1. 张林波,迟学斌,莫则尧,李若 编著,《并行计算导论》,清华大学出版社, 2006。
    An Introduction to Parallel Computing, edited by Lin-Bo Zhang, Xue-Bin Chi, Ze-Yao Mo and Ruo Li, Tsinghua University Press, 2006.

Journal and Proceeding Papers:


  1. Z.-C. Hu, R. Li and Z.-H. Qiao, Acceleration for Microflow Simulations of High-Order Moment Models by Using Lower-Order Model Correction, accepted by Journal of Computational Physics.

  2. Published:

  3. R. Li, T. Lu and Z.-P. Sun, Parity-decomposition and moment analysis for stationary Wigner equation with inflow boundary conditions, Frontier of Mathematics in China, 12(4), pp. 907-919, 2017 DOI 10.1007/s11464-017-0612-9.

  4. Y.-N. Di, Y.-W. Fan, R. Li and L.-C. Zheng, Linear stability of hypebolic moment models for Boltzmann equation, Numerical Mathematics: Theory, Method and Application, Vol. 10, No. 2, pp. 255-277, May 2017
    doi: 10.4208/nmtma.2017.s04

  5. Y.-N. Di, Y.-W. Fan and R. Li, 13-Moment System with Global Hyperbolicity for Quantum Gas, Journal of Statistical Physics, First Online: 31 March 2017
    DOI: 10.1007/s10955-017-1768-0

  6. 2017

  7. 蔡振宁,樊玉伟,胡志成,李若,王何宇, 矩方法在动理学 中的发展与应用, 《中国科学:信息科学》, 46(10), 页码:1465-1488, 2016
    Z.-N. Cai, Y.-W. Fan, Z.-C. Hu, R. Li and H.-Y. Wang, The development and application of the moment method in the gas kinetic theory(in Chinese), accepted by SCIENTIA SINICA Informationis, 46(10), pp. 1465-1488, 2016
    DOI: 10.1360/N112016-00098

  8. 蔡振宁,樊玉伟,李若, 从离散速度模型到矩方法 ,《计算数学》2016年第3期,页码:227-244
    Z.-N. Cai, Y.-W. Fan and R. Li, From discrete velocity model to moment method, Journal of Computational Mathematics (in Chinese), 2016(3), pp. 227-244.

  9. Z.-C. Hu, R. Li and Z.-H. Qiao, Extended Hydrodynamic Models and Multigrid Solver of a Silicon Diode Simulation, Communications in Computational Physics, 20(3), pp. 551-582, September, 2016. DOI: 10.4208/cicp.290615.020316a

  10. Y.-C. Jiang, R. Li and S.-N. Wu, A Second Order Time Homogenized Model for Sediment Transport, SIAM Multiscale Modelling and Simulation, 14(3), pp. 965-996, July, 2016, DOI: 10.1137/15M1041778

  11. G. Alldredge, R. Li and W.-M. Li, Approximating the $M_2$ Method by the Extended Quadrature Method of Moments for Radiative Transfer in Slab Geometry, Kinetic and Related Models, 9(2), pp. 237-249, June, 2016. DOI: 10.3934/krm.2016.9.237

  12. L. Chen and R. Li, An Integrated Linear Reconstruction for Finite Volume Scheme on Unstructured Grids, Journal of Scientific Computing, pp. 1-26, 2016. DOI: 10.1007/s10195-016-0173-1. First online: 11 February, 2016.

  13. Y.-H. Guo, R. Li and C.-B. Yao, A Numerical Method on Eulerian Grids for Two-phase Compressible Flow, Advances in Applied Mathematics and Mechanics, 8(2), pp. 187-212, 2016. DOI: 10.4208/aamm.2014.m706, Published online: 27 January 2016.

  14. Y.-W. Fan, J. Koellermeier, J. Li, R. Li and M. Torrilhon, Model Reduction of Kinetic Equations by Operator Projection, Journal of Statistical Physics, 162(2), pp 457-486, 2016. First online: 29 October, 2015. DOI: 10.1007/s10955-015-1384-9

  15. 2016

  16. 樊玉伟, 李若, 基于广义Hermite展开的全局双曲矩方程组, 《中国科学:数学》45卷, 页码:1635-1676, doi: 10.1360/012015-23.
    Y.-W. Fan and R. Li, Globally hyperbolic moment system by generalized Hermite expansion, (in Chinese). Sci Sin Math, 2015, 45: 1635-1676,

  17. Z.-N. Cai, Y.-W. Fan and R. Li, A Framework on Moment Model Reduction for Kinetic Equation, SIAM Journal on Applied Mathematics, 75(5), pp 2001-2023, 2015 http://epubs.siam.org/toc/smjmap/75/5, DOI: 10.1137/14100110X

  18. Y.-N. Di, Z.-Z. Kou and R. Li, High Order Moment Closure for Vlasov-Maxwell Equations, Front. Math. China, 10(5), 2015, pp. 1087-1100. DOI: 10.1007/s11464-015-0463-1

  19. 2015

  20. 杨青, 李若, 蔡振宁, 六自由度外弹道方程组的快速数值方法, 《高校计算数学学报》,第36卷第3期,2014,页码:253-270.

  21. Z.-C. Hu and R. Li, A Nonlinear Multigrid Steady-State Solver for 1D Microflow, Computer and Fluids, 103, 2014, pp. 193-203.

  22. Z.-N. Cai, Y.-W. Fan and R. Li, On Hyperbolicity of 13-Moment System, Kinetic and Related Models, 7(3), 2014, pp. 415-432.

  23. R. Li, T. Lu and Z.-P. Sun, Stationary Wigner Equation with Inflow Boundary Conditions: Will a Symmetric Potential Yield a Symmetric Solution?, SIAM Journal on Applied Mathematics, 74(3), 2014, pp.885-897, DOI: 10.1137/130941754, http://epubs.siam.org/toc/smjmap/74/3

  24. R. Li, T. Lu and W.-Q. Yao, Discrete Kernel Preserving Model for 1D Electron-Optical Phonon Scattering, Journal of Scientific Computing, February 2015, 62(2), pp 317-335 DOI: 10.1007/s10915-014-9858-5

  25. Z.-N. Cai and R. Li, The NRxx Method for Polyatomic Gases, Journal of Computational Physics, Available online 28 February 2014. 267(15), June 2014, pp.63-91 DOI: 10.1016/j.jcp.2014.02.026

  26. Z.-C. Hu, R. Li, T. Lu, Y.-L. Wang and W.-Q. Yao, Simulation of an n+-n-n+ Diode by Using Globally-Hyperbolically-Closed High-Order Moment Models, Journal of Scientific Computing, 59(3), Page 761-774, 2014, DOI: 10.1007/s10915-013-9781-1

  27. R. Li, T. Lu, Y.-L. Wang and W.-Q. Yao, Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation, Communcations in Computational Physics, Vol. 15, pp. 569--595, 2014. DOI: 10.4208/cicp.091012.120813a.

  28. Z.-N. Cai, Y-W. Fan, R. Li, and Z.-H. Qiao, Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision, Communications in Computational Physics, 15(5), pp. 1368-1406, May 2014, DOI: 10.4208/cicp.220313.281013a.

  29. Z.-N. Cai, R. Li and Y.-L. Wang, Solving Vlasov Equations Using NRxx Method, SIAM Journal on Scientific Computing, 35(6), pp. A2807-A2831, 5 December, 2014, DOI: 10.1137/120871791

  30. 2014

  31. 闫凯, 李若, 田宙, 郭永辉, 曹渊, 强爆炸火球数值模拟中的算子分裂方法, 《计算物理》, 第30卷第3期,2013,页码:379-386.

  32. W.-Q. Yao, R. Li, T. Lu, X.-Y. Liu, G. Du and K. Zhao, Globally hyperbolic moment method for BTE including phonon scattering, The International Conference on Simulation of Semiconductor Processes and Devices (SISPAD 2013) 3-5 September, 2013, Glasgow, Scotland, UK. Pages: 300-303, Product Type: Conference Publications

  33. Z.-N. Cai, Y.-W. Fan and R. Li, Globally Hyperbolic Regularization of Grad's Moment System, Communications on Pure and Applied Mathematics, First online at 1 July 2013, DOI: 10.1002/cpa.21465. Published as 67(3):464-518, 2014.

  34. Z.-N. Cai, R. Li and Z.-H. Qiao, Globally Hyperbolic Regularized Moment Method with Applications to Microflow Simulation, Computer and Fluids, 81, 20 July 2013, Pages 95-109.

  35. J. Deng, R. Li, T. Sun and S.-N. Wu, A Robust Simulation for Shallow Flows on Complex Rough Topography, Numerical Mathematics: Theory , Methods and Applications, 6(2), 2013, pp 384-407.

  36. Z.-N. Cai, Y.-W. Fan, R. Li, T. Lu and W.-Q. Yao, Quantum Hydrodynamic Model of Density Functional Theory, Journal of Mathematical Chemistry, Vol. 51, No. 5, pp. 1747--1771, 2013, DOI: 10.1007/s10910-013-0176-1.

  37. R. Li and S.-N. Wu, $H$-adaptive Mesh Method with Double Tolerance Adaptive Strategy for Hyperbolic Conservation Laws, Journal of Scientific Computing, 56(3), pp. 616--636, 2013 DOI: 10.1007/s10915-013-9692-1

  38. 2013

  39. Z.-N. Cai, Y.-W. Fan and R. Li, Globally Hyperbolic Regularization of Grad's Moment System in One Dimensional Space, Communications in Math Sciences, 11(2), 2012, pp. 547-571.

  40. Z.-N. Cai, Y.-W. Fan, R. Li, T. Lu and Y.-L. Wang, Quantum Hydrodynamic Model by Moment Closure of Wigner Equation, Journal of Mathematical Physics, 53(10), 2012, DOI: 10.1063/1.4748971, http://link.aip.org/link/?JMP/53/103503

  41. R. Li, P.-B. Ming and F.-Y. Tang, An Efficient High Order Heterogeneous Multiscale Method for Elliptic Problems, SIAM Multiscale Modelling and Simulation, 10(1), 2012, pp. 259-283 DOI: 10.1137/110836626, http://link.aip.org/link/?MMS/10/259

  42. Z.-N. Cai, R. Li and Z.-H. Qiao, NRxx Simulation of Microflows with Shakhov Model, SIAM Journal on Scientific Computing, 34(1), 2012, pp. A339-A369 DOI: 10.1137/110828551, http://link.aip.org/link/?SCE/34/A339

  43. Z.-N. Cai, R. Li and Y.-L. Wang, Numerical Regularized Moment Method for High Mach Number Flow, Communication in Computational Physics, 11(5), 2012, pp. 1415-1438.

  44. 2012

  45. Z.-N. Cai, R. Li and Y.-L. Wang, An Efficient NRxx Method for Boltzmann-BGK Equation, Journal of Scientific Computing, 50, 2012, pp. 103-119 DOI: 10.1007/s10915-011-9475-5.

  46. G. Yuan and R. Li, Sharp a Posteriori Error Estimate for Elliptic Equation with Singular Data, Frontiers of Mathematics in China, 6(1), 2011, pp. 177-202.

  47. G.-H. Hu, R. Li, and T. Tang, A robust WENO type finite volume solver for steady Euler equations on unstructured grids, Communications in Computational Physics, 9 (2011), pp. 627-648. journal download

  48. 2011

  49. K. Kunisch, W.-B. Liu, Y.-Z. Chang, N.-N. Yan and R. Li, Adaptive finite element approximation for a class of parameter estimation problems, Journal of Computational Mathematics (28), 01/2010, pp 645-675.

  50. Z.-N. Cai and R. Li, Numerical Regularized Moment Method of Arbitrary Order for Boltzmann-BGK Equation, SIAM Journal on Scientific Computing, Volume 32, Issue 5, September 23, 2010, pp. 2875-2907. doi:10.1137/100785466.

  51. D. Wang, R. Li and N.-N. Yan, An Edge-based Anisotropic Mesh Refinement Algorithm and its Application to Interface Problems, Communications in Computational Physics Volume 8 (2010), pp. 511-540 local download, journal download

  52. Z.-N. Cai and R. Li, An $h$-Adaptive Mesh Method for Boltzmann-BGK/Hydrodynamics Coupling, Journal of Computational Physics Volume 229, Issue 5, 1 March 2010, Pages 1661-1680. doi:10.1016/j.jcp.2009.10.050.

  53. G.-H. Hu, R. Li and T. Tang, A Robust High-order Residual Distribution Type Scheme for Steady Euler Equations on Grids, Journal of Computational Physics Volume 229, Issue 5, 1 March 2010, Pages 1681-1697. doi:10.1016/j.jcp.2009.11.002

  54. 2010

  55. X.-L. Hu, R. Li and T. Tang, A Multi-Mesh Adaptive Finite Element Approximation to Phase Field Equations, Commun. Comput. Phys., 5 (2009), pp. 1012-1029. local download, Journal download.

  56. Y.-N. Di and R. Li, Computation of Dendritic Growth with Level Set Model Using a Multi-Mesh Adaptive Finite Element Method, Journal of Scientific Computing 39 (2009), pp. 441-453. doi:10.1007/s10915-009-9275-3.

  57. 2009

  58. T. Y. Hou and R. Li, Numerical Study of Nearly Singular Solutions of the 3-D Incompressible Euler Equations, Mathematics and Computation, a Contemporary View, Abel Symposium 3 (2008), pp. 39-66. doi:10.1007/978-3-540-68850-1_3.

  59. Y.-N. Di, R. Li and T. Tang, A General Moving Mesh Framework in 3D and Its Application for Simulating the Mixture of Multi-Phase Flows, Communications in Computational Physics 3(3), 2008, 582-602 local download, Journal download.

  60. R. Li, X. Wang and W.-B. Zhao, A Multigrid Block LU-SGS Algorithm for Euler Equations on Unstructured Grids, Numerical Mathematics: Theory, Methods and Applications 1(1), 2008, 92-112 local download, Journal download.

  61. T. Y. Hou and R. Li, Blowup or No Blowup? The Interplay between Theory and Numerics, Physics D, published online Jan. 25, 2008, doi:10.1016/j.physd.2008.01.018.

  62. H.-Y. Wang, R. Li and T. Tang, An Efficient $r$-adaptive Finite Element Method for Phase Field Model of Dendritic Growth, Journal of Computational Physics, 2008, vol 227, pp. 5984-6000, doi:10.1016/j.jcp.2008.02.016.

  63. W. Gong, R. Li, N.-N. Yan and W.-B. Zhao, An Improved Error Analysis for Finite Element Approximation of Bioluminescence Tomography, Journal of Computational Mathematics 26(3), 2008, pp. 297-309 local download, Journal download.

  64. H.-Y. Wang and R. Li, Mesh Sensitivity for Numerical Solutions of Phase-field Equations Using r-adaptive Finite Element Methods, Communications in Computational Physics 3(2), 2008, 357-375 local download, Journal download.

  65. 2008

  66. R. Li, W.-B. Liu and N.-N. Yan, A Posteriori Error Estimates of Recovery Type for Distributed Convex Optimal Control Problems, Journal of Scientific Computing 33(2), November 2007, 155-182 doi:10.1007/s10915-007-9147-7.

  67. Y.-N. Di, R. Li, T. Tang and P.-W. Zhang, Level Set Calculations for Incompressible Two-phase Flows on a Dynamically Adaptive Grid, Journal of Scientific Computing, 31(2007), 1-2, pp75-98, doi:10.1007/s10915-006-9119-3.

  68. T. Y. Hou and R. Li, Computing Nearly Singular Solutions Using Pseudo-Spectral Methods, Journal of Computational Physics, 226 , 379-397, 2007 doi:10.1016/j.jcp.2007.04.014.

  69. D.-M. Li, R. Li and P.-W. Zhang, A Cellular Automaton Technique for Modelling of a Binary Dendritic Growth with Convection, Applied Mathematical Modelling, 31(2007), pp 971-982. doi:10.1016/j.apm.2006.04.004.

  70. T. Y. Hou and R. Li, Nonexistence of Local Self-Similar Blow-up for the 3D Incompressible Navier-Stokes Equations, Discrete and Continuous Dynamical Systems, Series A , 18(4) , 637-642, 2007, Journal download.

  71. Y.-Q. Huang, R. Li and W.-B. Liu, Preconditioned Descending Algorithms for $p$-Laplacian, Journal of Scientific Computing 32(2), 2007, 342-371 doi:10.1007/s10915-007-9134-z.

  72. 2007

  73. D.-M. Li, R. Li, P.-W. Zhang, A Cellular Automaton Technique for the Modeling of Solidification Microstructure in Multi-Component Alloys, Computer and Computational Sciences, 2006. IMSCCS '06. First International Multi-Symposiums on; 07/2006.

  74. R. Li and T. Tang, Moving Mesh Discontinuous Galerkin Method for Hyperbolic Conservation Laws, Journal of Scientific Computing, 27, 2006, pp.347-363, doi:10.1007/s10915-005-9045-9

  75. J. Deng, T. Y. Hou, R. Li and X.-W. Yu, Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation, Methods and Applications of Analysis 13(2), 2006, 157-180 Journal download.

  76. Y.-N. Di, R. Li, T. Tang and P.-W. Zhang, Moving Mesh Methods for Singular Problems on a Sphere Using Perturbed Harmonic Mappings, SIAM Journal on Scientific Computing, 28(2006), pp1490-1508, doi:10.1137/050642514.

  77. T. Y. Hou and R. Li, Dynamic Depletion of Vortex Stretching and Non-blowup of the 3D Incompressible Euler Equations, Journal of Nonlinear Science, 16(6), 639-664, 2006. doi:10.1007/s00332-006-0800-3.

  78. D.-M. Li, R. Li, P.-W. Zhang, A Cellular Automaton Technique for the Modeling of Solidification Microstructure in Multi-component Alloys, First International Multi-Symposiums on Computer and Computational Sciences (IMSCCS 2006), Proceedings, Vol 2, 2006, pp 800-806 doi:10.1109/IMSCCS.2006.142

  79. 2006

  80. Y.-N. Di, R. Li, T. Tang and P.-W. Zhang, Moving Mesh Finite Element Methods for the Incompressible Navier-Stokes Equations, SIAM Journal on Scientific Computing, 26 (2005), 1036-1056, doi:10.1137/030600643.

  81. R. Li, on Multi-Mesh $h$-Adaptive Algorithm, Journal of Scientific Computing 24(3), 2005, pp.321-341, doi:10.1007/s10915-004-4793-5.

  82. 2005

  83. D.-M. Li, R. Li and P.-W. Zhang, A New Coupled Model for Alloy Solidification, Science in China Series A-Mathematics 47: 41-52 Suppl. S Apr 2004, Journal download.

  84. R. Li, C. Luo and P.-W. Zhang, Numerical Simulation of Doi Model of Polymeric Fluids, Adv. in Sci. Comput. & Appl. (Y. Lu, W. Sun and T. Tang eds), 2004, pp 258-273. doi:

  85. 2004

  86. R. Li, W.-B. Liu and H.-P. Ma, Moving Mesh Finite Element Approximations for Variational Inequality I: Static Obstacle Problem, Journal of Scientific Computing, 21(1), pp. 31-55 (2003), doi:10.1023/B:JOMP.0000027954.83289.00.

  87. 2003

  88. R. Li, T. Tang and P.-W. Zhang, A Moving Mesh Finite Element Algorithm for Singular Problems in Two and Three Space Dimensions, Journal of Computational Physics 177, 365-393 (2002), doi:10.1006/jcph.2002.7002.

  89. R. Li, W.-B. Liu, H.-P. Ma and T. Tang, Adaptive Finite Element Approximations for Distributed Optimal Control Problems, SIAM Journal on Control and Optimization, 41 : pp. 1321-1349 (2002), doi:10.1137/S0363012901389342.

  90. 2002

  91. R. Li, T. Tang and P.-W. Zhang, Moving Mesh Methods in Multiple Dimensions Based on Harmonic Maps, Journal of Computational Physics 170, 562-588 (2001), doi:10.1006/jcph.2001.6749.

  92. R. Li, W.-B. Liu, T. Tang and P.-W. Zhang, Moving Mesh Finite Element Methods Based on Harmonic Maps, Proc. of 2nd Intl. Workshop on Sci. Comput. and Appl. (P. Minev and Y. Lin eds), 2001, pp. 143-156, http://citeseerx.ist.psu.edu/viewdoc/download?doi=

  93. Q. Du, D.-Z. Li, Y.-Y. Li, R. Li and P.-W. Zhang, Simulating a Double Casting Technique Using Level Set Method, Computational Materials Science, 22, 200-212, 2001, doi:10.1016/S0927-0256(01)00190-2.

  94. 2001