# Publications

- J. Qian and W. W. Symes, Paraxial eikonal solvers for anisotropic Quasi-P traveltimes.
*J. Comput. Phys.*173(2001), 256-278. pdf - 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 - J. Qian and W. W. Symes, An adaptive finite-difference method for traveltimes and amplitudes.
*Geophysics*67(2002), 167-176. pdf - J. Qian and W. W. Symes, Finite-difference Quasi-P traveltimes for anisotropic media.
*Geophysics*67(2002), 147-155. pdf - J. Qian and W. W. Symes, Paraxial geometrical optics for quasi-P waves: theories and numerical methods.
*Wave Motion*35(2002), 205-221. pdf - 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
- 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 - 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 - 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 - 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 - 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 . - 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 - 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 - Y. T. Zhang, H. K. Zhao and J. Qian, Higher order fast sweeping methods for eikonal equations.
*SEG 2004, PP. 1901-1904.*pdf - 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 - 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 - S. Y. Leung and J. Qian, A Transmission Tomography Problem Based on Multiple Arrivals from Paraxial Liouville Equations.
*SEG 2005, PP 2589-2592.* - J. Qian, Approximations for viscosity solutions of Hamilton-Jacobi equations with locally varying time and space grids.
*SIAM Numer. Anal.*43(2006), 2371-2401. - J. Qian and S. Y. Leung, A local level set method for paraxial geometrical optics.
*SIAM J. Sci. Comput.*28(2006), 206--223. - 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 - 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 - S. Serna and J. Qian, Fifth Order Weighted Power-ENO Schemes for Hamilton-Jacobi Equations.
*J. Sci. Comput.*29(2006), 57-81. pdf - 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 - 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 - 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. - 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 - 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 - 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. - S. Leung and J. Qian, Transmission traveltime tomography based on paraxial Liouville equations and level set formulations.
*Inverse Problems*23(2007), 799-821. - N. M. Tanushev, J. Qian, and J. Ralston, Mountain waves and Gaussian beams.
*SIAM J. Multiscale Modeling and Simulation*6(2007), 688-709. pdf - S. Leung, J. Qian and R. Burridge, Eulerian Gaussian beams for high frequency wave propagation.
*Geophysics*72(2007), SM61-SM76. pdf - 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 - T. C. Cecil, S. J. Osher and J. Qian, Essentially Non-Oscillatory Adaptive Tree Methods.
*J. Scientific Computing 35(2008), 25-41.*pdf - 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 - S. Leung and J. Qian, Eulerian Gaussian beams for Schrodinger equations in the semi-classical regime.
*J. Computational Physics 228(2009) 2951-2977.*pdf - 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 - 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 - J. Qian and L. Ying, Fast Gaussian wavepacket transforms and Gaussian beams for the Schrodinger equation.
*J. Computational Physics 229 (2010) 7848-7873.*pdf - 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 - 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 - 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 - 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 - 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 - 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 - 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 - S. Luo, J. Qian, and H.-K. Zhao, High-order schemes for 3-D traveltimes and amplitudes.
*Geophysics 77(2012): T47-T56.*pdf - 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 - 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 - 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 - 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 - J. Qian, C. Yang, A. Schirotzek, F. Maia, and S. Marchesini, Efficient Algorithms for Ptychographic Phase Retrieval.
*Contemporary Mathematics 615(2014): 261-280.*pdf - 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 - 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 - 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 - 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 - 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 - 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 - 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 - W. Lu and J. Qian, A Local Level Set Method for Three-dimensional Inversion of Gravity Gradient Data.
*Geophysics 80 (2015): G35-G51.*pdf - 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 - 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 - 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 - 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 - 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 - W. Li, W. Lu, and J. Qian, A level set method for imaging salt structure using gravity data.
*Geophysics, to appear.*pdf - X. Wang, J. Qian, and H. Wang, Efficient angle-domain common-imaging gathers using Cauchy condition based polarization vectors.
*Geophysics, to appear.*pdf - 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 - 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 - W. Li and J. Qian, Joint inversion of gravity and traveltime data using structural parameterization.
*Submitted.*pdf - W. Li, W. Lu, and J. Qian, A multiple level set method for three-dimensional inversion of magnetic data.
*Submitted.*pdf