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 67 (2016): 883-908. pdf

  65. W. Li, W. Lu, and J. Qian, A level set method for imaging salt structure using gravity data. Geophysics 81 (2016), No. 2: G35-G51. pdf

  66. X. Wang, J. Qian, and H. Wang, Efficient angle-domain common-imaging gathers using Cauchy condition based polarization vectors. Geophysics 81 (2016), No. 2: S69-S77. 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. SIAM Multi-scale Modeling Simulation 16(2016): 595-636. 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. Journal of Computational Physics 313(2016): 478-510. pdf

  69. R. Glowinski, S. Leung, and J. Qian, Operator-splitting based fast sweeping methods for isotropic wave propagation in a moving fluid. SIAM J. Scientific Computing 38 (2016): A1195-A1223. pdf

  70. W. Li and J. Qian, Joint inversion of gravity and travel-time data using a level-set based structural parameterization. Geophysics, 81 (2016), No. 6: G107-G119. pdf

  71. W. Lu, J. Qian, and R. Burridge, Babich-like ansatz for three-dimensional point-source Maxwell's equations in an inhomogeneous medium at high frequencies. SIAM Multiscale Modeling Simulation, 14 (2016), No. 3: 1089-1122. pdf

  72. W. Li, W. Lu, J. Qian, and Y. Li, A multiple level set method for three-dimensional inversion of magnetic data. Geophysics 82(2017), No. 5, J61-J81. pdf

  73. J. Fang, J. Qian, L. Zepeda-Nunez, and H.-K. Zhao, Learning Dominant Wave Directions For Plane Wave Methods For High-Frequency Helmholtz Equations. Research in the Mathematical Sciences (2017) 4:9. pdf

  74. W. Kwan, S. Leung, X-P Wang, and J. Qian, A Fast Huygens Sweeping Method for Capturing Paraxial Multi-color Optical Self-focusing in Nematic Liquid Crystals. Journal of Computational Physics 348 (2017) 108-138. pdf

  75. E. Chung, C. Lam, and J. Qian, A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media. Journal of Computational Physics 348 (2017) 660-682. pdf

  76. J. Qian, H. Tran, and Y. Yu, Min-Max formulas and other properties of certain classes of non-convex effective Hamiltonian. Mathematische Annalen, (2018) 372: 91-123. pdf

  77. W. Lu, Y. Lu and J. Qian, Perfectly-matched-layer boundary integral equation method for wave scattering in a layered medium. SIAM J. Applied Math., Vol. 78 (2018), No. 1, pp. 246-265. pdf

  78. R. Glowinski, S. Leung, and J. Qian, A simple explicit operator-splitting method for effective Hamiltonians. SIAM J. Scientific Computing, Vol. 40 (2018), No. 1, pp. A484-A503. pdf

  79. J. Fang, J. Qian, L. Zepeda-Nunez, and H.-K. Zhao, A hybrid approach to solve the high-frequency Helmholtz equation with source singularity. Journal of Computational Physics, 371 (2018) 261-279. pdf

  80. W. Lu, J. Qian, and R. Burridge, Extending Babich's ansatz for point-source Maxwell's equations using Hadamard's method. Multiscale Modeling and Simulation, 16 (2018), 727-751. pdf

  81. R. Glowinski, H. Liu, S. Leung, and J. Qian, A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two-dimensional Elliptic Monge-Ampere Equation. Journal of Scientific Computing 79:1-47, 2019. pdf

  82. G. Huang, X. Zhang, and J. Qian, Kantorovich-Rubinstein misfit for inverting gravity-gradient data by the level-set method. Geophysics, 84 (5): G55-G73, 2019. pdf

  83. C. Lam and J. Qian, Numerical microlocal analysis by fast Gaussian wavepacket transforms and applications to high-frequency Helmholtz problems. SIAM J. Sci. Comput. 41: A2717-A2746, 2019. pdf

  84. G. Huang and J. Qian, Analysis of Regularized Kantorovich-Rubinstein Metric and Its Application to Inverse Gravity Problems. SIAM J. Imaging Sciences. 12 (2019): 1528-1560. pdf

  85. W. Li, J. Qian, and Y. Li, Joint inversion of surface and borehole magnetic data: a level-set approach. Geophysics, VOL. 85, NO. 1 (2020); P. J15-J32. pdf

  86. H. Liu, R. Glowinski, S. Leung, and J. Qian, A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three-dimensional Elliptic Monge-Ampere Equation. Journal of Scientific Computing, 81 (2019): 2271-2302. pdf

  87. W. Li and J. Qian, Newton-type Gauss-Seidel Lax-Friedrichs high-order fast sweeping methods for generalized eikonal equations at large-scale discretization. Computers and Mathematics with Applications, 79 (2020) 1222-1239. pdf

  88. R. Glowinski, H. Liu, S. Leung, and J. Qian, On the numerical solution of nonlinear eigenvalue problems for the Monge-Ampere operator. ESAIM: COCV 26 (2020) 118. pdf

  89. B. Xu, J. Cheng, S. Leung, and J. Qian, Efficient algorithms for computing multidimensional integral fractional Laplacians via spherical means. SIAM J. Sci. Comput. Vol. 42 (2020), No. 5, pp. A2910--A2942. pdf

  90. W. Li and J. Qian, A level-set algorithm for the inverse problem of full magnetic gradient tensor data. Applied Mathematics Letters 107 (2020) 106416. pdf

  91. W. Ao, W. Li and J. Qian, A data and knowledge driven approach for SPECT using convolutional neural networks and iterative algorithms. J. Inverse Ill-Posed Probl. 29(2021): 543-555. pdf

  92. J. Hu, J. Qian, J. Cao, J. Song and S. Leung, Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media. Geophysics, VOL. 86 (2021), NO. 4; P. T179-T192. pdf

  93. J. Hu, J. Qian, J. Cao, H. Wang and S. Leung, Ray-illumination compensation for adjoint-state first-arrival traveltime tomography. Geophysics, VOL. 86 (2021), NO. 5; P. U109-U119. pdf

  94. S. Leung, J. Qian and J. Hu, A LEVEL-SET ADJOINT-STATE METHOD FOR TRANSMISSION TRAVELTIME TOMOGRAPHY IN IRREGULAR DOMAINS SIAM J. SCI. COMPUT. Vol. 43 (2021), No. 3, pp. A2352-A2380 pdf

  95. K. Ho, S. Leung, and J. Qian, Fast Huygens sweeping methods for a class of nonlocal Schrodinger equations Journal of Scientific Computing (2021) 88:54 pdf

  96. M. Alzuhiri, J. Song, B. Li, D. Kumar, Z. Qiu, J. Qian, and Y. Deng, Enhanced Pulsed Thermoacoustic Imaging by Noncoherent Pulse Compression Journal of Applied Physics, Vol. 130 (2021), 174902. pdf

  97. G. Piao, J. Li, L. Udpa, J. Qian, and Y. Deng, Motion-induced eddy current array method for high-speed rail rolling contact fatigue defects detection. IEEE Transactions on Magnetics, Vol. 57 (2021), No. 12, 6201010. pdf

  98. W. Li and J. Qian, SIMULTANEOUSLY RECOVERING BOTH DOMAIN AND VARYING DENSITY IN INVERSE GRAVIMETRY BY EFFICIENT LEVEL-SET METHODS Inverse Problems and Imaging, Volume 15 (2021), No. 3, 387-413 pdf

  99. J. Qian, J. Song, W. Lu and R. Burridge, HADAMARD--BABICH ANSATZ FOR POINT-SOURCE ELASTIC WAVE EQUATIONS IN VARIABLE MEDIA AT HIGH FREQUENCIES MULTISCALE MODEL. SIMUL. Vol. 19 (2021), No. 1, pp. 46-86 pdf

  100. J. Qian and C. Song, FAST MULTISCALE GAUSSIAN BEAM METHOD FOR THREE-DIMENSIONAL ELASTIC WAVE EQUATIONS IN BOUNDED DOMAINS SIAM J. NUMER. ANAL., Vol. 59 (2021), No. 5, pp. 2536-2570. pdf

  101. H. Wang, J. Yang, Y. Zhang, J. Qian*, and J. Wang*, Reconstruct high-resolution 3D genome structures for diverse cell-types using FLAMINGO. Nature Communications, (2022) 13:2645. pdf

  102. T. Yeung, K. Cheung, E. Chung, S. Fu, and J. Qian, Learning rays via deep neural network in a ray-based IPDG method for high-frequency Helmholtz equations in inhomogeneous media. Journal of Computational Physics, 465(2022) 111380. pdf

  103. S. Leung, J. Hu and J. Qian, Liouville partial-differential-equation methods for computing 2D complex multivalued eikonals in attenuating media. Geophysics, VOL. 87 (2022), NO. 2; P. T71-T84. pdf

  104. W. Li and J. Qian, KANTOROVICH-RUBINSTEIN METRIC BASED LEVEL-SET METHODS FOR INVERTING MODULUS OF GRAVITY-FORCE DATA. Inverse Problems and Imaging, Vol. 16 (2022), No. 6; pp. 1643-1667. pdf

  105. H. Liu, S. Leung, and J. Qian, An efficient operator-splitting method for the eigenvalue problem of the Monge-Ampere equation. Communications in Optimization Theory, to appear. pdf

  106. J. Qian, J. Song, W. Lu, and R. Burridge, Truncated Hadamard-Babich ansatz and fast Huygens sweeping methods for time-harmonic high-frequency elastic wave equations in inhomogeneous media. Minimax Theory and Applications, to appear. pdf

  107. Y. Liu, J. Song, R. Burridge and J. Qian, A Fast Butterfly-compressed Hadamard-Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources. Multiscale Modeling and Simulation, Vol. 21 (2023), No. 1, 269-308. pdf

  108. G. Huang, J. Qian, and Y. Yang, Piecewise Acoustic Source Imaging with Unknown Speed of Sound Using a Level-Set Method. Communications on Applied Mathematics and Computation, to appear, 2023. pdf

  109. Y. Wei, J. Cheng, R. Burridge, and J. Qian, Hadamard integrator for time-dependent wave equations: Lagrangian formulation via ray tracing. Journal of Computational Physics, to appear, 2023. pdf

  110. H. Liu, S. Leung, and J. Qian, Operator Splitting/Finite Element Methods for the Minkowski Problem. Submitted, 2023. pdf

    Last updated: November 16, 2023.