The Level Set Method

• An Eulerian Formulation for Solving Partial Differential Equations Along a Moving Interface, J. Xu, H.K. Zhao, J. Sci. Comp. Vol. 19, 2003, pp573-594. (ps file, pdf file)


• A PDE Based Fast Local Level Set Method, D. Peng, B. Merriman, S. Osher, H.K. Zhao, M. Kang. J. Comp. Phys. Vol. 155, 1999, pp 410-438.  (ps file,pdf file)


• Capturing the Behavior of Bubbles and Drops Using the Variational Level Set Approach, H.K. Zhao, B. Merriman, S. Osher, L. Wang. J. Comp. Phys. Vol. 143, 1998, pp 495-518. (ps file, pdf file)


• A Variational Level Set Approach to Multiphase Motion, H.K. Zhao, T.F. Chan, B. Merriman, S.Osher. J. Comp. Phys. Vol. 127, 1996, pp 179-195. (ps file, pdf file)

• A Grid Based Particle Method for Evolution of Open Curves and Surfaces, S. Leung and H. Zhao, to appear J. Comp. Phys. (pdf file)


• A novel grid based particle method for moving interface problem, S. Leung and H. Zhao, J. Comp. Phys., Vol. 228 (8), pp. 2993-3024, 2009. (pdf file)


• A Hybrid Method for Moving Interface Problems with Application to the Hele-Shaw Flow, T.Y. Hou, Z.L. Li, S. Osher, H.K. Zhao. J. Comp. Phys. Vol. 134, 1997, pp 236-252. (ps file, pdf file)


• A Numerical Study of Electro-migration Voiding by Evolving Level Set Functions on a Fixed Cartesian Grid, Z. Li, H.K. Zhao, H. Gao. J. Comp. Phys. Vol. 152, 1999, pp 281-304. (ps file, pdf file)


• Reactive Autophobic Spreading of Drops,J.K. Hunter, Z. Li and H.K. Zhao J. Comp. Phys. Vol. 183, No. 2, pp. 335-366, 2002. (ps file,pdf file)

• A Level Set Method for Interfacial Flows with Surfactant, J. Xu, Z. Li, J. Lowengrub and H. Zhao, J. Comp. Phys. Vol. 212(2), pp. 590-616, 2006. (pdf)

• Euclidean Skeletons Using Closest Points, S. Luo, L. Guibas and H. Zhao, submitted. (pdf file)


• Expectation-Maximization algorithm with local adaptivity for image analysis, S. Leung, G. Liang, K. Solna and H. Zhao, to appear SIAM Journal on Imaging Sciences. (pdf file)


• A Surface Reconstruction Method for Highly Noisy Point Clouds D. Lu, H. Zhao, M. Jiang, S. Zhou, and T. Zhou, Lecture Notes in Computer Science, Springer. (pdf file)


• Swept Volumes, M.  Peternell, H.  Pottmann, T. Steiner, H. Zhao, Computer-Aided Design and Applications, Vol. 2, No. 5, 2005. (pdf file)


• A New Modeling-Based Algorithm for Implicit Surface Polygonization, Y. Xi, G. Heckenberg, Y. Duan and H. Zhao, Proceedings of Vision Geometry XIII, SPIE 2005, January 2005, San Jose, CA, to appear.


• The d^2-Tree: A Hierarchical Representation of the Squared Distance Function,   H. Pottmann, S. Leopoldseder, H. Zhao, Preprint (pdf file)
  


•  Visualization, Analysis and Shape Reconstruction of Unorganized Data Sets,     H. Zhao and S. Osher, contributed chapter in S. Osher and N. Paragios, editors, Geometric Level Set Methods in Imaging, Vision and Graphics, Springer, 2002. (ps file, pdf file)


• Simultaneous Spatio-Temporal Target Segmentation and Motion Estimation in a Variational Formulation,       A.Q. Li, V. Chalana, H.K. Zhao.   Proceedings of SPIE on Applied Imagery Pattern Recognition (AIPR), vol 3584, Washington DC, 1998


• Implicit and Non-parametric Shape Reconstruction from Unorganized Points Using Variational Level Set Method,     H.K. Zhao, S. Osher, B. Merriman, M. Kang.    Computer Vision and Image Understanding. Vol. 80, 2000, pp 295-319. (ps file,  pdf file)


• Fast Surface Reconstruction Using the Level Set Method,  H.K.Zhao, S. Osher, R. Fedkiw.  Proceedings of IEEE Workshop on Variational and Level Set Methods in Computer Vision (VLSM 2001),  July, 2001.  (ps file, pdf file)
   

• Analysis and Visualization of Large Set of Unorganized Data Points Using the Distance Function,    H.K. Zhao, preprint  (ps file, pdf file)

• A Fast Forward Solver of Radiative Transfer Equation in Optical Imaging, H. Gao and H. Zhao, to appear in Transport Theory and Statistical Physics. (pdf file)


• A phase and space coherent direct imaging algorithm, S. Hou, K. Huang, K. Solna, H. Zhao, Journal of Acoustic Society of America, (2009). (pdf file)


• A Direct Imaging Method Using Far Field Data,  S. Hou, K. Solna, H. Zhao, Inverse Problem, Vol. 23, 1533-1546, 2007. (pdf)
  


• A New Phase Space Method for Recovering Index of Refraction From Travel Times,  E. Chung, J. Qian, G. Uhlmann, H. Zhao,  Inverse Problems, 23 No 1, pp. 309-329, 2007. (ps file)


• A Direct Imaging Algorithm For Extended Targets,  S. Hou, K. Solna, H. Zhao, Inverse Problem, Vol. 22, 1151-1178, 2006. (pdf)
  


• Efficient Numerical Simulation for Long Range Wave Propagation, K. Huang, G. Papanicolaou, K. Solna, C. Tsogka, H. Zhao,  J. Comp. Phys. Vol. 215(2), pp. 448-464, 2006. (pdf file)
  


• Coupled Parabolic Equations for Wave Propagation, K. Huang, K. Solna, H. Zhao, Methods and Applications of Analysis, Vol. 11 (3), pp 399-412, 2004. (ps file, pdf file)
  


• Imaging of Location and Geometry for Extended Targets Using the Response Matrix,  S. Hou, K. Solna, H. Zhao,  J. Comp. Phys.  Vol. 199 (1), 2004, pp. 317-338. (ps file, pdf file)


• Analysis of the Response Matrix for an Extended Target,  H. Zhao, SIAM Applied Mathematics, Vol. 64 (3), (2004), pp.725-745. (ps file, pdf file)


• Super-resolution in Time Reversal Acoustics,    P. Blomgren, G. Papanicolaou, H.K. Zhao.   Journal of the Acoustical Society of America, Vol 111, (2002), pp. 230-248. (ps file, pdf file)

• Fast sweeping method for the factored eikonal equation, S. Fomel, S. Luo and H. Zhao, to appear J. Comp. Phys. (pdf file)


• Second Order discontinuous Galerkin Fast Sweeping Method For Eikonal Equations, F. Li, C.-W. Shu, Y.-T. Zhang and H. Zhao, J. Comp. Phys. Vol. 227(17), pp. 8191-8208, 2008. (pdf file)


• A Fast sweeping method for static convex Hamilton-Jacobi equations,  J. Qian, Y. Zhang, H. Zhao.  Journal of Scientific Computing, Vol. 31, No. 1/2, pp. 237-271, 2007. (pdf file)
  

• Parallel Implementations of the Fast Sweeping Method, H. Zhao, Journal of Computational Mathematics, Vol. 25, No. 4, pp. 421-429, 2007. (pdf file)


• Fixed-point Iterative Sweeping Methods for Static Hamilton-Jacobi Equations,  Y. Zhang,  H. Zhao,  S. Chen, to appear Methods and Applications of Analysis.  (pdf)

• Fast sweeping methods for Eikonal equations on triangulated meshes,  J. Qian, Y. Zhang, H. Zhao.  SIAM  Journal on Numerical Analysis, Vol 45, pp. 83-107, (2007). (pdf)
  

• High order fast sweeping methods for static Hamilton-Jacobi equations, Y. Zhang,  J.Qian,  H. Zhao.  Journal of Scientific Computing, Vol. 29, pp. 25-56, 2006. (pdf)

• Fast Sweeping Method for Eikonal Equations H.K. Zhao, Mathematics of Computation, Vol. 74, (2005), 603-627. (ps file, pdf file) 

• Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations,Y.R. Tsai,  L.T. Cheng,  S. Osher, H.K. Zhao,   SIAM  Journal on Numerical Analysis, Vol 41, No 2, 2003, pp. 673-694. (ps file, pdf file).

• Absorbing Boundary Conditions for Domain Decomposition,  B. Engquist, H.K. Zhao. Applied Numerical Mathematics, Vol. 27, 1998, pp341-365.  (ps file, pdf file)
 
• Overlapping Schwarz Waveform Relaxation for the Heat Equation in n-Dimensions,         M.J. Gander, H.K. Zhao.  BIT, Vol. 42, No. 4, pp. 779-795, 2002. (ps file, pdf file)

• On Removal of Charge Singularity in Poisson-Boltzmann Equation, Q. Cai, J. Wang, H. Zhao, and R. Luo, preprint. (pdf file)


• Achieving Energy Conservation in Poisson-Boltzmann Molecular Dynamics: Accuracy and Precision with Finite-Difference Algorithms, J. Wang, Q. Cai, Z.-L. Li, H. Zhao, and R. Luo, to appear in Chemical Physics Letters. (pdf file)


• The Geometry of Wulff Crystal Shapes and Its Relations with Riemann Problems,      D. Peng, S. Osher, B. Merriman, H.K. Zhao. Contemporary Mathematics, Vol. 238, AMS, Providence, 1999, pp 251-303,  eds G.-Q Chen and E. DiBenedetto. (ps file,  pdf file)
   

• View-Based Recognition: A Comparision of Three Methods,   A.M. Rodriguez, B.M. Bennett, D.D. Hoffman, H.K. Zhao.   submitted.  (ps file,   pdf file)

• Generalized Snell's Law for Weighted Minimal Surface in Heterogeneous Media,   Z.  Li,  X.  Lin,  M. Torres, H. Zhao.  Methods and Applications of Analysis, Vol. 10(2),  2003,  pp 199-214. (ps file,  pdf file)