Research Interests

  • Efficient Numerical Methods for PDEs and Stiff ODEs

  • Inverse Modeling and Adjoint-Based Optimization

  • Computational Fluid Dynamics

  • HPC and Parallel Algorithm

    Publications


    1. W. Liao, A Strongly A-Stable Rosenbrock method for solving nonlinear parabolic PDEs, Submitted.

    2. W. Liao, PDE-constrained optimization computational method to recover Lamé parameters in an elastic wave equation, Submitted.

    3. W. Liao, High-order ADI finite difference scheme for 3D reaction-diffusion equation with Neumann boundary condition, Submitted.

    4. W. Liao, A computational method to estimate the unknown coefficient in a wave equation using boundary measurements, To appear in Inverse Problems in Science & Engineering .

    5. W. Liao, A transformation-based compact finite difference method for solving the unsteady convection-diffusion equation with low Reynolds number, To appear in International Journal for Computational Methods in Engineering Science & Mechanics.

    6. W. Liao, A numerical method to identify the acoustic coefficients in a two-dimensional wave equation, Proceedings of the 4th IEEE International Conference on Computer Science and Information Technology, Vol. 4, pp. 395 - 399, 2011.

    7. W. Liao and Y. Yan, Singly Diagonally Implicit Runge-Kutta Method for Time-Dependent Reaction-Diffusion Equation, Numerical Methods for Partial Differential Equations , vol. 27, 6, pp. 1423 - 1441, (2011).

    8. W. Liao and J. Zhu, Efficient and accurate finite difference schemes for solving one-dimensional Burgers' equation, International Journal of Computer Mathematics. vol. 88, 12, pp. 2575-2590 (2011)

    9. W. Liao, A fourth-order finite difference method for solving the system of two-dimensional Burgers' equations, International Journal for Numerical Methods in Fluids Volume 64, Issue 5, 2010, Pages 565 - 590.

    10. O. Volkov, B. Protas, W. Liao and D. Glander, Adjoint-based optimization of thermo-fluid phenomena in welding processes, Journal of Engineering Mathematics.Volume 65, Number 3, November 2009, Pages 201 - 220.

    11. W. Liao, M. Dehghan and A. Mohebbi, Direct numerical method for an inverse problem of a parabolic partial differential equation, Journal of Computational and Applied Mathematics, Volume 232, Issue 2, 15 October 2009, Pages 351-360.

    12. W. Liao and Abdul Q. M. Khaliq, High-order compact scheme for solving nonlinear Black-Scholes equations with transaction cost, International Journal of Computer Mathematics, vol. 86, 6, 2009, pp. 1009-1023.

    13. W. Liao and J. Zhu, An accurate and efficient numerical method for solving Black-Scholes equation in option pricing, International Journal of Mathematics in operational Research, vol. 1, 1, 2009, pp. 191-210.

    14. W. Liao, An implicit fourth-order compact finite difference scheme for one-dimensional Burgers' equation, Applied Mathematics and Computation, vol 206, 2(December 2008), pp. 755-764.

    15. W. Liao and J. Zhu, A new method for solving convection-diffusion equations, Proceedings of the 11th IEEE International Conference on Computational Science and Engineering, pp. 107 - 114, IEEE Computer Society, 2008.

    16. B. Protas and W. Liao, Adjoint-based optimization of PDEs in moving domains, Journal of Computational Physics, vol 227, 4 (Feburary, 2008), pp. 2707-2723.

    17. W. Liao, A. Sandu, G.R. Carmichael, and T. Chai, Total Energy Singular Vector Analysis for Atmospheric Chemical Transport Models, Monthly Weather Review, Vol. 134, No. 9, p.2443-2465, 2006.

    18. W. Liao, J. Zhu and A.Q.M. Khaliq, A fourth-order compact algorithm for nonlinear reaction-diffusion equations with Neumann boundary conditions, Numerical Methods for Partial Differential Equations, Volume 22, Issue 3, Date: May 2006, Pages: 600-616.

    19. A. Sandu, W. Liao, G.R. Carmichael, D.K. Henze, and J.H. Seinfeld, Inverse Modeling of Aerosol Dynamics using Adjoints - Theoretical and Numerical Considerations, Aerosol Science and Technology, Vol. 39 Issue 8, p677-694, Aug. 2005.

    20. A. Sandu, E.M. Constantinescu, W. Liao, G.R. Carmichael, T. Chai, J.H. Seinfeld, and D. Duaescu, Ensemble-Based Data Assimilation for Atmospheric Chemical Transport Models, Lecture Notes in Computer Science, Vol. 3515, p. 648-655, Springer-Verlag GmbH, 2005.

    21. Emil M. Constantinescu, Wenyuan Liao, and Adrian Sandu, Mesh refinement strategies in air quality modeling, High Performance Computing Symposium, 2005, pages 158-163, San Diego, CA.

    22. E.M. Constantinescu, W. Liao, and A. Sandu, On Adaptive Mesh Refinement in High Resolution Air Quality Modeling, Lecture Notes in Computer Science, Vol. 3515, p. 798-805, Springer-Verlag GmbH, 2005.

    23. W. Liao and A. Sandu, Total Energy Singular Vectors for Atmospheric Chemical Transport Models, Lecture Notes in Computer Science, Vol. 3515, p. 806-813, Springer-Verlag GmbH, 2005.

    24. D.K. Henze, J.H. Seinfeld, W. Liao, A. Sandu, G.R. Carmichael, Inverse Modeling of Aerosol Dynamics: Condensational Growth, Journal of Geophysical Research, Vol. 109, D14201, doi:10.1029/2004JD004593, 14 pages, July 2004.

    25. A. Sandu, W. Liao, G.R. Carmichael, D. Henze, J.H. Seinfeld, T. Chai, and D. Daescu, Computational Aspects of Data Assimilation for Aerosol Dynamics, Lecture Notes in Computer Science, Springer-Verlag GmbH, Vol. 3038, p. 709-716, 2004.

    26. Y. Gu, W. Liao and J. Zhu, An efficient high-order algorithm for solving systems of 3-D reaction-diffusion equations, Journal of Computational and Applied Mathematics, Volume 155, Issue 1, 1 June 2003, Pages 1-17.

    27. W. Liao, J. Zhu and A.Q.M. Khaliq, An efficient high-order algorithm for solving systems of reaction-diffusion equations, Numerical Methods for Partial Differential Equations, Volume 18 Issue 3, 2002, Pages 340-354.

    28. W. Liao and Q. Li, A class of semi-implicit multistep Runge-Kutta methods for stiff ODEs, Journal of Tsinghua University, 39 (1999), no. 6, 1-6.

    29. W. Liao and Q. Li, A class of multistep interpolation methods for solving stiff ordinary differential equations and parallel implementation, Journal on Numerical Methods and Computer Applications, 20 (1999), no. 2, 98-106.

    30. W. Liao and Q. Li, Implementation of parallel diagonal implicit Runge-Kutta algorithms of multistep Runge-Kutta methods, Journal on Numerical Methods and Computer Applications, 20 (1999), no. 1, 70-80.

    31. W. Liao and Q. Li, A class of mixed type methods for solving stiff ODEs and the parallel implementation, Tsinghua Science and Technology, 3 (1998), no. 4, 1221-1226,1232.