Selected Recent Publications
- H.F. Ji, D. Liang, Q. Zhang, "A mini immersed finite element method for two-phase Stokes problems on Cartesian meshes", IMA J. Numer. Anal., (doi.org/10.1093/imanum/drae053), published online 9 Sept (2024).
- Khan E. Hossain, D. Liang, H.M. Zhu, "Developing PDE-constrained optimal control of multicomponent contamination flows in porous media", Comput. Math. Appl., (doi.org/10.1016/j.camwa.2024.10.033), 176 (2024), 224 - 243. published online 4 Nov 2024.
- Y. Zhou, D. Liang, "Modelling and FDTD Discretization of Stochastic Maxwell's Equations with Drude dispersion", J. Comput. Phys., 509 (2024), 113033. Available online 23 April 2024.
- Y. Shi, D. Liang, S. Xie, K. Fu, "Fourth-Order Compact Block-Centered Splitting Domain Decomposition Method for Parabolic Equations", J. Comput. Appl. Math., 448 (2024), 115933.
- D. Liang, C. Wang, "Global energy-preserving local mesh-refined S-FDTD schemes for two dimensional Maxwell’s equations in Drude metamaterials", Comput. Phys. Commun., 294 (2024), 108936, published online Oct 2023.
- D. Qin, K. Fu, D. Liang, "Positivity preserving temporal second-order spatial fourth-order conservative characteristic methods for convection dominated diffusion equations", Comput. Math. Appl., 149 (2023), 190 - 202.
- Q. Zhang, H.F. Ji, D. Liang, "Unfitted finite element methods based on correction functions for Stokes flows with singular forces of low regularity", Comput. Fluids, 256 (2023), 105861.
- C. Niu, H. Ma, D. Liang, "Legendre-tau Chebyshev collocation spectral element method for Maxwell's equations with material interfaces of two dimensional transverse magnetic mode", Comput. Math. Appl., 147 (2023), 222 - 238.
- Y.J. Yuan, D. Liang, "Developing the optimization control of pollution constrained by the convection diffusion equations", J. Comput. Sci., 66 (2023), 101933, Published online on Dec 22, 2022.
- Z. Zhou, D. Liang, Y.S. Wong, "An efficient MMOCAA-DDM for solving advection diffusion equations", Comput. Math. Appl., 131 (2023), 35 - 53, Published online on Dec 6, 2022.
- C. Niu, H. Ma, D. Liang, "Energy-Conserved Splitting Multidomain Legendre-Tau Spectral Method for Two Dimensional Maxwell's Equations", J. Sci. Comput., 90 (2022), 77.
- Y. Shi, S. Xie, D. Liang, "A fourth-order block-centered compact difference scheme for nonlinear contaminant transport equations with adsorption", Appl. Numer. Math., 171 (2022), 212 - 232.
- J. Xie, D. Liang, Z. Zhang, "Energy-preserving local mesh-refined splitting FDTD schemes for two dimensional Maxwell’s equations", J. Comput. Phys., 425 (2021), 109896.
- S. Sriskandarajah, D. Liang, H.M. Zhu, "Using the EC-S-FDTD Scheme to Approximate Eddy Currents Induced by Z-Gradient Coils", IEEE Trans. Antennas Propagat., 69 (2021), 4715 - 4726.
- B. Hou, D. Liang, "The energy-preserving time high-order AVF compact finite difference scheme for nonlinear wave equations in two dimensions", Appl. Numer. Math., 170 (2021), 298 - 320.
- Hom N. Kandel, D. Liang, "The mass-preserving solution-flux scheme for multi- layer interface parabolic equations", Appl. Numer. Math., 160 (2021), 42 - 64.
- Y. Shi, S. Xie, D. Liang, K. Fu, "High Order Compact Block-Centered Finite Difference Schemes for Elliptic and Parabolic Problems", J. Sci. Comput., 87 (2021), 86: 1-26.
- B. Hou, D. Liang, "Time fourth-order energy-preserving AVF finite difference method for nonlinear space-fractional wave equations", J. Comput. Appl. Math., 386 (2021), 113227.
- M. Sarai, D. Liang, "Even-Odd Cycled High-Order Splitting Finite Difference Time Domain Method for Maxwell's Equations", Int. J. Numer. Anal. Modeling, 18 (2021), 79-99.
- Y.J. Yuan, D. Liang, "Optimization of Identifying Point Pollution Sources for the Convection-Diffusion-Reaction Equations", Adv. Appl. Math. Mech., 13 (2021), 1-17.
- B. Hou, D. Liang, "Energy-preserving time high-order AVF compact finite difference schemes for nonlinear wave equations with variable coefficients", J. Comput. Phys., 421 (2020), 109738.
- D. Liang, Z. Zhou, "The conservative splitting domain decomposition method for multicomponenet contamination flows in porous media", J. Comput. Phys., 400 (2020), 108974, 1-27.
- W. Xu, D. Liang, H. Rui, X. Li, "A multipoint flux mixed finite element method for Darcy-Forchheimer incompressible miscible displacement problem", J. Sci. Comput., 82 (2020), 2: 1-20.
- J. Xie, D. Liang, Z. Zhang, "Two novel energy dissipative difference schemes for the strongly coupled nonlinear space fractional wave equations with damping", Appl. Numer. Math., 157 (2020), 178 - 209.
- W. Li, D. Liang, "The spatial fourth-order compact splitting FDTD scheme with modified energy-conserved identity for two-dimensional Lorentz model", J. Comput. Appl. Math., 367 (2020), 112428.
- D. Deng, D. Liang, "The energy-preserving finite difference methods and their analyses for system of nonlinear wave equations in two dimensions", Appl. Numer. Math., 151 (2020), 172 - 198.
- M. Cui, F. Li, D. Liang, "High-order Characteristic-Finite Volume Methods For Aerosol Dynamic Equations", J. Comput. Appl. Math., 370 (2020), 112593, 1-16.
- Z. Zhang, D. Liang, Q. Wang, "Immersed finite element method and its analysis for parabolic optimal control problems with interfaces", Appl. Numer. Math., 147 (2020), 174-195.
- C.G. Chen, D. Liang, S. Xie, "The time high-order energy-preserving schemes for the nonlocal Benjamin-Ono equation", Int. J. Numer. Anal. Modeling , 17 (2020), 543 - 556.
- J.L. Wang, Y.S. Wang, D. Liang, "Construction of the Local Structure-Preserving Algorithms for the General Multi-Symplectic Hamiltonian System", Commun. Comput. Phys., 27 (2020), 828-860.
- K. Fu, D. Liang, "A Mass-Conservative Temporal Second Order and Spatial Fourth Order Characteristic FV Method for Atmospheric Pollution Advection Diffusion Problems", SIAM J. Sci. Comput., 41 (2019), B1178-B1210.
- W. Li, D. Liang, "The Energy Conservative Splitting FDTD scheme and its Energy Identities for Metamaterial Electromagnetic Lorentz System", Comput. Phys. Commun., 239 (2019), 94-111.
- B. Hou, D. Liang, H.M. Zhu, "The Conservative Time High-Order AVF Compact Finite Difference Schemes for Two-Dimensional Variable Coefficient Acoustic Wave Equations", J. Sci. Comput., 80 (2019), 1279-1309.
- Yousef Akhavan, D. Liang, M. Chen, "Second Order in Time and Space Corrected Explicit-Implicit Domain Decomposition Scheme for Convection-Diffusion Equations", J. Comput. Appl. Math., 357 (2019), 38-55.
- Hom N. Kandel, D. Liang, "The long wave fluid flows on inclined porous media with nonlinear Forchheimer's law", AIP Advances, 9 (2019), 095302: 1-21.
- Y. Gao, D. Liang, Y. Li, "Optimal weighted upwind finite volume method for convection-diffusion equations in 2D", J. Comput. Appl. Math., 359 (2019), 73-87.
- J.L. Wang, D. Liang, Y.S. Wang, "Analysis of a conservative high-order compact finite difference scheme for the Klein-Gordon-Schodinger equation", J. Comput. Appl. Math., 358 (2019), 84-86.
- B. Wang, T. Sun, D. Liang, "The conservative and fourth-order compact finite difference schemes for regularized long wave equation", J. Comput. Appl. Math., 356 (2019), 98-117.
- J. Xie, Z. Zhang, D. Liang, "A conservative splitting difference scheme for the fractional-in-space Boussinesq equation", Appl. Numer. Math., 143 (2019), 61-74.
- B. Hou, D. Liang, "A time second-order characteristic finite element method for nonlinear advection-diffusion equations", Int. J. Numer. Anal. Modelling, 16 (2019), 276-296.
- J. Xie, Z. Zhang, D. Liang, "A new fourth-order energy dissipative difference method for high-dimensional nonlinear fractional generalized wave equations", Commum. Nonlinear Sci. Numer. Simul., 78 (2019), 104850, 1-21.
- D. Deng, J. Xie, Y. Jiang, D. Liang, "A second-order box solver for nonlinear delayed convection-diffusion equations with Neumann boundary conditions", Int. J. Computer Math., 96 (2019), 1879-1898.
- Z. Zhou, D. Liang, Y.S. Wong, "The new mass-conserving S-DDM scheme for two-dimensional parabolic equations with variable coefficients", Appl. Math. Comput., 338 (2018), 882-902.
- D. Deng, D. Liang, "The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations", Appl. Math. Comput., 329 (2018), 188-209.
- B. Wang, D. Liang, T.J. Sun, "The Conservative Splitting High-Order Compact Finite Difference Scheme for Two-Dimensional Schrodinger Equations", Int. J. Comput. Meths., 15 (2018), 1750079: 1-22.
- J.L. Wang, Y.S. Wang, D. Liang, "Analysis of a Fourier pseudo-spectral conservative scheme for the Klein–Gordon–Schrödinger equation", Int. J. Computer Math., 95 (2018), 36 - 60.
- J. Yan, Z. Zhang, T. Zhao, D. Liang, "High-order energy-preserving schemes for the improved Boussinesq equation", Numer. Methods Partial Diff. Eqns., 34 (2018), 1145-1165.
- K. Fu, D. Liang, "The Time Second Order Mass Conservative Characteristic FDM for Advection-Diffusion Equations in High Dimensions", J. Sci. Comput., 73 (2017), 26 - 49.
- Z. Zhou, D. Liang, "The mass-preserving and modified-upwind splitting DDM scheme for time-dependent convection-diffusion equations", J. Comput. Appl. Math., 317 (2017), 247 - 273.
- W. Li, D. Liang, Y.P. Lin, "Global energy-tracking identities and global energy-tracking splitting FDTD schemes for the Drude Models of Maxwell's equations in three-dimensional metamaterials", Numer. Methods Part. Diff. Eqns. , 33 (2017), 763 - 785.
- Y.J. Yuan, D. Liang, H.M. Zhu, "Optimal control of groundwater pollution combined with source abatement costs and taxes", J. Comput. Sci., 20 (2017), 17 - 29.
- W. Xu, D. Liang, and H. Rui, "A multipoint flux mixed finite element method for the compressible Darcy-Forchheimer models", Appl. Math. Comput. , 315 (2017), 259 - 277.
- D. Deng, Y. Jiang and D. Liang, "High-order finite difference methods for a second order dual-phase-lagging models of microscale heat transfer", Appl. Math. Comput., 309 (2017), 31 - 48.
- Y.J. Yuan and D. Liang, "Numerical Optimal Pollution Control Subject to The Convection Diffusion Transport Equations", Int. J. Numer. Anal. Modeling, 14 (2017), 437 - 455.
- Z. Zhou, D. Liang, "A Time Second-Order Mass-Conserved Implicit-Explicit Domain Decomposition Scheme for Solving the Diffusion Equations", Adv. Appl. Math. Mech., 9 (2017), 795 - 817.
- J. Yan, Q. Zhang, Z. Zhang and D. Liang, "A new high-order energy-preserving scheme for the modified Korteweg-de Vries equation", Numer. Algor., 74 (2017), 659 - 674.
- K. Fu and D. Liang, "The conservative characteristic FD methods for atmospheric aerosol transport problems", J. Comput. Phys., 305 (2016), 494 - 520.
- D. Liang, K. Fu and W. Wang, "Modelling multi-component aerosol transport problems by the efficient splitting characteristic method", Atmos. Environ., 144 (2016), 297 - 314.
- W. Li and D. Liang, "Symmetric energy-conserved S-FDTD scheme for two-dimensional Maxwell's equations in negative index metamaterials", J. Sci. Comput. , 69 (2016), 696 - 735.
- Z. Zhou and D. Liang, "The mass-preserving S-DDM scheme for two-dimensional parabolic equations", Commun. Comput. Phys., 19 (2016), 411 - 441.
- W. Li, Y. Zhang, Y.S. Wong and D. Liang, "ADI-FDTD method for two-dimensional transient electromagnetic problem", Commun. Comput. Phys., 19 (2016), 94 - 123.
- M. Cui, Y. Su, D. Liang, "High-order Finite Volume Methods for Aerosol Dynamic Equations", Adv. Appl. Math. Mech., 8 (2016), 213 - 235.
- K. Fu, D. Liang, et al., "The time second-order characteristic FEM for nonlinear multicomponent aerosol dynamic equations in environment", Int. J. Numer. Anal. Modelling, 12 (2015), 211 - 229.
- W. Li and D. Liang, "Analysis of the energy-conserved S-FDTD scheme for variable coefficient Maxwell's equations in disk domains", Math. Methods Appl. Sci., (published online), (2015)
- J. Lou, H. Zhou, D. Liang, et al., "The Coupled Within- and Between-Host Dynamics in the Evolution of HIV/AIDS in China", J. Appl. Anal. Comput., 5 (2015), 731 - 750.
- S.H. Zhang and D. Liang, "LOD-ASEI and LOD-ASCN methods for two-dimension parabolic equations", Int. J. Computer Math., 92 (2015), 513 - 531.
- D. Liang and C. Du, "The Efficient S-DDM Scheme and its Analysis for Solving Parabolic Equations", J. Comput. Phys., 272 (2014), 46 - 69.
- M. Cui, K. Fu, D. Liang, et al., "Numerical analysis of the second-order characteristic FEM for nonlinear aerosol dynamic equations", J. Comput. Appl. Math., 261 (2014), 48-61.
- F. Zeng, H. Ma and D. Liang, "Energy-conserved splitting spectral methods for two dimensional Maxwell's equations", J. Comput. Appl. Math., 265 (2014), 301 - 321.
- Y. Akhavan, M. Chen, D. Liang, "Global Optimization of Total Power Generated from Wind Farm", POWERCON2014: The 2014 International Conference on Power System Technology, IEEE publisher, ISBN: 978-1-4799-5032-4, (2014), 2945-2950.
- D. Liang and Q. Yuan, "The spatial fourth-order energy-conserved S-FDTD scheme for Maxwell's equations", J. Comput. Phys., 243 (2013), 344 - 364.
- F. Gao and D. Liang, "A new weighted upwind finite volume element method based on non-standard covolume for time-dependent convection diffusion problems", Int. J. Numer. Meth. Fluids, 73 (2013), 953 - 975.
- W. Li, D. Liang and Y.P. Lin, "A new energy-conserved S-FDTD scheme for Maxwell's equations in metamaterials", Int. J. Numer. Anal. Modelling, 10 (2013), 775 - 794.
- D. Liang, P. Weng and J. Wu, "Traveling Wave Solutions in A Delayed Predator-Prey Diffusion PDE System: Point-to-Periodic and Point-to-Point Waves", IMA J. Appl. Math., 77 (2012), 516-545.
- L. Gao and D. Liang, "New Energy-Conserved Identities and Super-Convergence of the Symmetric EC-S-FDTD Scheme for Maxwell's Equations in 2D", Commun. Comput. Phys., 11 (2012), 1673 - 1696.
- K. Fu, D. Liang, W. Wang, Y. Cheng, S. Gong, "Multi-component atmospheric aerosols prediction by a multi-functional MC-HDMR approach", Atmos. Res., 113 (2012), 43-56.
- Q. Yuan and D. Liang, "A New Multiple Sub-domain RS-HDMR Method and its Application to Tropospheric Alkane Photochemistry Model", Int. J. Numer. Anal. Modeling, Ser. B, 2 (2011), 73 - 90.
- X. Yu, W. Weng, P. Taylor and D. Liang,"Relaxation Factor Effects in the Non-Linear Mixed Spectral Finite Difference Model of Flow over Topographic Features", Boundary-Layer Meteorology, 140 (2011), 23 - 35.
- D. Liang, G. Sun and W. Wang, "Second order characteristic schemes in time and age for a nonlinear age-structured population model", J. Comput. Appl. Math., 235 (2011), 3841-3858.
- C. Du and D. Liang,"An Efficient S-DDM Iterative Approach for Compressible Contamination Fluid Flows in Porous Media", J. Comput. Phys., 229 (2010), 4501-4521.
- W. Chen, X. Li and D. Liang, "Energy-conserved Splitting Finite Difference Time Domain Methods for Maxwell's Equations in Three Dimensions", SIAM J. Numer. Anal., 48 (2010), 1530-1554.
- Y. Cheng, D. Liang, W. Wang, S. Gong and M. Xue, "An Efficient Approach of Aerosol Thermodynamic Equilibrium Predictions by the HDMR Method", Atmos. Environ., 44 (2010), 1321-1330.
- D. Liang and C. Du, "An Efficient Splitting Domain Decomposition Approach for Parabolic-type Time-dependent Problems in Porous Media", High Performance Computing and Applications, Lecture Notes in Computer Sci. 5938, (Springer), (2010), 69-77.
- D. Liang, W. Wang and Y. Cheng, "An Efficient Second Order Characteristic Finite Element Method for Nonlinear Aerosol Dynamic Equations", Int. J. Numer. Methods Engng., 80 (2009), 338 - 354.
- M. Zivkovic Gojovic, D. Liang and J. Wu, "Structured Influenza Model for Meta-population", Int. J. Biomath., 2 (2009), 525 - 541.
- G. Sun, D. Liang and W. Wang, "Numerical analysis to discontinuous Galerkin methods for the age structured population model of marine invertebrates", Numer. Methods Partial Diff. Eqns., 25 (2009), 470 - 493.
- D. Liang, Q. Guo and S. Gong, "Wavelet Galerkin Methods for Aerosol Dynamic Equations in Atmospheric Environment", Commun. Comput. Phys., 6 (2009), 109 - 130.
- Thomas Y. Hou and D. Liang, "Multiscale analysis for convection dominated transport equations", Dis. Cont. Dyn. Sys., Ser. A, 23 (2009), 281 - 298.
- W. Chen, X. Li and D. Liang, "Symmetric Energy-Conserved Splitting FDTD Scheme for the Maxwell's Equations", Commun. Comput. Phys., 6 (2009), 804 - 825.
- D. Liang, Q. Guo and S. Gong, "A New Splitting Wavelet Method for Solving the General Aerosol Dynamics Equation, J. Aerosol Sci., 39 (2008), 467-487.
- W. Chen, X. Li and D. Liang, "Energy-conserved splitting FDTD methods for Maxwells equations", Numerische Mathematik, 108 (2008), 445 - 485.
- P. Weng, D. Liang and J. Wu, "Asymptotic Patterns of a Structured Population Diffusing in a Two-Dimensional Strip", Nonlinear Anal. - Theory Methods and Applications, 69 (2008), 3931-3951.
- L. Gao, B. Zhang and D. Liang, "Splitting Finite Difference Methods on Staggeres Grids for Three-Dimensional Time-Dependent Maxwell Equations", Commun. Comput. Phys., 4 (2008) 405 - 432.
- D. Liang, C. Du and H. Wang, "A Fractional Step ELLAM Approach to High-Dimensional Convection-Diffusion Problems with Forward Particle Tracking", J. Comput. Phys., 221 (2007), 198 - 225.
- M. Gardam, D. Liang, S.M. Moghadas, J. Wu, Q. Zeng and H. Zhu, "The Impact of Prophylaxis of Healthcare Workers on Influenza Pandemic Burden", J. Royal Soc. Interf., 4 (2007), 727 - 734.
- S. Wang, D. Liang, X. Feng and L. Ye, "A Derivative Free Optimization Algorithm based Conditional Moments", J. Math. Anal. Appl., 331 (2007), 1337-1360.
- L. Gao, B. Zhang and D. Liang, "The Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations in Two Dimensions", J. Comput. Appl. Math., 205 (2007), 207 - 230.
- D. Liang and W. Zhao, "An Optimal Weighted Upwinding Covolume Method on Nonstandard Grids for Convection-Diffusion Problems in 2D", Int. J. Numer. Methods Engng., 67 (2006), 553-577.
- D. Liang, H. Wang and R.C. Sharpley, "Finite Element Approximations to One Phase Nonlinear Free Boundary Problem in Groundwater Contamination Flow", Numer. Methods Partial Diff. Eqns., 22 (2006), 1268-1288.
- N. Vaidya H. Huang and D. Liang, "Grown-in Defects Modelling of InSb Crystals and Computation", Commun. Comput. Phys., 1 (2006), 511 - 527.
- D. Liang, J. Wu and F. Zhang, "Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions", Math. Biosci. Engng., 2 (2005), 111-132.
- D. Liang and B. Zhang, "Numerical Analysis of Graded Mesh Methods for a Class of Second Kind Integral Equations on the Real Line", J. Math. Anal. Appl., 294 (2004), 482-502.
- H. Huang, D. Liang and B. Wetton, "Computation of a Moving Drop/Bubble on a Solid Surface Using a Front-Tracking Method", Commun. Math. Sci., 2 (2004), 535-552.
- L. Gao, D. Liang and B. Zhang, "Error Estimates for Mixed Finite Element Approximations of the Viscoelasticity Wave Equation", Math. Methods Appl. Sci., 27 (2004), 1997-2016.
- D. Liang and W. Zhao, "The Weighted Upwinding Finite Volume Method for the Convection-Diffusion Problem on a Nonstandard Covolume Grid", Appl. Numer. Anal. Comput. Math., 1 (2004), 180-194.
- D. Liang and J. Wu, "Travelling Waves and Numerical Approximations in a Reaction Advection Diffusion Equation with Non-local Delayed Effects", J. Nonlinear Sci., 13 (2003), 289-310.
- H. Wang, D. Liang, R.E. Ewing, S.L. Lyons and G. Qin, "An Improved Numerical Simulator for Compressible Flows in Porous Media", Numer. Methods Partial Diff. Eqns., 19 (2003), 343-362.
- D. Liang, "Upwinding Finite Covolume Methods for Unsteady Convection-Diffusion Problems", Contemp. Math. 329, American Mathematical Society, (2003), 245-252.
- H. Wang, D. Liang, R.E. Ewing, S.L. Lyons and G. Qin, "An ELLAM approximation for highly compressible multicomponent flows in porous media", Comput. Geosci., 6 (2002), 227-251.
- W. Zhao and D. Liang, "Modified High-Order Upwind Methods for Convection Diffusion Problems", Acta Math. Appl. Sinica, (Springer), 18 (2002), 131-146.
- Y.R. Yuan, D. Liang and H. Rui, "Numerical Predicting the Consequences of Seawater Intrusion and Protection Projects", Appl. Math. Mech., (Kluwer Academic), 22 (2001), 1291-1300.
- H. Wang, D. Liang, R.E. Ewing, S.L. Lyons, G. Qin, "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 J. Sci. Comput., 22 (2000), 561-581.
- H. Wang, D. Liang, R.E. Ewing, S.L. Lyons, G. Qin, "An ELLAM-MFEM Solution Technique for Compressible Fluid Flow in Porous Media with Point Sources and Sinks", J. Comput. Phys., 159 (2000), 344-376.
- D. Liang and B. Zhang, "A Finite Element Method for a Unidimensional Single-Phase Nonlinear Free Boundary Problem in Groundwater Flow", IMA J. Numer. Anal., 19 (1999), 563-579.
- Y.R. Yuan, D. Liang and H. Rui, "The Characteristic Finite Element Methods for the Seawater Intrusion in Aquifers", Acta Math. Appl. Sin., 14 (1998), 12 - 23.
- D. Liang and W. Zhao, "The High-Order Upwind Scheme for the Convection-Diffusion Problem, Comput. Methods Appl. Mech. Engrg., 147 (1997), 105 - 115.