Submitted or Accepted

• 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.
  

2024

• Yun Chen Tsai* and Shingyu Leung. Local Trajectory Variation Exponent (LTVE) for Visualizing Dynamical Systems. Accepted by Commun. Comput. Phys. [ArXiv]
  

2023

• 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.
• 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]
  
• 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.
  
• Ki Wai Fong and Shingyu Leung*. Spherical Essentially Non-Oscillatory (SENO) Interpolation. J. Sci. Comput., (2023) 94:28. [ArXiv]
  

2022

• 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.
  
• 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.
  

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.
  
• Guoqiao You* and Shingyu Leung. Eulerian algorithms for computing some Lagrangian flow network quantities. J. Comput. Phys., 445, 110620, 2021.
  
• 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.
  
• Kaho Ho, Shingyu Leung*, and Jianliang Qian. Fast Huygens Sweeping Methods for a Class of Nonlocal Schrodinger Equations. J. Sci. Comput. 88:54, 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.
  
• 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. Sci. Comput., 86:11, 2021.
  
• Guoqiao You* and Shingyu Leung. An Eulerian Approach to the Finite Time Lyapunov Exponent for Flows with Uncertainties. J. Comput. Phys, 405, 109905, 2021.
  

2020

• 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]
  
• Guoqiao You* and Shingyu Leung. Fast Construction of Forward Flow Maps using Eulerian Based Interpolation Schemes. J Sci Comput 82, 32 (2020).
  
• 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
  

2019

• Yee Fai Ng, Kwan Kit Chan, Huey Lei*, Phoebe Mok and Shingyu Leung. Pedagogy and innovation in science education: A case study of an experiential learning science undergraduate course. The European Journal of Social & Behavioral Sciences 25(2), 156-173.
• 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. Sci. Comput., 81(3), 2271-2302, 2019.
  
• 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]
  
• 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. Sci. Comput., 79(1), April 2019, pp 1-47.
  

2018

• Guoqiao You* and Shingyu Leung, An Improved Eulerian Approach for the Finite Time Lyapunov Exponent. J. of Sci. Comput., 76(3), 1407-1435, 2018.
  
• 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]
  
• 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.
  
• 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]
  
• 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]
  

2017

• 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.
  
• 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]
  
• 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]
  

2016

• Tony Wong and Shingyu Leung*, A Fast Sweeping Method for Eikonal Equations on Implicit Surfaces. J Sci Comput (2016) 67: 837. [pdf][SpringerNature SharedIt]
  
• 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.
  
• 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
  

2015

• 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]
  
• 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.
  
• 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]
  

2014

• 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)
  
• 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)
  
• 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]
  
• 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)
  
• 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]
  

2013

• 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]
  
• 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. Sci. Comput., Volume 56, 2013, Pages 243-266. [pdf].
  
• Shingyu Leung, The Backward Phase Flow Method for the Eulerian Finite Time Lyapunov Exponent Computations. Chaos 23, 043132, 2013. [pdf]
  

2012

• 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]
  

2011

• 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]
  
• 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]
  
• 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.
  
• 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, 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]
  

2010

• 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 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]
  

2009

• 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, 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 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]
  
• 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]
  

BEFORE 2009

• 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 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, 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]
  
• 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]
  
• 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]
  
• 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]
  
• 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 Level Set Based Eulerian Method for Paraxial Multivalued Traveltimes. J. Comput. Phys., Volume 197, Issue 2, July 1 2004, Pages 711-736. [pdf]