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. pdf.
  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 Multiscale Modeling and Simulation 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. 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
  45. 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
  46. S. Luo, J. Qian, and H.-K. Zhao, High-order schemes for 3-D traveltimes and amplitudes. Geophysics 77(2012): T47-T56. pdf
  47. S. Luo, and J. Qian, Fast sweeping method for factored anisotropic eikonal equations: multiplicative and additive factors. J. Scientific Computing 52(2012): 360-382. pdf
  48. B. Cockburn, I. Merev and J. Qian, Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations. Math. Comp. 82(2013): 187-212. pdf
  49. G. Bao, J. Qian, L. Ying, and H. Zhang, A Convergent Multiscale Gaussian-Beam Parametrix for the Wave Equation. Communications in Partial Differential Equations 38(2013): 92-134. pdf
  50. V. Isakov, S. Leung and J. Qian, A Three-dimensional Inverse Gravimetry Problem for Ice with Snow Caps. Inverse Problems and Imaging 7(2013): 523-544. pdf
  51. J. Qian, C. Yang, A. Schirotzek, F. Maia, and S. Marchesini, Efficient Algorithms for Ptychographic Phase Retrieval. Contemporary Mathematics 615(2014): 261-280. pdf
  52. S. Luo, J. Qian and R. Burridge, High-order Factorization based High-order hybrid fast sweeping methods for point-source eikonal equations. SIAM J. Numer. Analy. 52(2014): 23-44. pdf
  53. S. Luo, J. Qian and R. Burridge, Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime. Journal of Comput. Physics, 270(2014) 378-401. pdf
  54. G. Bao, J. Lai and J. Qian, Fast Multiscale Gaussian beam methods for wave equations in bounded domains. Journal of Comput. Physics 261(2014): 36-64. pdf
  55. E. Chung, C. Y. Lam, and J. Qian, A Neumann series based method for photoacoustic tomography on irregular domains. Contemporary Mathematics 615(2014): 89-104. pdf
  56. S. Luo, J. Qian and P. Stefanov, Adjoint State Method for the Identification Problem in SPECT: Recovery of Both the Source and the Attenuation in the Attenduated X-Ray Transform. SIAM J. Imaging Sciences 7(2014): 696-715. pdf
  57. S. Leung, J. Qian and S. Serna, Fast Huygens Sweeping Methods for Schrodinger Equations in the Semi-Classical Regime. Methods and Applications of Analysis 21 (2014): 031-066. pdf
  58. W. Li, S. Leung and J. Qian, A Level Set-Adjoint State Method for Crosswell Transmission-Reflection Traveltime Tomography. Geophysical Journanl International 199 (2014): 348-367. pdf
  59. W. Lu and J. Qian, A Local Level Set Method for Three-dimensional Inversion of Gravity Gradient Data. Geophysics 80 (2015): G35-G51. pdf
  60. J. Qian, S. Luo and R. Burridge, Fast Huygens sweeping methods for multiarrival Green's functions of Helmholtz equations in the high frequency regime. Geophysics 80 (2015): T91-T100. pdf
  61. W. Lu, S. Leung and J. Qian, An Improved Fast Local Level Set Method for Three-dimensional Inverse Gravimetry. Inverse Problems and Imaging 9 (2015): 479-509. pdf
  62. E. Chung, C. Y. Lam and J. Qian, A staggered discontinuous Galerkin method for the simulation of Rayleigh waves. Geophysics 80 (2015): T119-T135. pdf
  63. R. Glowinski, S. Leung, and J. Qian, A penalization-regularization-operator splitting method for eikonal-based traveltime tomography. SIAM J. Imaging Sciences 8 (2015): 1263-1292. pdf
  64. J. Qian, L. Yuan, Y. Liu, and R. Burridge, Babich's Expansion and High-order Eulerian Asymptotics for Point-source Helmholtz Equations. Journal of Scientific Computing, to appear. pdf
  65. W. Li, W. Lu, and J. Qian, A level set method for imaging salt structure using gravity data. Geophysics, to appear. pdf
  66. X. Wang, J. Qian, and H. Wang, Efficient angle-domain common-imaging gathers using Cauchy condition based polarization vectors. Geophysics, to appear. pdf
  67. J. Qian, W. Lu, L. Yuan, S. Luo, and R. Burridge, Eulerian geometrical optics and fast Huygens sweeping methods for three-dimensional time-harmonic high-frequency Maxwell's equations in inhomogeneous media. Submitted. pdf
  68. W. Lu, J. Qian, and R. Burridge, Babich's Expansion and the Fast Huygens Sweeping Method for the Helmholtz Wave Equation at High Frequencies. Submitted. pdf
  69. W. Li and J. Qian, Joint inversion of gravity and traveltime data using structural parameterization. Submitted. pdf
  70. W. Li, W. Lu, and J. Qian, A multiple level set method for three-dimensional inversion of magnetic data. Submitted. pdf