Hongkai Zhao | Scholars@Duke

Hongkai Zhao
Ruth F. DeVarney Distinguished Professor of Mathematics

Current Research Interests

My research interest is in computational and applied mathematics that includes modeling, analysis and developing numerical methods for problems arising from science and engineering. More specifically, I have worked on:

numerical analysis and scientific computing;
multi-scale, multi-physics and multi-phase problems in wave propagation, fluids, and materials;
inverse problems related to medical and seismic imaging;
computer vision and image processing.

My Google Scholar Citations

Office Hours

Wednesday 3-5pm

Current Appointments & Affiliations

Ruth F. DeVarney Distinguished Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2022
Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2020

Contact Information

hongkai.zhao@duke.edu

Background
Education, Training, & Certifications
- Ph.D., University of California - Los Angeles 1996
Recognition
In the News
- MAY 18, 2022
  
  University Awards 24 New Distinguished Professorships
- OCT 9, 2020
  
  Hongkai Zhao: Creating Efficient Algorithms for Science and Engineering Applications
Awards & Honors
Research
Selected Grants
- RTG: Training Tomorrow's Workforce in Analysis and Applications awarded by National Science Foundation 2021 - 2026
- Computational Forward and Inverse Radiative Transfer awarded by National Science Foundation 2020 - 2023
Fellowships, Supported Research, & Other Grants
- Computational Forward and Inverse Radiative Transfer awarded by NSF 2020 - 2023
- Intrinsic complexity of random fields and its connections to random matrices and stochastic differential equations awarded by NSF 2018 - 2021
Publications & Artistic Works
Selected Publications
- Academic Articles
  - Zhao, H., and Y. Zhong. “Quantitative PAT with simplified P N approximation.” Inverse Problems 37, no. 5 (May 1, 2021). https://doi.org/10.1088/1361-6420/abf318.
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  - Zhao, Hongkai, and Ji Li. “Scalable Incremental Nonconvex Optimization Approach for Phase Retrieval (Accepted).” Journal of Scientific Computing, 2021.
  - Zhao, Hongkai, Jennifer Bryson, and Roman Vershynin. “Marchenko-Pastur law with relaxed independence conditions.” Random Matrices: Theory and Applications, 2021. https://doi.org/10.1142/s2010326321500404.
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  - Zhong, Yimin, Hongkai Zhao, and Kui Ren. “Separability of the kernel function in an integral formulation for anisotropic radiative transfer equation.” Siam Journal on Mathematical Analysis 53, no. 5 (2021): 5613–5613.
  - Li, Ji, and Hongkai Zhao. “Robust Inexact Alternating Optimization for Matrix Completion with Outliers.” Journal of Computational Mathematics 38, no. 2 (June 2020): 337–54. https://doi.org/10.4208/jcm.1809-m2018-0106.
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  - Zhong, Yimin, and Hongkai Zhao. “A Fast Algorithm for Time-Dependent Radiative Transport Equation Based on Integral Formulation.” Csiam Transactions on Applied Mathematics 1, no. 2 (June 2020): 346–64. https://doi.org/10.4208/csiam-am.2020-0012.
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  - Li, Ji, and Hongkai Zhao. “Solving phase retrieval via graph projection splitting.” Inverse Problems 36, no. 5 (May 1, 2020): 055003–055003. https://doi.org/10.1088/1361-6420/ab79fa.
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  - Zhao, Hongkai, Rongjie Lai, and Rui Xiang. “Efficient and robust shape correspondence via sparsity-enforced quadratic assignment.” Proceedings / Cvpr, Ieee Computer Society Conference on Computer Vision and Pattern Recognition. Ieee Computer Society Conference on Computer Vision and Pattern Recognition 1 (2020): 9510–19. https://doi.org/10.1109/CVPR42600.2020.00953.
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  - Li, Sijing, Zhiwen Zhang, and Hongkai Zhao. “A Data-Driven Approach for Multiscale Elliptic PDEs with Random Coefficients Based on Intrinsic Dimension Reduction.” Multiscale Modeling &Amp; Simulation 18, no. 3 (January 2020): 1242–71. https://doi.org/10.1137/19m1277485.
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  - Li, Hongfeng, Hongkai Zhao, and Hong Li. “Neural-Response-Based Extreme Learning Machine for Image Classification.” Ieee Transactions on Neural Networks and Learning Systems 30, no. 2 (February 2019): 539–52. https://doi.org/10.1109/tnnls.2018.2845857.
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  - Bryson, J., H. Zhao, and Y. Zhong. “Intrinsic complexity and scaling laws: From random fields to random vectors.” Multiscale Modeling and Simulation 17, no. 1 (January 1, 2019): 460–81. https://doi.org/10.1137/18M1187908.
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  - Zhao, H., and Y. Zhong. “A hybrid adaptive phase space method for reflection traveltime tomography.” Siam Journal on Imaging Sciences 12, no. 1 (January 1, 2019): 28–53. https://doi.org/10.1137/18M117426X.
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  - Zhao, Hongkai, and Yimin Zhong. “Instability of an Inverse Problem for the Stationary Radiative Transport Near the Diffusion Limit.” Siam Journal on Mathematical Analysis 51, no. 5 (January 2019): 3750–68. https://doi.org/10.1137/18m1222582.
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  - Engquist, Björn, and Hongkai Zhao. “Approximate Separability of the Green's Function of the Helmholtz Equation in the High Frequency Limit.” Communications on Pure and Applied Mathematics 71, no. 11 (November 2018): 2220–74. https://doi.org/10.1002/cpa.21755.
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  - Fang, Jun, Jianliang Qian, Leonardo Zepeda-Núñez, and Hongkai Zhao. “A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media.” Journal of Computational Physics 371 (October 2018): 261–79. https://doi.org/10.1016/j.jcp.2018.03.011.
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  - Zhang, Cheng, Babak Shahbaba, and Hongkai Zhao. “Variational Hamiltonian Monte Carlo via Score Matching.” Bayesian Analysis 13, no. 2 (June 1, 2018). https://doi.org/10.1214/17-ba1060.
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  - Wang, Meng, Shingyu Leung, and Hongkai Zhao. “Modified Virtual Grid Difference for Discretizing the Laplace--Beltrami Operator on Point Clouds.” Siam Journal on Scientific Computing 40, no. 1 (January 2018): A1–21. https://doi.org/10.1137/16m1065690.
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  - Ying, Ningchen, Songming Hou, Shingyu Leung, and Hongkai Zhao. “A weak formulation for the multiphase Stokes flow problem without body fitting grids.” Pure and Applied Mathematics Quarterly 14, no. 1 (2018): 131–59. https://doi.org/10.4310/pamq.2018.v14.n1.a5.
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  - Fang, Jun, Jianliang Qian, Leonardo Zepeda-Núñez, and Hongkai Zhao. “Learning dominant wave directions for plane wave methods for high-frequency Helmholtz equations.” Research in the Mathematical Sciences 4, no. 1 (December 2017). https://doi.org/10.1186/s40687-017-0098-9.
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  - Zhang, Cheng, Babak Shahbaba, and Hongkai Zhao. “Hamiltonian Monte Carlo acceleration using surrogate functions with random bases.” Statistics and Computing 27, no. 6 (November 2017): 1473–90. https://doi.org/10.1007/s11222-016-9699-1.
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  - Zhang, Cheng, Babak Shahbaba, and Hongkai Zhao. “Precomputing strategy for Hamiltonian Monte Carlo method based on regularity in parameter space.” Computational Statistics 32, no. 1 (March 2017): 253–79. https://doi.org/10.1007/s00180-016-0683-1.
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  - Lai, Rongjie, and Hongkai Zhao. “Multiscale Nonrigid Point Cloud Registration Using Rotation-Invariant Sliced-Wasserstein Distance via Laplace--Beltrami Eigenmap.” Siam Journal on Imaging Sciences 10, no. 2 (January 2017): 449–83. https://doi.org/10.1137/16m1068827.
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  - Luo, Songting, and Hongkai Zhao. “Convergence analysis of the fast sweeping method for static convex Hamilton–Jacobi equations.” Research in the Mathematical Sciences 3, no. 1 (December 2016). https://doi.org/10.1186/s40687-016-0083-8.
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  - Zhao, Hongkai, Jian Liang, Rongjie Lai, and Tsz Wai Wong. “Geometric Understanding of Point Clouds Using Laplace-Beltrami Operator.” Proceedings of the Ieee Computer Society Conference on Computer Vision and Pattern Recognition (Cvpr), 2016, 214–21.
  - Zepeda-Nún͂ez, Leonardo, and Hongkai Zhao. “Fast Alternating BiDirectional Preconditioner for the 2D High-Frequency Lippmann--Schwinger Equation.” Siam Journal on Scientific Computing 38, no. 5 (January 2016): B866–88. https://doi.org/10.1137/16m1064660.
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  - Liu, Jiulong, Xue Zhang, Xiaoqun Zhang, Hongkai Zhao, Yu Gao, David Thomas, Daniel A. Low, and Hao Gao. “5D respiratory motion model based image reconstruction algorithm for 4D cone-beam computed tomography.” Inverse Problems 31, no. 11 (November 1, 2015): 115007–115007. https://doi.org/10.1088/0266-5611/31/11/115007.
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  - Li, Zhilin, Li Xiao, Qin Cai, Hongkai Zhao, and Ray Luo. “A semi-implicit augmented IIM for Navier–Stokes equations with open, traction, or free boundary conditions.” Journal of Computational Physics 297 (September 2015): 182–93. https://doi.org/10.1016/j.jcp.2015.05.003.
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  - Liu, Hongyu, Hongkai Zhao, and Changjian Zou. “Determining scattering support of anisotropic acoustic mediums and obstacles.” Communications in Mathematical Sciences 13, no. 4 (2015): 987–1000. https://doi.org/10.4310/cms.2015.v13.n4.a7.
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  - Schaeffer, Hayden, Yi Yang, Hongkai Zhao, and Stanley Osher. “Real-Time Adaptive Video Compression.” Siam Journal on Scientific Computing 37, no. 6 (January 2015): B980–1001. https://doi.org/10.1137/130937792.
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  - Wong, Tsz Wai, and Hong-kai Zhao. “Computing Surface Uniformization Using Discrete Beltrami Flow.” Siam Journal on Scientific Computing 37, no. 3 (January 2015): A1342–64. https://doi.org/10.1137/130939183.
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  - Xiao, Li, Qin Cai, Zhilin Li, Hongkai Zhao, and Ray Luo. “A multi-scale method for dynamics simulation in continuum solvent models. I: Finite-difference algorithm for Navier–Stokes equation.” Chemical Physics Letters 616–617 (November 2014): 67–74. https://doi.org/10.1016/j.cplett.2014.10.033.
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  - Hon, Sean Y., Shingyu Leung, and Hongkai Zhao. “A cell based particle method for modeling dynamic interfaces.” Journal of Computational Physics 272 (September 2014): 279–306. https://doi.org/10.1016/j.jcp.2014.04.032.
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  - Cai, Jian-Feng, Xun Jia, Hao Gao, Steve B. Jiang, Zuowei Shen, and Hongkai Zhao. “Cine Cone Beam CT Reconstruction Using Low-Rank Matrix Factorization: Algorithm and a Proof-of-Principle Study.” Ieee Transactions on Medical Imaging 33, no. 8 (August 2014): 1581–91. https://doi.org/10.1109/tmi.2014.2319055.
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  - Aslam, Tariq, Songting Luo, and Hongkai Zhao. “A static PDE Approach for MultiDimensional Extrapolation Using Fast Sweeping Methods.” Siam Journal on Scientific Computing 36, no. 6 (January 2014): A2907–28. https://doi.org/10.1137/140956919.
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  - Lou, Yifei, Ernie Esser, Hongkai Zhao, and Jack Xin. “Partially Blind Deblurring of Barcode from Out-of-Focus Blur.” Siam Journal on Imaging Sciences 7, no. 2 (January 2014): 740–60. https://doi.org/10.1137/130931254.
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  - Wong, Tsz Wai, and Hong-kai Zhao. “Computation of Quasi-Conformal Surface Maps Using Discrete Beltrami Flow.” Siam Journal on Imaging Sciences 7, no. 4 (January 2014): 2675–99. https://doi.org/10.1137/14097104x.
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  - Zhao, Hongkai, Gang Bao, Kai Huang, and Peijun Li. “A direct imaging method for inverse scattering using the generalized Foldy-Lax formulation.” Contemporary Mathematics 615 (2014): 49–70. https://doi.org/10.1090/conm/615/12264.
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  - Wang, Changhao, Jun Wang, Qin Cai, Zhilin Li, Hong-Kai Zhao, and Ray Luo. “Exploring accurate Poisson–Boltzmann methods for biomolecular simulations.” Computational and Theoretical Chemistry 1024 (November 2013): 34–44. https://doi.org/10.1016/j.comptc.2013.09.021.
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  - Hou, Songming, Peng Song, Liqun Wang, and Hongkai Zhao. “A weak formulation for solving elliptic interface problems without body fitted grid.” Journal of Computational Physics 249 (September 2013): 80–95. https://doi.org/10.1016/j.jcp.2013.04.025.
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  - Huang, Kai, Peijun Li, and Hongkai Zhao. “An efficient algorithm for the generalized Foldy–Lax formulation.” Journal of Computational Physics 234 (February 2013): 376–98. https://doi.org/10.1016/j.jcp.2012.09.027.
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  - Liang, Jian, Frederick Park, and Hongkai Zhao. “Robust and Efficient Implicit Surface Reconstruction for Point Clouds Based on Convexified Image Segmentation.” Journal of Scientific Computing 54, no. 2–3 (February 2013): 577–602. https://doi.org/10.1007/s10915-012-9674-8.
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  - Liu, Xingping, Changhao Wang, Jun Wang, Zhilin Li, Hongkai Zhao, and Ray Luo. “Exploring a charge-central strategy in the solution of Poisson's equation for biomolecular applications.” Phys. Chem. Chem. Phys. 15, no. 1 (2013): 129–41. https://doi.org/10.1039/c2cp41894k.
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  - Botello-Smith, Wesley M., Xingping Liu, Qin Cai, Zhilin Li, Hongkai Zhao, and Ray Luo. “Numerical Poisson–Boltzmann model for continuum membrane systems.” Chemical Physics Letters 555 (January 2013): 274–81. https://doi.org/10.1016/j.cplett.2012.10.081.
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  - Lai, Rongjie, Jiang Liang, and Hong-Kai Zhao. “A local mesh method for solving PDEs on point clouds.” Inverse Problems &Amp; Imaging 7, no. 3 (2013): 737–55. https://doi.org/10.3934/ipi.2013.7.737.
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  - Liang, Jian, and Hongkai Zhao. “Solving Partial Differential Equations on Point Clouds.” Siam Journal on Scientific Computing 35, no. 3 (January 2013): A1461–86. https://doi.org/10.1137/120869730.
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  - Ren, Kui, Hao Gao, and Hongkai Zhao. “A Hybrid Reconstruction Method for Quantitative PAT.” Siam Journal on Imaging Sciences 6, no. 1 (January 2013): 32–55. https://doi.org/10.1137/120866130.
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  - Ren, Kui, and Hongkai Zhao. “Quantitative Fluorescence Photoacoustic Tomography.” Siam Journal on Imaging Sciences 6, no. 4 (January 2013): 2404–29. https://doi.org/10.1137/130912323.
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  - Gao, Hao, and Hongkai Zhao. “Analysis of a numerical solver for radiative transport equation.” Mathematics of Computation 82, no. 281 (April 11, 2012): 153–72. https://doi.org/10.1090/s0025-5718-2012-02605-6.
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  - Luo, Songting, Jianliang Qian, and Hongkai Zhao. “Higher-order schemes for 3D first-arrival traveltimes and amplitudes.” Geophysics 77, no. 2 (March 2012): T47–56. https://doi.org/10.1190/geo2010-0363.1.
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  - Chung, Eric, Jianliang Qian, Gunther Uhlmann, and Hongkai Zhao. “An adaptive phase space method with application to reflection traveltime tomography.” Inverse Problems 27, no. 11 (November 1, 2011): 115002–115002. https://doi.org/10.1088/0266-5611/27/11/115002.
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  - Xu, Jian-Jun, Zhilin Li, John Lowengrub, and Hongkai Zhao. “Numerical Study of Surfactant-Laden Drop-Drop Interactions.” Communications in Computational Physics 10, no. 2 (August 2011): 453–73. https://doi.org/10.4208/cicp.090310.020610a.
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  - Gao, Hao, Jian-Feng Cai, Zuowei Shen, and Hongkai Zhao. “Robust principal component analysis-based four-dimensional computed tomography.” Physics in Medicine and Biology 56, no. 11 (June 7, 2011): 3181–98. https://doi.org/10.1088/0031-9155/56/11/002.
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  - Leung, Shingyu, John Lowengrub, and Hongkai Zhao. “A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion.” Journal of Computational Physics 230, no. 7 (April 2011): 2540–61. https://doi.org/10.1016/j.jcp.2010.12.029.
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  - Luo, Songting, Yifeng Yu, and Hongkai Zhao. “A New Approximation for Effective Hamiltonians for Homogenization of a class of Hamilton–Jacobi Equations.” Multiscale Modeling &Amp; Simulation 9, no. 2 (April 2011): 711–34. https://doi.org/10.1137/100799885.
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  - Luo, Songting, Leonidas J. Guibas, and Hong-Kai Zhao. “Euclidean skeletons using closest points.” Inverse Problems &Amp; Imaging 5, no. 1 (2011): 95–113. https://doi.org/10.3934/ipi.2011.5.95.
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  - Qian, Jianliang, Plamen Stefanov, Gunther Uhlmann, and Hongkai Zhao. “An Efficient Neumann Series–Based Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed.” Siam Journal on Imaging Sciences 4, no. 3 (January 2011): 850–83. https://doi.org/10.1137/100817280.
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  - Zhang, Yong-Tao, Shanqin Chen, Fengyan Li, Hongkai Zhao, and Chi-Wang Shu. “Uniformly Accurate Discontinuous Galerkin Fast Sweeping Methods for Eikonal Equations.” Siam Journal on Scientific Computing 33, no. 4 (January 2011): 1873–96. https://doi.org/10.1137/090770291.
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  - Gao, Hao, Hongkai Zhao, Wenxiang Cong, and Ge Wang. “Bioluminescence tomography with Gaussian prior.” Biomedical Optics Express 1, no. 5 (December 1, 2010): 1259–1259. https://doi.org/10.1364/boe.1.001259.
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  - Benamou, J. -. D. “A Compact Upwind Second Order Scheme for the Eikonal Equation.” Journal of Computational Mathematics 28, no. 4 (June 2010): 489–516. https://doi.org/10.4208/jcm.1003-m0014.
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  - Gao, Hao, Yuting Lin, Gultekin Gulsen, and Hongkai Zhao. “Fully linear reconstruction method for fluorescence yield and lifetime through inverse complex-source formulation: simulation studies.” Optics Letters 35, no. 11 (June 1, 2010): 1899–1899. https://doi.org/10.1364/ol.35.001899.
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  - Huang, Kai, Knut Solna, and Hongkai Zhao. “Generalized Foldy-Lax formulation.” Journal of Computational Physics 229, no. 12 (June 2010): 4544–53. https://doi.org/10.1016/j.jcp.2010.02.021.
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  - Li, Zhilin, Ming-Chih Lai, Guowei He, and Hongkai Zhao. “An augmented method for free boundary problems with moving contact lines.” Computers &Amp; Fluids 39, no. 6 (June 2010): 1033–40. https://doi.org/10.1016/j.compfluid.2010.01.013.
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  - Zhao, Shingyu Leung and Hongkai. “Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method.” Communications in Computational Physics 8, no. 4 (June 2010): 758–96. https://doi.org/10.4208/cicp.190809.090210a.
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  - Gao, Hao, and Hongkai Zhao. “Multilevel bioluminescence tomography based on radiative transfer equation Part 2: total variation and l1 data fidelity.” Optics Express 18, no. 3 (February 1, 2010): 2894–2894. https://doi.org/10.1364/oe.18.002894.
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  - Gao, Hao, and Hongkai Zhao. “Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization.” Optics Express 18, no. 3 (February 1, 2010): 1854–1854. https://doi.org/10.1364/oe.18.001854.
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  - Zhao, Hongkai, Ye Duan, and Yongjian Xi. “A Nonparametric Approach for Noisy Point Data Preprocessing.” International Journal of Cad/Cam 9, no. 1 (2010): 31–36. https://doi.org/10.1109/CADCG.2009.5246900.
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  - Leung, Shingyu, and Hongkai Zhao. “A grid based particle method for evolution of open curves and surfaces.” Journal of Computational Physics 228, no. 20 (November 2009): 7706–28. https://doi.org/10.1016/j.jcp.2009.07.017.
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  - Gao, Hao, and Hongkai Zhao. “A Fast-Forward Solver of Radiative Transfer Equation.” Transport Theory and Statistical Physics 38, no. 3 (September 25, 2009): 149–92. https://doi.org/10.1080/00411450903187722.
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  - Fomel, Sergey, Songting Luo, and Hongkai Zhao. “Fast sweeping method for the factored eikonal equation.” Journal of Computational Physics 228, no. 17 (September 2009): 6440–55. https://doi.org/10.1016/j.jcp.2009.05.029.
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  - Leung, Shingyu, and Hongkai Zhao. “A grid based particle method for moving interface problems.” Journal of Computational Physics 228, no. 8 (May 2009): 2993–3024. https://doi.org/10.1016/j.jcp.2009.01.005.
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  - Cai, Qin, Jun Wang, Hong-Kai Zhao, and Ray Luo. “On removal of charge singularity in Poisson–Boltzmann equation.” The Journal of Chemical Physics 130, no. 14 (April 14, 2009): 145101–145101. https://doi.org/10.1063/1.3099708.
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  - Hou, Songming, Kai Huang, Knut Solna, and Hongkai Zhao. “A phase and space coherent direct imaging method.” The Journal of the Acoustical Society of America 125, no. 1 (January 2009): 227–38. https://doi.org/10.1121/1.3035835.
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  - Leung, Shingyu, Gang Liang, Knut Solna, and Hongkai Zhao. “Expectation-Maximization Algorithm with Local Adaptivity.” Siam Journal on Imaging Sciences 2, no. 3 (January 2009): 834–57. https://doi.org/10.1137/080731530.
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  - Wang, Jun, Qin Cai, Zhi-Lin Li, Hong-Kai Zhao, and Ray Luo. “Achieving energy conservation in Poisson–Boltzmann molecular dynamics: Accuracy and precision with finite-difference algorithms.” Chemical Physics Letters 468, no. 4–6 (January 2009): 112–18. https://doi.org/10.1016/j.cplett.2008.12.049.
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  - Zhao, Hongkai, and Hao Gao. “A multilevel and multigrid optical tomography based on radiative transfer equation.” Proceedings of Spie Osa Biomedical Optics (Optical Society of America, 2009) 7369 (2009). https://doi.org/10.1117/12.831665.
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  - Li, Fengyan, Chi-Wang Shu, Yong-Tao Zhang, and Hongkai Zhao. “A second order discontinuous Galerkin fast sweeping method for Eikonal equations.” Journal of Computational Physics 227, no. 17 (September 2008): 8191–8208. https://doi.org/10.1016/j.jcp.2008.05.018.
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  - Chung, E., J. Qian, G. Uhlmann, and Hong-Kai Zhao. “A phase-space formulation for elastic-wave traveltime tomography.” Journal of Physics: Conference Series 124 (July 1, 2008): 012018–012018. https://doi.org/10.1088/1742-6596/124/1/012018.
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  - Hou, Songming, Knut Solna, and Hongkai Zhao. “A direct imaging method using far-field data.” Inverse Problems 23, no. 4 (August 1, 2007): 1533–46. https://doi.org/10.1088/0266-5611/23/4/010.
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  - Qian, Jianliang, Yong-Tao Zhang, and Hong-Kai Zhao. “A Fast Sweeping Method for Static Convex Hamilton–Jacobi Equations.” Journal of Scientific Computing 31, no. 1–2 (May 2007): 237–71. https://doi.org/10.1007/s10915-006-9124-6.
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  - Chung, Eric, Jianliang Qian, Gunther Uhlmann, and Hongkai Zhao. “A new phase space method for recovering index of refraction from travel times.” Inverse Problems 23, no. 1 (February 1, 2007): 309–29. https://doi.org/10.1088/0266-5611/23/1/017.
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  - Qian, Jianliang, Yong‐Tao Zhang, and Hong‐Kai Zhao. “Fast Sweeping Methods for Eikonal Equations on Triangular Meshes.” Siam Journal on Numerical Analysis 45, no. 1 (January 2007): 83–107. https://doi.org/10.1137/050627083.
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  - Zhao, Hongkai. “Parallel Implementation of Fast Sweeping Method.” Journal of Computational Mathematics 25, no. 4 (2007): 421–29.
  - Zhang, Yong-Tao, Hong-Kai Zhao, and Jianliang Qian. “High Order Fast Sweeping Methods for Static Hamilton–Jacobi Equations.” Journal of Scientific Computing 29, no. 1 (October 24, 2006): 25–56. https://doi.org/10.1007/s10915-005-9014-3.
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  - Hou, Songming, Knut Solna, and Hongkai Zhao. “A direct imaging algorithm for extended targets.” Inverse Problems 22, no. 4 (August 1, 2006): 1151–78. https://doi.org/10.1088/0266-5611/22/4/003.
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  - Huang, Kai, George Papanicolaou, Knut Solna, Chrysoula Tsogka, and Hongkai Zhao. “Efficient numerical simulation for long range wave propagation.” Journal of Computational Physics 215, no. 2 (July 2006): 448–64. https://doi.org/10.1016/j.jcp.2005.11.003.
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  - Xu, Jian-Jun, Zhilin Li, John Lowengrub, and Hongkai Zhao. “A level-set method for interfacial flows with surfactant.” Journal of Computational Physics 212, no. 2 (March 2006): 590–616. https://doi.org/10.1016/j.jcp.2005.07.016.
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  - Zhao, Hongkai, Danfeng Lu, Ming Jiang, and Tie Zhou. “A Surface Reconstruction Method for Highly Noisy Point Clouds.” International Workshop on Variational, Geometric, and Level Set Methods in Computer Vision, 2006, 283–94.
  - Chen, Shanqin, Yong-Tao Zhang, and Hong-Kai Zhao. “Fixed-point Iterative Sweeping Methods for Static Hamilton-Jacobi Equations.” Methods and Applications of Analysis 13, no. 3 (2006): 299–320. https://doi.org/10.4310/maa.2006.v13.n3.a5.
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  - Peternell, Martin, Helmut Pottmann, Tibor Steiner, and Hongkai Zhao. “Swept Volumes.” Computer Aided Design and Applications 2, no. 5 (January 2005): 599–608. https://doi.org/10.1080/16864360.2005.10738324.
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  - Zhao, Hongkai, Ye Duan, Yongjian Xi, and Greg Heckenberg. “A New Modeling-Based Algorithm for Implicit Surface Polygonization.” Proceedings of Spie, Proceedings of Vision Geometry Xiii, 2005. https://doi.org/10.1117/12.585678.
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  - Hou, Songming, Knut Solna, and Hongkai Zhao. “Imaging of location and geometry for extended targets using the response matrix.” Journal of Computational Physics 199, no. 1 (September 2004): 317–38. https://doi.org/10.1016/j.jcp.2004.02.010.
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  - Zhao, Hongkai. “A fast sweeping method for Eikonal equations.” Mathematics of Computation 74, no. 250 (May 21, 2004): 603–27. https://doi.org/10.1090/s0025-5718-04-01678-3.
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  - Huang, Kai, Knut Solna, and Hongkai Zhao. “Coupled Parabolic Equations for Wave Propagation.” Methods and Applications of Analysis 11, no. 3 (2004): 399–412. https://doi.org/10.4310/maa.2004.v11.n3.a10.
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  - Zhao, Hongkai. “Analysis of the Response Matrix for an Extended Target.” Siam Journal on Applied Mathematics 64, no. 3 (January 2004): 725–45. https://doi.org/10.1137/s0036139902415282.
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  - Zhao, Hongkai, and Jianjun Xu. “An Eulerian formulation for solving partial differential equations along a moving interface.” Journal of Scientific Computing 19, no. 1–3 (2003): 573–94.
  - Li, Zhilin, Xiaobiao Lin, Monica Torres, and Hongkai Zhao. “Generalized Snell's Law for Weighted Minimal Surface in Heterogeneous Media.” Methods and Applications of Analysis 10, no. 2 (2003): 199–214. https://doi.org/10.4310/maa.2003.v10.n2.a3.
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  - Tsai, Yen-Hsi Richard, Li-Tien Cheng, Stanley Osher, and Hong-Kai Zhao. “Fast Sweeping Algorithms for a Class of Hamilton--Jacobi Equations.” Siam Journal on Numerical Analysis 41, no. 2 (January 2003): 673–94. https://doi.org/10.1137/s0036142901396533.
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  - Hunter, John K., Zhilin Li, and Hongkai Zhao. “Reactive Autophobic Spreading of Drops.” Journal of Computational Physics 183, no. 2 (December 2002): 335–66. https://doi.org/10.1006/jcph.2002.7168.
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  - Zhao, Hongkai, and Martin Gander. “Overlapping Schwarz Waveform Relaxation for the Heat Equation in n Dimensions.” Bit Numerical Mathematics 42, no. 4 (2002): 779–95.
  - Blomgren, Peter, George Papanicolaou, and Hongkai Zhao. “Super-resolution in time-reversal acoustics.” The Journal of the Acoustical Society of America 111, no. 1 (January 2002): 230–48. https://doi.org/10.1121/1.1421342.
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  - Zhao, Hongkai, Stanley Osher, and Ronald Fedkiw. “Fast Surface Reconstruction and Deformation Using the Level Set Method.” Proceedings Ieee Workshop on Variational and Level Set Methods in Computer Vision, 2001, 194–201. https://doi.org/10.1109/VLSM.2001.938900.
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  - Zhao, Hong-Kai, Stanley Osher, Barry Merriman, and Myungjoo Kang. “Implicit and Nonparametric Shape Reconstruction from Unorganized Data Using a Variational Level Set Method.” Computer Vision and Image Understanding 80, no. 3 (December 2000): 295–314. https://doi.org/10.1006/cviu.2000.0875.
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  - Peng, Danping, Barry Merriman, Stanley Osher, Hongkai Zhao, and Myungjoo Kang. “A PDE-Based Fast Local Level Set Method.” Journal of Computational Physics 155, no. 2 (November 1999): 410–38. https://doi.org/10.1006/jcph.1999.6345.
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  - Li, Zhilin, Hongkai Zhao, and Huajian Gao. “A Numerical Study of Electro-migration Voiding by Evolving Level Set Functions on a Fixed Cartesian Grid.” Journal of Computational Physics 152, no. 1 (June 1999): 281–304. https://doi.org/10.1006/jcph.1999.6249.
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  - Engquist, Bjorn, and Hong-Kai Zhao. “Absorbing boundary conditions for domain decomposition.” Applied Numerical Mathematics 27, no. 4 (August 1998): 341–65. https://doi.org/10.1016/s0168-9274(98)00019-1.
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  - Zhao, Hong-Kai, Barry Merriman, Stanley Osher, and Lihe Wang. “Capturing the Behavior of Bubbles and Drops Using the Variational Level Set Approach.” Journal of Computational Physics 143, no. 2 (July 1998): 495–518. https://doi.org/10.1006/jcph.1997.5810.
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  - Zhao, Hongkai, Danping Peng, Stanley Osher, and Barry Merriman. “The Geometry of Wulff Crystal Shapes and Its Relations with Riemann Problems.” Contemporary Mathematics 238 (1998): 251–303.
  - Hou, Thomas Y., Zhilin Li, Stanley Osher, and Hongkai Zhao. “A Hybrid Method for Moving Interface Problems with Application to the Hele–Shaw Flow.” Journal of Computational Physics 134, no. 2 (July 1997): 236–52. https://doi.org/10.1006/jcph.1997.5689.
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  - Zhao, Hong-Kai, T. Chan, B. Merriman, and S. Osher. “A Variational Level Set Approach to Multiphase Motion.” Journal of Computational Physics 127, no. 1 (August 1996): 179–95. https://doi.org/10.1006/jcph.1996.0167.
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- Book Sections
  - Zhao, Hongkai, Edward Castillo, and Jian Liang. “Point cloud segmentation and denoising via constrained least squares normal estimates.” In Innovations for Shape Analysis,Models and Algorithms, edited by Michael Breuß, Alfred Bruckstein, and Petros Maragos, 283–99. Springer, 2013. https://doi.org/10.1007/978-3-642-34141-0.
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  - Zhao, Hongkai, Hao Gao, and Stanley Osher. “Quantitative photoacoustic tomography.” In Mathematical Modeling in Biomedical Imaging II, edited by Habib Ammari, 131–58. Springer, 2012. https://doi.org/10.1007/978-3-642-22990-9.
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  - Zhao, Hongkai. “Time reversal based direct imaging methods.” In Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT), edited by Yair Censor, Ming Jiang, and Alfred Louis, 505–21. Springer, 2008.
  - Zhao, Hongkai, and Stanley Osher. “Visualization, Analysis and Shape Reconstruction of Unorganized Data Sets.” In Geometric Level Set Methods in Imaging, Vision and Graphics, edited by Stanley Osher and Nikos Paragios, 361–80, 2003.
- Other Articles
  - Zhao, Hongkai, and Rongjie Lai. “Solving PDEs on manifolds represented as point clouds and applications.” Edited by Ron Kimmel and Xue-Cheng Tai. Handbook of Numerical Analysis: Elsevier, 2019. https://doi.org/10.1016/bs.hna.2019.07.006.
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  - Zhao, Hongkai. “The Fast Sweeping Method for Stationary Hamilton–Jacobi Equations.” Edited by Remy Abgrall and Chi-Wang Shu. Elsevier, 2016. https://doi.org/10.1016/bs.hna.2016.09.012.
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- Conference Papers
  - Xiang, R., R. Lai, and H. Zhao. “A Dual Iterative Refinement Method for Non-rigid Shape Matching.” In Proceedings of the Ieee Computer Society Conference on Computer Vision and Pattern Recognition, 15925–34, 2021. https://doi.org/10.1109/CVPR46437.2021.01567.
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