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Publications & Preprints





  1.  S. Fomel, S. Luo and H. Zhao,  Fast sweeping method for the factored eikonal equation, J. Comput. Phys., Vol. 228, No. 17 (2009) 6440-6455. pdf
  2. J. D. Benamou, S. Luo and H. Zhao, A compact upwind second order scheme for the Eikonal equation, J. Comput. Math., Vol. 28, No.4, 2010, 489-516. pdf
  3. S. Luo, L. J. Guibas and H. Zhao, Euclidean Skeletons Using Closest Points, Inverse problem and Imaging, Vol. 5  Issue 1, 95-113 (2011). pdf
  4. S. Luo, Y. Yu and H. Zhao, A new approximation for effective Hamiltonians for homogenizations of a class of Hamilton-Jacobi equations,  Multiscale Model. Simul., Vol. 9 Issue 2, 711-734 (2011).pdf
  5. S. Luo, S. Leung and J. Qian, An Adjoint State Method for Numerical Approximation of Continuous Traffic Congestion Equilibria, Commun. Comput. Phys., 10, 1113-1131. (2011). pdf
  6. S. Luo and J. Qian, Factored singularities and high-order Lax-Friedrichs sweeping schemes for point-source traveltimes and amplitudes, J. Comput. Phys.. 230 (2011) 4742-4755. pdf
  7.  S. Luo, J. Qian and H. Zhao, Higher-order schemes for 3-D first arrival traveltimes and amplitudes, Geophysics, 77(2):T47-T56, 2012. pdf
  8.  S. Luo and J. Qian, Fast sweeping method for anisotropic eikonal equations: additive and multiplicative factors, J. Sci. Comput., Volume 52, Issue 2, pp 360-382, 2012. pdf
  9. S. Luo, A uniformly second order fast sweeping method for eikonal equations, J. Comput. Phys., Vol. 241 (2013) pp 104-117. pdf 
  10. G. Bao, G. Hu, D. Liu and S. Luo, MultiPhysical Modeling and Multiscale Computation of Nano Optical Responses, Contemporary Mathematics, vol. 586, Amer. Math. Soc., Providence, RI, 2013, pp. 43-55. pdf
  11. G. Bao, D. Liu and S. Luo, A Multiscale Method for Optical Responses of NanoStructures, SIAM J. Appl. Math., 73(2), 741-756, 2013. pdf
  12. S. Luo, J. Qian and R. Burridge, High-order Factorizations and High-order Schemes for Point-source Eiknoal equations, SIAM J. Numer. Anal., 52-1 (2014), pp. 23-44. pdf
  13. 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 attenuated X-ray transform, SIAM J. Imaging Sci., 7(2) (2014), 696-715.  pdf
  14. S. Luo, J. Qian and R. Burridge, Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime, Journal of Computational Physics, Volume 270 (2014), pp. 378-401. pdf
  15. T. Aslam, S. Luo and H. Zhao, A static PDE approach to multi-dimensional extrapolations using fast sweeping methods, SIAM J. Sci. Comput., 36(6), A2907-A2928, 2014. pdf
  16.  Qian, S. Luo and R. Burridge, Fast Huygens sweeping methods for multi-arrival Green's functions of Helmholtz equations in the high frequency regime, Geophysics, 80(2), T91-T100, 2015. pdf
  17. Qian, L. Yuan, Y. Liu, S. Luo and R. Burridge, Babich's Expansion and High-Order Eulerian Asymptotics for Point-Source Helmholtz Equations, J. Sci. Comput., Volume 67, Issue 3, pp 883-908, 2016. pdf
  18. S. Luo, H. Tran and Y. Yu, Some inverse problems in periodic homogenization of Hamilton-Jacobi equations, Archive for Rational Mechanics and Analysis, Volume 221, Issue 3, pp 1585-1617 (first online 1-33, March 2016).  pdf
  19. 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 Multiscale Model. Simul., 14(2), 595-636, 2016. pdf
  20. G. Bao, D. Liu, and S. Luo, Multiscale Modeling and Computation of Optically Manipulated Nano Devices,  J. Comput. Phys., Volume 316, 1, 558-572, 2016. pdf
  21.  S. Luo and H. Zhao, Convergence Analysis of Fast Sweeping Method for Static Convex Hamilton-Jacobi equations, Research in the Mathematical Sciences, Volume 3, 35-62, 2016. pdf
  22. S. Luo and N. Payne, Properties-preserving high order numerical methods for a kinetic eikonal equation, Journal of Computational Physics, Volume 331, 73-89, 2017. pdf
  23. S. Luo and N. Payne, An asymptotic method based on a Hopf-Cole transformation for a kinetic BGK equation in the hyperbolic limit, Journal of Computational Physics, Volume 341, 295-312, 2017.  pdf
  24. G. Huang, Q. Hu, S. Luo, H. Li, H. Zhang, D. C. Nobes, 2-D fast sweeping method for the factored Eikonal equation and its improvement on inversion accuracy, Journal of Applied Geophysics, Volume 166, Pages 68-76, 2019. link
  25. S. Luo, Fast Huygens Sweeping Methods for Time-Dependent Schrödinger Equation with Perfectly Matched Layers, SIAM Journal on Scientific Computing, Volume 41, Number 22,  A877-A899, 2019. link
  26. G. Huang and S. Luo and T. Ari and H. Li and D. C. Nobes, First-arrival tomography with fast sweeping method solving the factored eikonal equation, Exploration Geophysics, Volume 50, Number 2,  144-158, 2019. pdf
  27.  M. Jacobs and S. Luo, Asymptotic Solutions for High Frequency Helmholtz Equations in Anisotropic Media with Hankel Functions, Journal of Scientific Computing, Volume 80, Number 2,  808-833, 2019.  link
  28. G. Huang, S. Luo, J. Deng and V. Vavrycuk, Traveltime Calculations for qP, qSV, and qSH Waves in Two‐Dimensional Tilted Transversely Isotropic Media, Journal of Geophysical Research: Solid Earth, 125, e2019JB018868. 2020. link
  29. Huang, G., Luo, S. Hybrid Fast Sweeping Methods for Anisotropic Eikonal Equation in Two-Dimensional Tilted Transversely Isotropic Media. J. Sci .Comput., 84, 32 (2020). link
  30. G. Bao, R. Delgadillo, G. Hu, D. Liu, and S. Luo, Modeling and Computation of Nano Optics, The CSIAM Transactions on Applied Mathematics, 1 (2020), pp.
  31. N. Cui, G. Huang, S. Luo, H. Li and H. Zhang, A hybrid fast sweeping method for the isotropic eikonal equation, Exploration Geophysics, 2021, online first Link
  32. Gao, Y., Mayfield, J. & Luo, S. A Second-Order Fast Huygens Sweeping Method for Time-Dependent Schrödinger Equations with Perfectly Matched Layers. J. Sci. Comput., 88, 49 (2021). Link
  33. M. Jacobs and S. Luo, Numerical solutions for point-source high frequency Helmholtz equation through efficient time propagators for Schrodinger equation, Journal of Computational Physics, Volume 438, 2021, 110357,  Link.
  34. Jay Mayfield, Yijin Gao, and Songting Luo, An asymptotic Green's function method for the wave equation, Journal of Computational Physics, 2021, Link.
  35. Yijin Gao, Jay Mayfield, Gang Bao, Di Liu, and Songting Luo, An asymptotic Green's function method for time-dependent Schrödinger equations with application to Kohn-Sham equations, Journal of Computational Physics, Volume 463, 2022, 111272, Link
  36. Songting Luo and Qing Huo Liu, A Fixed-Point Iteration Method for High Frequency Helmholtz Equations. J. Sci. Comput., 93, 74 (2022). Link
  37. Yijin Gao, Jay Mayfield, and Songting Luo, Numerical solutions of the time-dependent Schrödinger equation with position-dependent effective mass, Numer. Methods Partial Differ. Eq.. (2023), 1– 24.