Course Information

• MATH3241/EECS3121, Numerical Methods I , Fall 2020/2021, Tuesdays and Thursdays, 1:00p.m.-2:30p.m
  
• MATH6651/PHYS5070A/MATH4141, Advanced Numerical Methods , Fall 2020/2021, Tuesdays and Thursdays, 2:30p.m. - 4:00p.m.
  

Research Interests

• Numerical Analysis & Scientific Computing
  
• Computational Fluid Dynamics & Porous Media Flow
  
• Environmental Computation & Energy Simulation
  
• Computational Electromagnetics & Nonlinear Wave Propogation
  

Editorial Members

• International Journal of Numerical Analysis & Modeling

Recent Academic Activites

1. 2019 CMS Winter Meeting - Canadian Mathematical Society , December 6 - 9, 2019, at Toronto
   
2. The V AMMCS International Conference (AMMCS2019) , August 18 - 23, 2019, at Waterloo
   
3. The 5th International Conference on Water Resource and Environment (WRE 2019) , July 16 - 19, 2019, Macao
   
4. International Conference on Mathematical Modeling and Numerical Methods (ICMMNM 2019) , May 30 - June 2, 2019, at Qingdao, China
   
5. The 11th International Conference on Scientific Computing and Applications (ICSCA 2019) , May 27 - 30, 2019, at Xiamen, China
   
6. Symposium on Advanced Numerical Methods and Applications in Science and Engineering , January 22, 2019, York University
   
7. ICERM: Computational Aspects of Time Dependent Electromagnetic Wave Problems in Complex Materials , June 25 - 29, 2018, at Brown University, USA
   
8. Workshop on High Accuracy and Conservative Schemes for PDEs , June 9 - 11, 2018, at Qingdao, China
   
9. The IV AMMCS International Conference (AMMCS2017) , Aug 20 - 25, 2017, at Waterloo
   
10. International Workshop on Computational Mathematics and Scientific Computing (IWCMSC2017) , June 28 - July 02, 2017, Qingdao, China
    
11. The Third International Conference on Engineering and Computational Mathematics (ECM 2017) , May 31 - June 2, 2017, at Hong Kong
    
12. BIRS workshop: Modelling and Simulation: Practical Engineering Applications, Sept 1 - 3, 2017, at Banff.
13. The Tenth International Conference on Scientific Computing and Applications (ICSCA2016) , June 6 - 10, 2016, at the Fields Institute, Toronto
    
14. The International Workshop on Mathematical Analysis of Metamaterials and Applications (MAMA 2016) , Dec 5 - 10, 2016, at Math Sci Center of Tsinghua Univ., Sanya, China
    
15. The annual confernce of CSIAM 2016 , August 12 - 14, 2016, Xiangtan, Hunan, China
    
16. The Satellite Meeting of ICIAM2015: "Recent Developments in Computational Mathematics and Applications", August 3 - 8, 2015, Jing Gang Shan Univ, Jiangxi, China
    
17. High Performance and Parallel Computing Program , January 1 - March 31, 2015, National University of Singapore, Singapore
    
18. 8th International Conference on Nonlinear PDEs & Their Numerical Analysis, May 24 - 28, 2015, Hangzhuo, China
19. Int'l Conf on Computational Mathematics and Sciences, June 6 - 8, 2015, Xian, China
    
20. ADVCOMP 2015: The Ninth International Conference on Advanced Engineering Computing and Applications in Sciences, July 19 - 24, 2015, Nice, France
    

Selected Publications ( more )

1. J. Xie, D. Liang, Z. Zhang, (2021), Energy-preserving local mesh-refined splitting FDTD schemes for two dimensional Maxwell's equations, J. Comput. Phys., 425, 109896.
   
2. S. Sriskandarajah, D. Liang, H.M. Zhu, (2021), Using the EC-S-FDTD Scheme to Approximate Eddy Currents Induced by Z-Gradient Coils, IEEE Trans. Antennas Propagat., DOI: 10.1109/TAP.2020.3048550.
   
3. B. Hou, D. Liang, (2020), Energy-preserving time high-order AVF compact finite difference schemes for nonlinear wave equations with variable coefficients, J. Comput. Phys., 421, 109738.
   
4. D. Liang and Z. Zhou, (2020), The conservative splitting domain decomposition method for multicomponenet contamination flows in porous media, J. Comput. Phys., 400, 108974, 1-27.
   
5. K. Fu and D. Liang, (2019), A Mass-Conservative Temporal Second Order and Spatial Fourth Order Characteristic FV Method for Atmospheric Pollution Advection Diffusion Problems, SIAM J. Sci. Comput., 41, B1178-B1210.
   
6. W. Li and D. Liang, (2019), The Energy Conservative Splitting FDTD scheme and its Energy Identities for Metamaterial Electromagnetic Lorentz System, Comput. Phys. Commun., 239, 94-111.
   
7. K. Fu, D. Liang, (2017), The Time Second Order Mass Conservative Characteristic FDM for Advection-Diffusion Equations in High Dimensions, J. Sci. Comput., 73, 26 - 49.
   
8. Z. Zhou, D. Liang, (2017), The mass-preserving and modified-upwind splitting DDM scheme for time-dependent convection-diffusion equations, J. Comput. Appl. Math. , 317, 247 - 273.
   
9. D. Liang, K. Fu and W. Wang, (2016), Modelling multi-component aerosol transport problems by the efficient splitting characteristic method, Atmos. Environ., 144, 297-314.
   
10. K. Fu and D. Liang, (2016), The conservative characteristic FD methods for atmospheric aerosol transport problems, J. Comput. Phys., 305, 494-520.
    
11. D. Liang and C. Du, (2014), The Efficient S-DDM Scheme and its Analysis for Solving Parabolic Equations, J. Comput. Phys., 272, 46-69.
    
12. D. Liang and Q. Yuan, (2013), The spatial fourth-order energy-conserved S-FDTD scheme for Maxwell's equations, J. Comput. Phys., 243, 344-364.
    
13. 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 J. Appl. Math., 77, 516-545.
    
14. C. Du and D. Liang, (2010), An Efficient S-DDM Iterative Approach for Compressible Contamination Fluid Flows in Porous Media, J. Comput. Phys., 229, 4501-4521.
    
15. W. Chen, X. Li and D. Liang, (2010), Energy-conserved Splitting Finite Difference Time Domain Methods for Maxwell's Equations in Three Dimensions, SIAM J. Numer. Anal., 48, 1530-1554.
    
16. Y. Cheng, D. Liang, W. Wang, S. Gong and M. Xue, (2010), An Efficient Approach of Aerosol Thermodynamic Equilibrium Predictions by the HDMR Method, Atmos. Environ., 44, 1321-1330.
    
17. D. Liang, W. Wang and Y. Cheng, (2009), An Efficient Second Order Characteristic Finite Element Method for Nonlinear Aerosol Dynamic Equations, Int. J. Numer. Methods Engng., 80, 338-354.
    
18. D. Liang, Q. Guo and S. Gong, (2008), A New Splitting Wavelet Method for Solving the General Aerosol Dynamics Equation, J. Aerosol Sci., 39, 467-487.
    
19. W. Chen, X. Li and D. Liang, (2008), Energy-Conserved Splitting FDTD Methods for Maxwell's Equations, Numerische Mathematik, 108, 445-485.
    
20. D. Liang, C. Du and H. Wang, (2007), A Fractional Step ELLAM Approach to High-Dimensional Convection-Diffusion Problems with Forward Particle Tracking, J. Comput. Phys., 221, 198-225.
    
21. D. Liang and W. Zhao, (2006), An Optimal Weighted Upwinding Covolume Method on Nonstandard Grids for Convection-Diffusion Problems in 2D , Int. J. Numer. Methods Engng., 67, 553-577.
    
22. D. Liang and J. Wu, (2003), Travelling Waves and Numerical Approximations in a Reaction Advection Diffusion Equation with Non-local Delayed Effects, J. Nonlinear Sci., 13, 289-310.
    
23. H. Wang, D. Liang, R.E. Ewing, S.L. Lyons and 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 J. Sci. Comput., 22, 561-581.
    
24. H. Wang, D. Liang, R.E. Ewing, S.L. Lyons and G. Qin, (2000), An ELLAM-MFEM Solution Technique for Compressible Fluid Flow in Porous Media with Point Sources and Sinks, J. Comput. Phys., 159, 344-376.
    
25. D. Liang and B. Zhang, (1999), A Finite Element Method for a Unidimensional Single-Phase Nonlinear Free Boundary Problem in Groundwater Flow, IMA J. Numer. Anal., 19, 563-579.