179-T192, July-August 2021.
• Kwunlun Chu and Shingyu Leung. A Level Set Method for the Dirichlet k-Partition Problem. J. of Sci. Comput., 86:11, 2021.
• Roland Glowinski, Shingyu Leung, Hao Liu*, and Jianliang Qian. On the Numerical Solution of Nonlinear Eigenvalue Problems for the Monge-Ampere Operator. ESAIM: Control, Optimization and Calculus of Variations, 26 (2020) 118. [pdf]
• Boxi Xu, Jin Cheng, Shingyu Leung and Jianliang Qian. Efficient algorithms for computing multi-dimensional fractional Laplacians via spherical means. SIAM J. Sci. Comput., 42-5 (2020), pp. A2910-A2942.

• Hao Liu and Shingyu Leung. A Simple Semi-Implicit Scheme for Partial Differential Equations with Obstacle Constraints. Numer. Math. Theor. Meth. Appl., 13(3), 620-643, 2020. [pdf]
• Hao Liu and Shingyu Leung. An Alternating Direction Explicit Method for Time Evolution Equations with Applications to Fractional Differential Equations. Methods and Applications of Analysis, 26(3), 249-268, 2019.[arxiv] [pdf]
  
• Hao Liu, Roland Glowinski, Shingyu Leung and Jianliang Qian. A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three dimensional Monge-Ampere Equation. J. of Sci. Comput., 81(3), 2271-2302, 2019.
  
• Roland Glowinski, Hao Liu, Shingyu Leung and Jianliang Qian. A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation. J. of Sci. Comput., 79(1), April 2019, pp 1-47.
  
• Roland Glowinski, Shingyu Leung and Jianliang Qian. A Simple Explicit Operator-Splitting Method for Effective Hamiltonians. SIAM J. Sci. Comput., 40(1), A484–A503, 2018.
  
• Wingfai Kwan, Shingyu Leung, Xiao-Ping Wang and Jianliang Qian. A Fast Huygens Sweeping Method for Capturing Paraxial Multi-color Optical Self-focusing in Nematic Liquid Crystals. J. Comput. Phys., v348, 2017, Pages 108-138.
  
• Roland Glowinski, Shingyu Leung and Jianliang Qian. Operator-Splitting Based Fast Sweeping Methods for Isotropic Wave Propagation in a Moving Fluid. SIAM J. Sci. Comput., 38(2), A1195-A1223, 2016.

• Shingyu Leung, Jianliang Qian and Susana Serna, Fast Huygen Sweeping Methods for Schrodinger Equations in the Semi-Classical Regime. Methods and Applications of Analysis, 21(1), 2014, Pages 31-66. (UCLA CAM 13-71)
• Shingyu Leung and Jianliang Qian, The Backward Phase Flow and FBI-Transform-Based Eulerian Gaussian Beams for the Schrodinger Equation. UCLA-CAM 10-85. J. Comput. Phys., Volume 229, Issue 23, November 20 2010, Pages 8888-8917. [pdf]
• Shingyu Leung and Jianliang Qian, Eulerian Gaussian Beams for Semi-Classical Solutions of Schrodinger Equations. J. Comput. Phys., Volume 228, Issue 8, May 1 2009, Pages 2951-2977. [pdf]
• Shingyu Leung, Jianliang Qian and Robert Burridge, Eulerian Gaussian Beams for High Frequency Wave Propagation. Geophysics, Volume 72, Issue 5, September-October 2007, Pages SM61-SM76. [pdf]
• Shingyu Leung, Jianliang Qian and Stanley Osher, A Level Set Method for Three-dimensional Paraxial Geometrical Optics with Multiple Sources. Commun. Math. Sci., Volume 2, Issue 4, December 2004, Pages 643-672. [pdf]
• Jianliang Qian and Shingyu Leung, A Local Level Set Method for Paraxial Geometrical Optics. SIAM J. Sci. Comp., Volume 28, Issue 1, Pages 206-223. [pdf]
• Jianliang Qian and Shingyu Leung, A Level Set Based Eulerian Method for Paraxial Multivalued Traveltimes. J. Comput. Phys., Volume 197, Issue 2, July 1 2004, Pages 711-736. [pdf]

• Shingyu Leung*. Some Applications of the Adjoint State Method to Inverse Problems from Seismology and Tomography. Accepted by Proceedings of the Eighth International Congress of Chinese Mathematicians.
• Shingyu Leung, Jiangtao Hu, Jianliang Qian*. Liouville partial-differential-equation methods for computing 2D complex multivalued eikonals in attenuating media. Geophysics 87(2), T71-84, 2022.
• Siyang Wei and Shingyu Leung. An Adjoint State Method for an Inverse Problem for the Schrodinger Equation. In Mathematical Methods in Image Processing and Inverse Problems, Editors: Tai, Xue-Cheng, Wei, Suhua, Liu, Haiguang (Eds.), 2021.
• Jiangtao Hu*, Jianliang Qian, Junxing Cao, Xingjian Wang, Huazhong Wang and Shingyu Leung. Ray Illumination Compensation for Adjoint-State First-Arrival Traveltime Tomography. Geophysics, 86:5, 2021.

• Shingyu Leung, Jianliang Qian*, and Jiangtao Hu. A Level-Set Adjoint-State Method for Transmission Traveltime Tomography in Irregular Domains. SIAM J. Sci. Comput.43(3), A2352-A2380, 2021.
  
• Roland Glowinski, Shingyu Leung, Jianliang Qian. A Penalization-Regularization-Operator Splitting Method for Eikonal-based Traveltime Tomography. SIAM J. on Imaging Sciences, Vol. 8, No. 2, 2015, pp. 1263-1292. (UCLA CAM 15-02)
  
• Wangtao Lu, Shingyu Leung and Jianliang Qian. An Improved Fast Local Level Set Method for Three-Dimensional Inverse Gravimetry. Inverse Problems and Imaging., Volume 9, No. 2, 2015, Pages 479-509. [pdf]
  
• Wenbin Li, Shingyu Leung and Jianliang Qian. A Level-Set Adjoint-State Method for Crosswell Transmission-Reflection Traveltime Tomography. Geophysical J. Int., 199(1), 2014, Pages 348-367. (UCLA CAM 13-76)
  
• Wenbin Li and Shingyu Leung, A fast local level set adjoint state method for first arrival transmission traveltime tomography with discontinuous slowness. Geophysical J. Int., 195(1), 2013, Pages 582-596. (CAM 13-75) [pdf]
  

• Victor Isakov, Shingyu Leung and Jianliang Qian, A Three-Dimensional Inverse Gravimetry Problem for Ice With Snow Caps. Inverse Problems and Imaging, Volume 7, No. 2, 2013. [pdf]
• Songting Luo, Shingyu Leung and Jianliang Qian, An Adjoint State Method for Numerical Approximation of Continuous Traffic Congestion Equilibria. Commun. Comput. Phys., Volume 10, Number 5, November 2011, Pages 1113-1131. [pdf]
• Victor Isakov, Shingyu Leung and Jianliang Qian, A Fast Local Level Set Method for Inverse Gravimetry. Commmun. Comput. Phys., Volume 10, Number 4, October 2011, Pages 1044-1070. [pdf]
• Shingyu Leung and Jianliang Qian, An Adjoint State Method for 3D Transmission Traveltime Tomography Using First Arrival. Commun. Math. Sci., Volume 4, Number 1, March 2006, Pages 249-266. UCLA CAM 06-06. [pdf]
• Shingyu Leung and Jianliang Qian, Transmission Traveltime Tomography Based on Paraxial Liouville Equations and Level Set Formulations. Inverse Problems 23 (2007) 799-821. [pdf]
• Shingyu Leung and Jianliang Qian, A Transmission Tomography Problem Based on Multiple Arrivals from Paraxial Liouville Equations, In Expanded Abstract for the SEG 75th Annual Meeting, Houston, USA, 2005. [pdf]

• Chun Kit Hung and Shingyu Leung*. A Simple Embedding Method for Scalar Hyperbolic Conservation Laws on Implicit Surfaces. SIAM J. Sci. Comput., 45(6), A2813-A2835, 2023.
  
• Young Kyu Lee and Shingyu Leung*. A Simple Embedding Method for the Laplace-Beltrami Eigenvalue Problem on Implicit Surfaces. Special issue in honor of Prof. Stanley Osher on the occasion of his 80th birthday, Communications on Applied Mathematics and Computation.
• Ningchen Ying, Songming Hou, Shingyu Leung and Hongkai Zhao. A Weak Formulation for the Muliphase Stokes Flow Problem without Body Fitting Grids. Pure and Applied Mathematics Quarterly, 14(1), 131-159, 2018.[pdf]

• Meng Wang, Shingyu Leung and Hongkai Zhao, Modified Virtual Grid Difference for Discretizing the Laplace-Beltrami Operator on Point Clouds. SIAM J. Sci. Comput. 40(1), A1–A21, 2018. [arXiv]
• Tony Wong and Shingyu Leung, A Fast Sweeping Method for Eikonal Equations on Implicit Surfaces. J Sci Comput (2016) 67: 837. [pdf][SpringerNature SharedIt]
  
• Sean Y. Hon, Shingyu Leung and Hongkai Zhao, A Cell Based Particle Method for Modeling Dynamic Interfaces. J. Comput. Phys., Volume 272, 2014, Pages 279-306. (UCLA CAM 13-74)
• Shingyu Leung, John Lowengrub and Hongkai Zhao, A Grid Based Particle Method for Solving Partial Differential Equations on Evolving Surfaces and Modeling High Order Geometrical Motion. UCLA-CAM 11-54. J. Comput. Phys., Volume 230, Issue 7, April 1 2011, Pages 2540-2561. [pdf]
• Shingyu Leung and Hongkai Zhao, Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method. UCLA-CAM 09-71. Commmun. Comput. Phys., Volume 8, Number 4, May 17 2010, Pages 758-796. [pdf]
• Shingyu Leung and Hongkai Zhao, A Grid Based Particle Method for Evolution of Open Curves and Surfaces. J. Comput. Phys., Volume 228, Issue 20, November 1 2009, Pages 7706-7728. [pdf]
• Shingyu Leung and Hongkai Zhao, A Grid Based Particle Method for Moving Interface Problems. UCLA-CAM 08-08. J. Comput. Phys., Volume 228, Issue 8, May 1 2009, Pages 2993-3024. [pdf]

• Ke Wei, Jian-Feng Cai, T.F. Chan and Shingyu Leung. Guarantees of Riemannian Optimization for Low Rank Matrix Completion. Inverse Problems and Imaging, 14(2), 233-265, 2020. arXiv:1603.06610
  
• Hao Liu, Zhigang Yao, Shingyu Leung and Tony F. Chan. A Level Set Based Variational Principal Flow Method for Nonparametric Dimension Reduction on Riemannian Manifolds. SIAM J. Sci. Comput., 39(4), A1616-A1646, 2017. [pdf]
• Ke Wei, Jian-Feng Cai, T.F. Chan and Shingyu Leung. Guarantees of Riemannian Optimization for Low Rank Matrix Recovery. SIAM J. on Matrix Anal. & Appl., 37(3), 2016, Pages 1198-1222. arXiv:1511.01562
  
• Ke Wei, X.C. Tai, T.F. Chan and Shingyu Leung, Primal-Dual Method for Continuous Max-Flow Approaches. UCLA-CAM 15-67. Proceedings of the 5th Eccomas Thematic Conference on Computational Vision and Medical Image Processing (VipIMAGE 2015), 2015.
• Jun Liu, Xue-cheng Tai, Shingyu Leung and Haiyang Huang, A New Continuous Max-flow Algorithm for Multiphase Image Segmentation using Super-level Set Functions. UCLA-CAM 12-81. Journal of Visual Communication and Image Representation, Volume 25, Issue 6, 2014, Pages 1472-1488. [pdf]

• Jun Liu, Xue-Cheng Tai, and Shingyu Leung, A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation. EMMCVPR Lecture Notes in Computer Science Volume 8081, 2013, pp 251-265. [pdf]
• Jun Liu and Shingyu Leung, A Splitting Algorithm for Image Segmentation on Manifolds Represented by the Grid based Particle Method. UCLA-CAM 12-80. J. of Sci. Comput., Volume 56, 2013, Pages 243-266. [pdf].
• Jun Liu, Yin Bon Ku and Shingyu Leung, Expectation-Maximization Algorithm with Total Variation Regularization for Vector-Valued Image Segmentation. UCLA-CAM 12-79. Journal of Visual Communication and Image Representation, Volume 23, No. 8, 2012, Pages 1234-1244. [pdf]
• J.H. Ha, A. Hokugo, C.M. Mengatto, S. Leung, S. Osher, I. Nishimura, Mathematical Restoration Techniques to Improve Micro-CT Images of Implant Osseointegration. In: IADR/AADR/CADR 89th General Session, 2011, San Diego, Calif. Journal of Dental Research - Spec Issue A. US: JDR, 2011. v.90.
• Shingyu Leung, Gang Liang, Knut Solna and Hongkai Zhao, Expectation-Maximization Algorithm with Local Adaptivity. SIAM J. Imaging Sci., Volume 2, Issue 3, Pages 834-857, 2009. [pdf]
• Shingyu Leung and Stanley Osher, Fast Global Minimization of the Active Contour Model with TV-Inpainting and Two-phase Denoising. Proceeding of the 3rd IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, 2005, Pages 149-160. [pdf]

• Yun Chen Tsai* and Shingyu Leung. Local Trajectory Variation Exponent (LTVE) for Visualizing Dynamical Systems. Accepted by Commun. Comput. Phys. [ArXiv], 2024.
  
• Yu-Keung Ng, Guoqiao You* and Shingyu Leung. Sparse Subsampling of Flow Measurements for Finite-Time Lyapunov Exponent in Domains with Obstacles. Journal of Computational and Applied Mathematics, 431 (2023) 115255.
  

• Wai Ming Chau and Shingyu Leung*. Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems. Commun. Comput. Phys., 33(3), 824-848, 2023. [ArXiv]
  
• Guoqiao You and Shingyu Leung. Eulerian algorithms for computing some Lagrangian flow network quantities. J. Comput. Phys., 445, 110620, 2021.
• Guoqiao You and Shingyu Leung. Computing the Finite Time Lyapunov Exponent for Flows with Uncertainties. J. Comput. Phys, 405, 109905, 2021.
• Guoqiao You and Shingyu Leung. Fast Construction of Forward Flow Maps using Eulerian Based Interpolation Schemes. J Sci Comput 82, 32 (2020).
• Yu-Keung Ng and Shingyu Leung, Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories. Commun. Comput. Phys., 26(4), 1143-1177, 2019.
• Shingyu Leung, Guoqiao You, Tony Wong and Yu Keung Ng, Recent Developments in Eulerian Approaches for Visualizing Continuous Dynamical Systems. Proceedings of the Seventh International Congress of Chinese Mathematicians, 2, 579-622, 2019. [pdf]
• Guoqiao You and Shingyu Leung, An Improved Eulerian Approach for the Finite Time Lyapunov Exponent. J. of Sci. Comput., 76(3), 1407-1435, 2018.

• Guoqiao You and Shingyu Leung. Eulerian Based Interpolation Schemes for Flow Map Construction and Line Integral Computation with Applications to Coherent Structures Extraction. J. of Sci. Comput., Volume 74, Issue 1, pp 70–96, 2018. [pdf]
• Guoqiao You, Tony Wong and Shingyu Leung, Eulerian Methods for Visualizing Continuous Dynamical Systems using Lyapunov Exponents. SIAM J. Sci. Comput., 39(2), A415-A437, 2017. [arXiv:1603.06446]
• Guoqiao You and Shingyu Leung, A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems. Commu. Comp. Phys., 18(1), 2015, pp. 203-229. [pdf]
• Guoqiao You and Shingyu Leung, VIALS: An Eulerian Tool Based on Total Variation and the Level Set Method for Studying Dynamical Systems. J. Comput. Phys., Volume 266, 2014, Pages 139-160. [pdf]
• Guoqiao You and Shingyu Leung, An Eulerian Method for Computing the Coherent Ergodic Partition of Continuous Dynamical Systems. J. Comput. Phys., Volume 264, 2014, Pages 112-132. (UCLA CAM 13-73) [pdf]
• Shingyu Leung, The Backward Phase Flow Method for the Eulerian Finite Time Lyapunov Exponent Computations. Chaos 23, 043132, 2013. [pdf]
• Shingyu Leung, An Eulerian Approach for Computing the Finite Time Lyapunov Exponent. UCLA-CAM 11-53. J. Comput. Phys., Volume 230, Issue 29, May 1 2011, Pages 3500-3524. [pdf]