Publications

  1. J. Qian and W. W. Symes, Paraxial eikonal solvers for anisotropic Quasi-P traveltimes, J. Comput. Phys. 173(2001), 256-278. pdf

  2. J. Qian, W. W. Symes and J. A. Dellinger, A full aperture anisotropic eikonal solver for Quasi-P traveltimes, 71st Internat. Mtg, Soc. Expl. Geophys. Expanded Abstracts., 2001, pp. 129-132. pdf

  3. J. Qian and W. W. Symes, An adaptive finite-difference method for traveltimes and amplitudes, Geophysics 67(2002), 167-176. pdf

  4. J. Qian and W. W. Symes, Finite-difference Quasi-P traveltimes for anisotropic media, Geophysics 67(2002), 147-155. pdf

  5. J. Qian and W. W. Symes, Paraxial geometrical optics for quasi-P waves: theories and numerical methods, Wave Motion 35(2002), 205-221. pdf

  6. B. Cockburn and J. Qian, Continuous dependence results for Hamilton-Jacobi equations, Collected lectures on the preservation of stability under discretization, Edited by D. Estep and S. Tavener, SIAM, 2002. pdf

  7. J. Qian, L.-T. Cheng and S. Osher, A level set based Eulerian approach for anisotropic wave propagations, Wave Motion 37(2003), 365-379. pdf

  8. W. W. Symes and J. Qian, A slowness matching Eulerian method for multivalued solutions of eikonal equations, J. Sci. Comput. 19(2003), 501-526. pdf

  9. J. Qian, L.-T. Cheng and S. Osher, Level set based Eulerian method for multivalued traveltimes in both isotropic and anisotropic wave propagations, SEG 2003, PP. 1801-1804. pdf

  10. J. Qian and W. W. Symes, A paraxial formualtion for the viscosity solution of quasi-P eikonal equations, Computers and Mathematics with Applications 46(2003), 1691-1701. pdf

  11. C. Kao, S.J. Osher and J. Qian. Lax-Friedrichs sweeping scheme for Static Hamilton-Jacobi equations, J. Comput. Phys. 196(2004), 367-391. pdf .

  12. T. Cecil, J. Qian and S. Osher, Numerical methods for high dimensional Hamilton-Jacobi equations using Radial Basis Functions, J. Comput. Phys. 196(2004), 327-347. pdf

  13. J. Qian and S. Y. Leung, A level set method for multivalued solutions of paraxial eikonal equations, J. Comput. Phys. 197(2004), 711-736. pdf

  14. Y. T. Zhang, H. K. Zhao and J. Qian, Higher order fast sweeping methods for eikonal equations, SEG 2004, PP. 1901-1904. pdf

  15. S. Y. Leung, J. Qian and S. J. Osher, A Level Set Method for Three-dimensional Paraxial Geometrical Optics with Multiple Sources, Commun. Math. Sci. 2(2004), 643--672. pdf

  16. B. Cockburn, J. Qian, F. Reitich and J. Wang, An Accurate Spectral/Discontinuous Finite-Element Formulation of a Phase-Space-Based Level Set Approach to Geometrical Optics, J. Comput. Phys. 208(2005), 175-195. pdf

  17. S. Y. Leung and J. Qian, A Transmission Tomography Problem Based on Multiple Arrivals from Paraxial Liouville Equations, SEG 2005, PP 2589-2592.

  18. J. Qian, Approximations for viscosity solutions of Hamilton-Jacobi equations with locally varying time and space grids, SIAM Numer. Anal. 43(2006), 2371-2401.

  19. J. Qian and S. Y. Leung, A local level set method for paraxial geometrical optics, SIAM J. Sci. Comput. 28(2006), 206--223.

  20. Y.T. Zhang, H.K. Zhao and J. Qian, High order fast sweeping methods for static Hamilton-Jacobi equations, J. Sci. Comput. 29(2006), 25-56. pdf

  21. R. Burridge and J. Qian, The fundamental solution of the time dependent system of crystal optics, Euro. J. Applied Math. 17(2006), 63-94. pdf

  22. S. Serna and J. Qian, Fifth Order Weighted Power-ENO Schemes for Hamilton-Jacobi Equations, J. Sci. Comput. 29(2006), 57-81. pdf

  23. T. C. Cecil, S. Osher and J. Qian, Simplex Free Adaptive Tree Fast Sweeping and Evolution Methods for Solving Level Set Equations in Arbitrary Dimension, J. Comput. Phys. 213(2006), 458-473. pdf

  24. S. Leung and J. Qian, An adjoint state method for 3-D transmission traveltime tomography using first-arrivals, Comm. Math. Sci. 4(2006), 249-266. pdf

  25. J. Qian, Y. T. Zhang and H.-K. Zhao, Fast sweeping methods for eikonal equations on triangulated meshes, SIAM J. Numer. Analy. 45(2007), 83-107.

  26. J. Wu, V. K. Dhir and J. Qian, Numerical simulations of subcooled nucleate boiling by coupling level set method with moving mesh method, Numerical Heat Transfer, Part B. 51(2007), 535-563. pdf

  27. J. Qian, Y. T. Zhang and H.-K. Zhao, Fast sweeping methods for stationary Hamilton-Jacobi equations on triangulated meshes, J. Scientific Computing 31(2007), 237-271. pdf

  28. E. Chung, J. Qian, G. Uhlmann, and H.-K. Zhao, A new phase space method for recovering index of refraction from travel times, Inverse Problems 23(2007), 309-329. UCLA CAM07-02.

  29. S. Leung and J. Qian, Transmission traveltime tomography based on paraxial Liouville equations and level set formulations, Inverse Problems 23(2007), 799-821.

  30. N. M. Tanushev, J. Qian, and J. Ralston, Mountain waves and Gaussian beams, SIAM J. Multiscale Modeling and Simulation 6(2007), 688-709. pdf

  31. S. Leung, J. Qian and R. Burridge, Eulerian Gaussian beams for high frequency wave propagation, Geophysics 72(2007), SM61-SM76. pdf

  32. E. Chung, J. Qian, G. Uhlmann and H. K. Zhao, A phase-space formulation for elastic traveltime tomography, Journal of Physics: Conference Series 124(2008): 012018. pdf

  33. T. C. Cecil, S. J. Osher and J. Qian, Essentially Non-Oscillatory Adaptive Tree Methods, J. Scientific Computing 35(2008), 25-41. pdf

  34. C. Y. Kao, S. J. Osher and J. Qian, Legendre transform based fast sweeping methods for static Hamilton-Jacobi equations on triangulated meshes, J. Computational Physics 227 (2008) 10209-10225. pdf

  35. S. Leung and J. Qian, Eulerian Gaussian beams for Schrodinger equations in the semi-classical regime, J. Computational Physics 228(2009) 2951-2977. pdf

  36. S. Serna and J. Qian, A stopping criterion for higher-order sweeping schemes for static Hamilton-Jacobi equations, J. Computational Mathematics 28 (2010), 552-568. pdf

  37. B. Cockburn, B. Dong, J. Guzman, and J. Qian, Optimal convergence of the original DG method on special meshes for variable transport velocity, SIAM J. Numer. Analy. 48 (2010), 133-146. pdf

  38. J. Qian and L. Ying, Fast Gaussian wavepacket transforms and Gaussian beams for the Schrodinger equation, J. Computational Physics 229 (2010) 7848-7873. pdf

  39. J. Qian and L. Ying, Fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beams for the wave equation, SIAM MMS 8(2010), 1803-1837. pdf

  40. S. Leung and J. Qian, The Backward Phase Flow and FBI-transform-based Eulerian Gaussian Beams for the Schrodinger Equation, J. Computational Physics 229 (2010), 8888-8917. pdf

  41. S. Luo, S. Leung, and J. Qian, An Adjoint State Method for Numerical Approximation of Continuous Traffic Congestion Equilibria, Communications in Computational Physics 10 (2011), 1113-1131. pdf.

  42. V. Isakov, S. Leung and J. Qian, A Fast Local Level Set Method for Inverse Gravimetry, Communications in Computational Physics 10 (2011), 1044-1070. pdf.

  43. S. Luo, and J. Qian, Factored singularities and high-order Lax-Friedrichs sweeping schemes for point-source traveltimes and amplitudes, J. Computational Physics 230 (2011), 4742-4755. pdf.

  44. S. Luo, J. Qian, and H.-K. Zhao, High-order schemes for 3-D traveltimes and amplitudes. Geophysics, to appear, 2011. pdf.

  45. S. Luo, and J. Qian, Fast sweeping method for factored anisotropic eikonal equations: multiplicative and additive factors. J. Scientific Computing, to appear, 2011. pdf.

  46. B. Cockburn, I. Merev and J. Qian, Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations. Math. Comp., to appear, 2011. pdf.

  47. E. Chung, J. Qian, G. Uhlmann, and H.-K. Zhao, Adaptive phase space method for transmission and reflection traveltime tomography. Inverse Problems, 27 (2011) 115002 (22pp). pdf.

  48. J. Qian, P. Stefanov, G. Uhlmann, and H.-K. Zhao, An efficient Neumann-Series based algorithm for thermoacoustic tomography with variable sound speed. SIAM J. Imaging Sciences, 4 (2011), 850-883. pdf.

Last update: Jan. 11, 2012.