Publications

Selected Publications (Click here for more recent publications)

  1. Y. Zhou, D. Liang, (2024), Modeling and FDTD Discretization of Stochastic Maxwell's Equations with Drude dispersion, Journal of Computational Physics, 509, 113033.
  2. Y. Shi, D. Liang, S. Xie, K. Fu, (2024), Fourth-Order Compact Block-Centered Splitting Domain Decomposition Method for Parabolic Equations, Journal of Computational and Applied Mathematics, 448, 115933.
  3. D. Liang, C. Wang, (2023), Global energy-preserving local mesh-refined S-FDTD schemes for two dimensional Maxwell’s equations in Drude metamaterials, Computer Physics Communications, 294 (2024), 108936, published online Oct 2023.
  4. C. Niu, H. Ma, D. Liang, (2022), Energy-Conserved Splitting Multi-domain Legendre-Tau Spectral Method for Two Dimensional Maxwell's Equations, Journal of Scientific Computing, 90, 77.
  5. J. Xie, D. Liang, Z. Zhang, (2021), Energy-preserving local mesh-refined splitting FDTD schemes for two dimensional Maxwell’s equations, Journal of Computational Physics, 425, 109896.
  6. Suj. Sriskandarajah, D. Liang, H.M. Zhu, (2021), Using the EC-S-FDTD Scheme to Approximate Eddy Currents Induced by Z-Gradient Coils, IEEE Transactions on Antennas and Propagation, 69, 4715 - 4726.
  7. Hom N. Kandel, D. Liang, (2021), The mass-preserving solution-flux scheme for multilayer interface parabolic equations, Applied Numerical Mathematics, 160, 42 - 64.
  8. B. Hou, D. Liang, (2020), Energy-preserving time high-order AVF compact finite difference schemes for nonlinear wave equations with variable coefficients, Journal of Computational Physics, 421, 109738.
  9. D. Liang, Z. Zhou, (2020), The conservative splitting domain decomposition method for multicomponenet contamination flows in porous media, Journal of Computational Physics, 400, 108974.
  10. W. Xu, D. Liang, H. Rui, X. Li, (2020), A multipoint flux mixed finite element method for Darcy-Forchheimer incompressible miscible displacement problem, Journal of Scientific Computing, 82, 2.
  11. K. Fu, D. Liang, (2019), A Mass-Conservative Temporal Second Order and Spatial Fourth Order Characteristic FV Method for Atmospheric Pollution Advection Diffusion Problems, SIAM Journal on Scientific Computing, 41, B1178 - 1210.
  12. Yousef Akhavan, D. Liang, M. Chen, (2019), Second Order in Time and Space Corrected Explicit-Implicit Domain Decomposition Scheme for Convection-Diffusion Equations, Journal of Computational and Applied Mathematics, 357, 38 - 55.
  13. D. Deng, D. Liang, (2018), The time fourth-order compact ADI methods for solving two dimensional nonlinear wave equations, Applied Mathematics and Computation, 329, 188 - 209.
  14. Z. Zhou, D. Liang, (2017), The mass-preserving and modified-upwind splitting DDM scheme for time-dependent convection-diffusion equations, Journal of Computational and Applied Mathematics, 317, 247 - 273.
  15. W. Li, D. Liang, Y.P. Lin, (2017), Global energy-tracking identities and global energy-tracking splitting FDTD schemes for the Drude Models of Maxwell's equations in three-dimensional metamaterials, Numerical Methods for Partial Differential Equations, 33, 763 - 785.
  16. K. Fu and D. Liang, (2016), The conservative characteristic FD methods for atmospheric aerosol transport problems, Journal of Computational Physics, 305, 494 - 520.
  17. D. Liang, K. Fu and W. Wang, (2016), Modelling multi-component aerosol transport problems by the efficient splitting characteristic method, Atmospheric Environment, 144, 297 - 314.
  18. D. Liang and C. Du, (2014), The Efficient S-DDM Scheme and its Analysis for Solving Parabolic Equations, Journal of Computational Physics, 272, 46 - 69.
  19. D. Liang and Q. Yuan, (2013), The spatial fourth-order energy-conserved S-FDTD scheme for Maxwell's equations, Journal of Computational Physics, 243, 344 - 364.
  20. D. Liang, P. Weng and J. Wu, (2012), Traveling Wave Solutions in A Delayed Predator-Prey Diffusion PDE System: Point-to-Periodic and Point-to-Point Waves, IMA Journal of Applied Mathematics, 77, 516 - 545.
  21. Frank X. Yu, W. Weng, P. Taylor and D. Liang, (2011), "Relaxation Factor Effects in the Non-Linear Mixed Spectral Finite Difference Model of Flow over Topographic Features, Boundary Layer Meteorology, 140, 23 - 35.
  22. C. Du and D. Liang, (2010), An Efficient S-DDM Iterative Approach for Compressible Contamination Fluid Flows in Porous Media, Journal of Computational Physics, 229, 4501 - 4521.
  23. W. Chen, X. Li and D. Liang, (2010), Energy-conserved Splitting Finite Difference Time Domain Methods for Maxwell's Equations in Three Dimensions, SIAM Journal on Numerical Analysis, 48, 1530 - 1554.
  24. Y. Cheng, D. Liang, W. Wang, S. Gong and M. Xue, (2010), An Efficient Approach of Aerosol Thermodynamic Equilibrium Predictions by the HDMR Method, Atmospheric Environment, 44, 1321 - 1330.
  25. D. Liang, W. Wang and Y. Cheng, (2009), An Efficient Second Order Characteristic Finite Element Method for Nonlinear Aerosol Dynamic Equations, International Journal for Numerical Methods in Engineering, 80, 338 - 354.
  26. Thomas Y. Hou and D. Liang, (2009), Multiscale analysis for convection dominated transport equations, Discrete & Continuous Dynamical Systems, Ser. A, 23, 281 - 298.
  27. D. Liang, Q. Guo and S. Gong, (2008), A New Splitting Wavelet Method for Solving the General Aerosol Dynamics Equation, Journal of Aerosol Science, 39, 467 - 487.
  28. W. Chen, X. Li and D. Liang, (2008), Energy-conserved splitting FDTD methods for Maxwells equations, Numerische Mathematik, 108, 445 - 485.
  29. D. Liang, C. Du and H. Wang, (2007), A Fractional Step ELLAM Approach to High-Dimensional Convection-Diffusion Problems with Forward Particle Tracking, Journal of Computational Physics, 221, 198 - 225.
  30. M. Gardam, D. Liang, S.M. Moghadas, J. Wu, Q. Zeng and H. Zhu, (2007), The Impact of Prophylaxis of Healthcare Workers on Influenza Pandemic Burden, Journal of The Royal Society Interface, 4, 727 - 734.
  31. D. Liang and W. Zhao, (2006), An Optimal Weighted Upwinding Covolume Method on Nonstandard Grids for Convection-Diffusion Problems in 2D, International Journal for Numerical Methods in Engineering, 67, 553 - 577.
  32. D. Liang, H. Wang and R.C. Sharpley, (2006), Finite Element Approximations to One Phase Nonlinear Free Boundary Problem in Groundwater Contamination Flow, Numerical Methods for Partial Differential Equations, 22, 1268 - 1288.
  33. D. Liang and B. Zhang, (2004), Numerical Analysis of Graded Mesh Methods for a Class of Second Kind Integral Equations on the Real Line, Journal of Mathematical Analysis and Applications, 294, 482 - 502.
  34. H. Huang, D. Liang and B. Wetton, (2004), Computation of a Moving Drop/Bubble on a Solid Surface Using a Front-Tracking Method, Communications in Mathematical Sciences, 2, 535 - 552.
  35. D. Liang and J. Wu, (2003), Travelling Waves and Numerical Approximations in a Reaction Advection Diffusion Equation with Non-local Delayed Effects, Journal of Nonlinear Science, 13, 289 - 310.
  36. H. Wang, D. Liang, R.E. Ewing, S.L. Lyons and G. Qin, (2002), An ELLAM approximation for highly compressible multicomponent flows in porous media, Computational Geosciences, 6, 227 - 251.
  37. H. Wang, D. Liang, R.E. Ewing, S.L. Lyons, G. Qin, (2000), An Approximation to Miscible Displacement in Porous Media with Point Sources and Sinks by an Eulerian-Lagrangian Localized Adjoint Method and Mixed Finite Element Methods, SIAM Journal on Scientific Computing, 22, 561 - 581.
  38. H. Wang, D. Liang, R.E. Ewing, S.L. Lyons, G. Qin, (2000), An ELLAM-MFEM Solution Technique for Compressible Fluid Flow in Porous Media with Point Sources and Sinks, Journal of Computational Physics, 159, 344 - 376.
  39. D. Liang and B. Zhang, (1999), A Finite Element Method for a Unidimensional Single-Phase Nonlinear Free Boundary Problem in Groundwater Flow, IMA Journal of Numerical Analysis, 19, 563 - 579.