# Publications

## Preprints

75. A Local Macroscopic Conservative (LoMaC) low rank tensor method with the discontinuous Galerkin method for the Vlasov dynamics, W. Guo, J. Ema, J.-M. Qiu, arXiv

74. Fourth-order conservative non-splitting semi-Lagrangian Hermite WENO schemes for kinetic and fluid simulations, N. Zheng, X. Cai, J.-M. Qiu, J. Qiu, submitted. arXiv

73. A mass conservative Eulerian-Lagrangian Runge-Kutta discontinuous Galerkin method for wave equations with large time stepping, X. Hong and J.-M. Qiu, submitted. arXiv

72. A Local Macroscopic Conservative (LoMaC) low rank tensor method for the Vlasov dynamics, W. Guo and J.-M. Qiu, submitted. arXiv

71. SIAM Book review: Numerical Methods for Conservation Laws From Analysis to Algorithms, by Jan S. Hesthaven. SIAM Computational science and engineering, paperback, 2018. ISBN: 978-1-611975-09-3.

70. An Eulerian-Lagrangian Runge-Kutta finite volume (EL-RK-FV) method for solving convection and convection-diffusion equations, J. Nakao, J. Chen, J.-M. Qiu, submitted. arXiv

69. A fourth-order conservative semi-Lagrangian finite volume WENO scheme without operator splitting for kinetic and fluid simulations, Computer Methods in Applied Mechanics and Engineering, N. Zheng, X. Cai, J.-M. Qiu, J. Qiu, acceptted.

68. A conservative low rank tensor method for the Vlasov dynamics, SIAM Journal of Scientific Computing, W. Guo and J.-M. Qiu, submitted. arXiv

67. Eulerian-Lagrangian Runge-Kutta discontinuous Galerkin method for transport simulations on unstructured meshes, SIAM Journal of Scientific Computing, X. Cai and J.-M. Qiu, accepted. arXiv

66. High Order Semi-implicit WENO Schemes for All Mach Full Euler System of Gas Dynamics, SIAM Journal of Scientific Computing, B. Sebastiano, J.-M. Qiu, G. Russo, T. Xiong, SIAM Journal on Scientific computing, 2022. link

65. Semi-Lagrangian nodal discontinuous Galerkin method for the BGK Model, M. Ding and J.-M. Qiu, preprint.

64. A Generalized Eulerian-Lagrangian Discontinuous Galerkin Method for Transport Problems, Journal of Computational Physics, X. Hong and J.-M. Qiu, Journal of Computational Physics, 2022. link

63. A Low Rank Tensor Representation of Linear Transport and Nonlinear Vlasov Solutions and Their Associated Flow Maps, W. Guo and J.-M. Qiu, Journal of Computational Physics, accepted. link

62. Accuracy and stability analysis of the Semi-Lagrangian method for stiff hyperbolic relaxation systems and kinetic BGK model, M. Ding, J.-M. Qiu and R.-W. Shu, SIAM Multiscale Modeling and Simulation, accepted. arXiv

## Publications in Refereed Journals

61. A High Order Semi-Lagrangian Finite Difference Method for nonlinear Vlasov and BGK Models, L. Li, J.-M. Qiu and G. Russo, Communications on Applied Mathematics and Computation, (2022), Pages 1-29.

60. A conservative semi-Lagrangian hybrid Hermite WENO scheme for linear transport equations and the nonlinear Vlasov-Poisson system, N. Zheng, X. Cai, J.-M. Qiu, J. Qiu, SIAM Journal of Scientific Computing, v43 (2021), Pages 3580-3606.

59. An Eulerian-Lagrangian discontinuous Galerkin method for transport problems and its application to nonlinear dynamics , X. Cai, J.-M. Qiu, and Yang Yang, Journal of Computational Physics, 2021. link

58. High Order Semi-Lagrangian Discontinuous Galerkin Method Coupled with Runge-Kutta Exponential Integrators for Nonlinear Vlasov Dynamics, X. Cai, S. Boscarino, and J.-M. Qiu, Journal of Computational Physics, v427 (2021), Pages 110036.

57. Stability-enhanced AP IMEX1-LDG method: energy-based stability and rigorous AP property, Z. Peng, Y. Cheng, J.-M. Qiu, and F. Li, SIAM Journal on Numerical Analysis, v59 (2021), Pages 925-954.

56. Adaptive Order WENO Reconstructions for the Semi-Lagrangian Finite Difference Scheme for advection problem, J. Chen, X. Cai, J. Qiu, J.-M. Qiu, Communications in Computational Physics, v30(2021), Pages 67-96.

55. Comparison of semi-Lagrangian discontinuous Galerkin schemes for linear and nonlinear transport simulations, X. Cai, W. Guo and J.-M. Qiu, Communications on Applied Mathematics and Computation, 2020, Pages 1-31.

54. A three-phase fundamental diagram from three-dimensional traffic data, Maria Laura Delle Monachea, Karen Chi, Yong Chen, Paola Goatinc, Ke Han, Jing-Mei Qiu, Benedetto Piccoli, Axioms, v10 (2021), Pages 17.

53. A semi-Lagrangian discontinuous Galerkin (DG) - local DG method for solving convection-diffusion-reaction equations, M. Ding$^s$, X. Cai$^p$, W. Guo and J.-M. Qiu, Journal of Computational Physics, v409(2020), Pages 109-295.

52. Stability-enhanced AP IMEX-LDG schemes for linear kinetic transport equations under a diffusive scaling, Z. Peng, Y. Cheng, J.-M. Qiu, and F. Li, Journal of Computational Physics, v415 (2020), Pages 109-485.

51. Optimal convergence and superconvergence of semi-Lagrangian discontinuous Galerkin methods for linear convection equations in one space dimension, Y. Yang, X. Cai, and J.-M. Qiu, Mathematics of Computation, v89 (2020), Pages 2113-2139.

50. A High Order Semi-implicit IMEX WENO Scheme for the all-Mach Isentropic Euler System, B. Sebastiano, J.-M. Qiu, G. Russo, T. Xiong, Journal of Computational Physics, v392 (2019), Pages 594-618.

49. A high order semi-Lagrangian discontinuous Galerkin method for the two-dimensional incompressible Euler equations and the guiding center Vlasov model without operator splitting, X. Cai$^p$, W. Guo and J.-M. Qiu, Journal of Scientific Computing, v79(2019), Pages 1111-1134.

48. Conservative Multi-Dimensional Semi-Lagrangian Finite Difference Scheme: Stability and Applications to the Kinetic and Fluid Simulations, T. Xiong, G. Russo and J.-M. Qiu, Journal of Scientific Computing, v79 (2019), Pages 1241 - 1270.

47. A high order semi-Lagrangian discontinuous Galerkin method for Vlasov-Poisson simulations without operator splitting, X. Cai$^p$, W. Guo and J.-M. Qiu, Journal of Computational Physics, v354 (2018), Pages 529-551.

46. High Order Multi-dimensional Characteristics Tracing for the Incompressible Euler Equation and the Guiding-center Vlasov Equation, T. Xiong, G. Russo and J.-M. Qiu, Journal of Scientific Computing, v77 (2018), pp 263-282.

45. Implicit-Explicit Integral Deferred Correction Methods for Stiff Problems and Applications to Partial Differential Equations, B. Sebastiano, J.-M. Qiu and G. Russo, SIAM Journal of Scientific Computing, v40 (2018), Pages A787-A816.

44. Finite volume HWENO schemes for nonconvex conservation laws, X. Cai$^p$, J. Qiu and J.-M. Qiu, Journal of Scientific Computing, v75 (2018), Pages 65-82.

43. A high order conservative semi-Lagrangian discontinuous Galerkin method for two-dimensional transport simulations, X. Cai$^p$, W. Guo and J.-M. Qiu, Journal of Scientific Computing, v73 (2017), Pages 514-542.

42. An h-adaptive RKDG method for the two-dimensional incompressible Euler equations and the guiding center Vlasov model, H. Zhu, J. Qiu and J.-M. Qiu, Journal of Scientific Computing, v73 (2017), Pages 1316-1337.

41. High Order Hierarchical Asymptotic Preserving Nodal Discontinuous Galerkin IMEX Schemes For The BGK Equation, T. Xiong$^p$ and J.-M. Qiu, Journal of Computational Physics, v336 (2017), Pages 164-191.

40. A High Order Multi-Dimensional Characteristic Tracing Strategy for the Vlasov-Poisson System, J.-M. Qiu and G. Russo, Journal of Scientific Computing, v71 (2017), Pages 414-434.

39. An h-adaptive RKDG method for the Vlasov-Poisson system, H. Zhu, J. Qiu and J.-M. Qiu, Journal of Scientific Computing, v69 (2016), Pages 1346-1365.

38. High Order Mass Conservative Semi-Lagrangian Methods for Transport Problems, J.-M. Qiu, Handbook of Numerical Methods for Hyperbolic Problems: Part A, Chapter 16.

37. Numerical methods for hyperbolic nets and networks, S. Canic, M.L. Delle Monache, B. Piccoli, J.-M. Qiu and J. Tambaca, Handbook of Numerical Methods for Hyperbolic Problems.

36. An Adaptive WENO Collocation Method for Differential Equations with Random Coefficients, W. Guo$^s$, G. Lin, A. Christlieb and J.-M. Qiu, MDPI, Special Issue “New Trends in Applications of Orthogonal Polynomials and Special Functions”, v4(2016), Pages 29.

35. A conservative semi-Lagrangian HWENO method for the Vlasov equation, X. Cai$^s$, J. Qiu and J.-M. Qiu, Journal of Computational Physics, v323 (2016), Pages 95-114.

34. Notes on RKDG methods for shallow-water equations in canal networks, M. Briani, B. Piccoli, J.-M. Qiu, Journal of Scientific Computing, v68(2016), Pages 1101-1123.

33. Parametrized Positivity Preserving Flux Limiters for the High Order Finite Difference WENO Scheme Solving Compressible Euler Equations, T. Xiong$^p$, J.-M. Qiu, Z. Xu, Journal of Scientific Computing, v67(2016), Pages 1066-1088.

32. Error Estimate of Integral Deferred Correction Implicit Runge-Kutta method for Stiff Problems, S. Boscarino and J.-M. Qiu, Mathematical Modelling and Numerical Analysis, v50(2016), Pages 1137-1166.

31. High Order Maximum Principle Preserving Finite Volume Method for Convection Dominated Problems, P. Yang$^s$, T. Xiong$^p$, J.-M. Qiu and Z. Xu, Journal of Scientific Computing, v67(2016), Pages 795-820.

30. High Order Asymptotic Preserving Nodal Discontinuous Galerkin IMEX Schemes for the BGK Equation, T. Xiong$^p$, J. Jang, F. Li and J.-M. Qiu, Journal of Computational Physics, v284 (2015), Pages 70-94.

29. High Order Maximum Principle Preserving Discontinuous Galerkin Method for Convection Diffusion Equations, T. Xiong$^p$, J.-M. Qiu and Z. Xu, SIAM Journal of Scientific Computing, v37 (2015), Pages 583-608.

28. A New Lax-Wendroff Discontinuous Galerkin Method with Superconvergence, W. Guo$^s$, J.-M. Qiu and J.-X. Qiu, Journal of Scientific Computing, v65 (2015), Pages 299-326.

27. Runge-Kutta Discontinuous Galerkin Method for Traffic Flow Model on Networks, S. Canic, B. Piccoli, J.-M. Qiu and T. Ren$^s$, Journal of Scientific Computing, v63 (2015), Pages 233-255.

26. High Order Asymptotic Preserving Discontinuous Galerkin Schemes for Discrete-Velocity Kinetic Equations in the Diffusive Scaling, J. Jang, F. Li, J.-M. Qiu, T. Xiong$^p$, Journal of Computational Physics, v281 (2015), Pages 199-224.

25. Runge-Kutta Central Discontinuous Galerkin BGK Method for the Navier-Stokes Equations, T. Ren$^s$, J. Hu, T.Xiong$^p$ and J.-M. Qiu, Journal of Computational Physics, v274 (2014), Pages 592-610.

24. High Order Maximum Principle Preserving Semi-Lagrangian Finite Difference WENO schemes for the Vlasov Equation, T. Xiong, J.-M. Qiu, Z. Xu, A. Christlieb, Journal of Computational Physics, v273 (2014), Pages 618-639.

23. Analysis of High Order Asymptotic Preserving Discontinuous Galerkin Schemes for Discrete-Velocity Kinetic Equations in the Diffusive Scaling, J. Jang, F. Li, J.-M. Qiu, T. Xiong$^p$, SIAM Journal of Numerical Analysis, v52 (2014), Pages 2048-2072.

22. A High Order Time Splitting Method Based on Integral Deferred Correction for Semi-Lagrangian Vlasov Simulations, A. Christlieb, W. Guo$^s$, M. Morton, J.-M. Qiu, Journal of Computational Physics, v267 (2014), Pages 7-27.

21. A Conservative Semi-Lagrangian Discontinuous Galerkin Scheme on the Cubed-Sphere, W. Guo$^s$, R. Nair and J.-M. Qiu, Monthly Weather Review, v142 (2014), Pages 457-475.

20. A Parametrized Maximum Principle Preserving Flux Limiter for Finite Difference RK-WENO Schemes with Applications in Incompressible Flows, T. Xiong$^p$, J.-M. Qiu and Z. Xu, Journal of Computational Physics, v252(2013), Pages 310-331.

19. Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Methods: Eigen-structure Analysis Based on Fourier Approach, W. Guo$^s$, X.-H. Zhong and J.-M. Qiu, Journal of Computational Physics, v235 (2013), Pages 458-485.

18. Hybrid Semi-Lagrangian Finite Element Finite Difference Methods for the Vlasov Equation, W. Guo$^s$ and J.-M. Qiu, Journal of Computational Physics, v234 (2013), Pages 108-132.

17. Positivity Preserving Semi-Lagrangian Discontinuous Galerkin Formulation: Theoretical Analysis and Application to the Vlasov-Poisson System, J.-M. Qiu and C.-W. Shu, Journal of Computational Physics, v230 (2011), Pages 8386-8409.

16. Adaptive Mesh Refinement Based on High Order Finite Difference WENO Scheme for Multi-scale Simulations, C.-P. Shen, J.-M. Qiu and A. Christlieb, Journal of Computational Physics, v230 (2011), Pages 3780-3802.

15. Conservative Semi-Lagrangian Finite Difference WENO Formulations with Applications to the Vlasov Equation, J.-M. Qiu and C.-W. Shu, Communications in Computational Physics, v10 (2011), Pages 979-1000.

14. Conservative High Order Semi-Lagrangian Finite Difference WENO Methods for Advection in Incompressible Flow, J.-M. Qiu and C .-W. Shu, Journal of Computational Physics, v230 (2011), Pages 863-889.

13. Semi-implicit Integral Deferred Correction Constructed with High Order Additive Runge-Kutta Methods, A. Christlieb, M. Morton, B. Ong and J.-M. Qiu, Communications in Mathematical Sciences, v9 (2011), Pages 879-902.

12. Integral Deferred Correction Methods Constructed with High Order Runge-Kutta Integrators, A. Christlieb, B. Ong and J.-M. Qiu, Mathematics of Computation, v79 (2010), Pages 761-783.

11. A Conservative High Order Semi-Lagrangian WENO Method for the Vlasov Equation, J.-M. Qiu and A. Christlieb, Journal of Computational Physics, v229 (2010), Pages 1130-1149.

10. Comments on High Order Integrators Embedded within Integral Deferred Correction Methods, A. Christlieb, B. Ong and J.-M. Qiu, Communications in Applied Mathematics and Computational Science, v4 (2009), Pages 27-56.

9. Time Evolution of Wouthuysen-Field Coupling, I. Roy, W. Xu, J.-M. Qiu, C.-W. Shu and L.-Z. Fang, The Astrophysical Journal, v694 (2009), Pages 1121-1130.

8. A WENO Algorithm for Radiative Transfer with Resonant Scattering and the Wouthuysen-Field Coupling, I. Roy, J.-M. Qiu, C.-W. Shu and L.-Z. Fang, New Astronomy, v14 (2009), Pages 513-520.

7. Wouthuysen-Field Coupling in 21 cm Region Around High Redshift Sources, I. Roy, W. Xu, J.-M. Qiu, C.-W. Shu and L.-Z. Fang, The Astrophyiscal Journal, v 703 (2009), Pages 1992-2003.

6. Convergence of Godunov-type Schemes for Scalar Conservation Laws under Large Time Steps, J.-M. Qiu and C.-W. Shu, SIAM Journal on Numerical Analysis, v46 (2008), Pages 2211-2237.

5. A WENO Algorithm for the Growth of Ionized Regions at the Reionization Epoch, J.-M. Qiu, C.-W. Shu, J. -R. Liu and L.-Z. Fang, New Astronomy, v13 (2008), Pages 1-11.

4. Convergence of High Order Finite Volume Weighted Essentially Non-oscillatory Scheme and Discontinuous Galerkin Method for Nonconvex Conservation Laws, J.-M. Qiu and C .-W. Shu, SIAM Journal on Scientific Computing, v31 (2008), Pages 584-607.

3. A WENO Algorithm of the Temperature and Ionization Profiles Around a Point Source, J.-M. Qiu, L.-L. Feng, C.-W. Shu and L.-Z. Fang, New Astronomy, v12 (2007), Pages 398-409.

2. 21 cm Signals From Early Ionizing Sources, J. Liu, J.-M. Qiu, L.-L. Feng, C.-W. Shu, L.-Z. Fang, The Astrophysical Journal, v663 (2007), Pages 1-9.

1. A WENO Algorithm for the Radiative Transfer and Ionized Sphere at Reionization, J.-M. Qiu, C.-W. Shu, L.-L. Feng and L.-Z. Fang, New Astronomy, v12 (2006), Pages 1-10.