Publications

Textbooks:

  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。

Journal and Proceeding Papers:

    Accepted:

  1. J. Deng, R. Li, T. Sun and S.-N. Wu, A Robust Simulation for Shallow Flows on Complex Rough Topography, Accepted by Numerical Mathematics: Theory , Methods and Applications.

    2. Published:

  2. 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

  3. 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

  4. 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.

    5. 2012

  5. 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.

  6. 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.

  7. 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

    8. 2011

  8. 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.

  9. 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

  10. 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.

  11. 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

    12. 2010

  12. 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.

  13. 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.

    14. 2009

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

    21. 2008

  21. 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.

  22. 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.

  23. 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.

  24. 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.

  25. 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.

  26. 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.

    27. 2007

  27. 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

  28. 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.

  29. 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.

  30. 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.

  31. 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

    32. 2006

  32. 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.

  33. 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.

    34. 2005

  34. 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.

  35. 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:10.1.1.110.7638

    36. 2004

  36. 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.

    37. 2003

  37. 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.

  38. 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.

    39. 2002

  39. 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.

  40. 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=10.1.1.32.435&rep=rep1&type=pdf.

  41. 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.

    42. 2001