Home » Publications » 2007-2012
  1. H.B. Chen, C.B. Miao, X.Q. Lv, A three-dimensional numerical internal tidal model involving adjoint method, Int. J. Numer. Meth. Fl., 69, 1584–1613, 2012.
  2. W.S. Don, G. Jacobs, A. Gregorio, J.P. Suarez, Assessing the Performance of a Three Dimensional Hybrid Central-WENO Finite Difference Scheme with Computation of a Sonic Injector in Supersonic Cross Flows, AAMM 4 (6): 719-736, 2012
  3. G.B. Jacobs, W.S. Don, T. Dittmann, High-Order Resolution Eulerian-Lagrangian Simulations of Particle Dispersion in the Accelerated Flow behind a Moving Shock, Theor. Comput. Fluid. Dynam. 26: 37-50, 2012
  4. R.V. Namm, G. Woo, S.S. Xie, S. Yi, Solution of semicoercive signorini problem based on a duality scheme with modified Lagrangian functional, J. Korean Math. Soc., 49(4): 843-854, 2012
  5. 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: 43-56, 2012
  6. H. Wang, H. Tian, A fast Galerkin method with efficient matrix assembly and storage for a Peridynamic model, J. Comput. Phys., 231: 7730-7738, 2012
  7. S.S. Xie, P. Li, Z. Gao, H. Wang, High order compact finite difference schemes for a system of third order boundary value problem, Appl. Math. Comp. 219: 2564-2573, 2012
  8. S.Y. Hao, S.S. Xie, S. Yi, The Galerkin method for the KdV equation using a new basis of smooth  piecewise cubic polynomials, Appl. Math. Comp., 218: 8659-8671, 2012
  9. S.S. Xie, S. Yi, T.I. Kwon, Fourth-order compact difference and alternating direction implicit schemes for telegraph equations, Comp. Phy. Comm., 183: 552-569, 2012
  10. Z. Gao, W.S. Don, Z.Q. Li, High order weighted essentially non-oscillation schemes for two-dimensional detonation wave simulations, J. Sci. Comput. 53: 80-101, 2012
  11. W.T. Long, D. Xu, X.Y. Zeng, Quasi-wavelet based numerical method for a class of partial integro-differential equation, Appl. Math. Comput., 218(24): 11842-11850, 2012.
  12. M. Castro, B. Costa, W.S. Don, High Order Weighted Essentially Non-Oscillatory WENO-Z schemes for Hyperbolic Conservation Laws, J. Comput. Phys. 230 (5): 1766-1792, 2011 (The 22nd most cited paper published in 2011)
  13. Z. Gao, W.S. Don, Z.Q. Li, High order weighted essentially non-oscillation schemes for one-dimensional detonation wave simulations, J. Comput. Math. 29 (6): 623-638, 2011
  14. S.L. Zhang, Z. Gao, D.X. Piao, Pseudo-almost periodic viscosity solutions of second-order nonlinear parabolic equations, Nonlinear Analysis: TMA 74: 6970-6980, 2011
  15. Z. Gao, Jan S. Hesthaven, Efficient solution of ordinary differential equations with high dimensional parametrized uncertainty, Commun. Comput. Phys. 10: 253-278, 2011
  16. Z. Gao, S.S. Xie, Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schodinger equations, Appl. Numer. Math. 61: 593-614, 2011
  17. M.L. Liu, Z. Gao, Jan S. Hesthaven, Adaptive sparse grid algorithms with Applications to electromagnetic scattering under uncertainty, Appl. Numer. Math. 61: 24-37, 2011
  18. A. Solomonoff, W.S. Don, Reduction of Linear Systems of ODEs with Optimal Replacement Variables, Commun. Comput. Phys. 9 (3): 756-779, 2011
  19. L.F. Wang, W.H. Ye, W.S. Don, Z.M. Sheng, Y.J. Li, X.T. He, Formation of large-scale structures in ablative Kelvin-Helmholtz instability, Phys. Plasmas. 17 (12): 1-9, 2010
  20. L.F. Wang, W.H. Ye, Z.M. Sheng, W.S. Don, Y.J. Li, X.T. He, Preheating ablation effects on the Rayleigh-Taylor instability in the weakly nonlinear regime, Phys. Plasmas. 17 (12): 1-8, 2010
  21. Z. Gao, Jan S. Hesthaven, On ANOVA expansions and strategies for choosing the anchor point, Appl. Math. Comp. 217: 3274-3285, 2010
  22. S.S. Xie, G.X. Li, S. Yi, S.Y. Heo, A compact finite difference method for solving Burgers equation, Int. J. Numer. Meth. Fluids, 62: 747-764, 2010
  23. S.S. Xie, G.X. Li, S. Yi, Compact Finite Difference Schemes with High Accuracy for One-dimensional Nonlinear Schrodinger Equation, Comput. Methods Appl. Mech. Engrg., 198(9-12): 1052-1060, 2009
  24. J.H. Jung, W.S. Don, Collocation Methods for Hyperbolic Partial Differential Equations with Singular Sources, AAMM 1 (6): 769-780, 2009
  25. W.S. Don, D. Gottlieb, J.H. Jung, A weighted multi-domain spectral penalty method with inhomogeneous grid for supersonic injective cavity flows, Commun. Comput. Phys. 5: 986-1011, 2009
  26. G. Jacobs, W.S. Don, A high-order WENO-Z finite difference based particle-source-in-cell method for computation of particle-laden flows with shocks, J. Comput. Phys. 228: 1365-1379, 2009
  27. R. Borges, M. Carmona, B. Costa, W.S. Don, An Improved Weighted Essentially Non-Oscillatory Scheme for Hyperbolic Conservation Laws, J. Comput. Phys. 227: 3191-3211, 2008 (The eighth most cited paper published in 2008)
  28. S.S. Xie, S. Kim, G. Woo, S. Yi, A Numerical Method for Generalized Regularized Long Wave Equation Using Reproducing Kernel Function, SIAM J. Sci. Comput., 30(5): 2263-2285, 2008
  29. S.S. Xie, S. Heo, S. Kim, G. Woo, S. Yi, Numerical Solution of One Dimensional Burgers Using Reproducing Kernel Function, J. Comput. Appl. Math., 214: 417-434, 2008
  30. B. Costa, W.S. Don, A. Simas, Spatial Resolution Properties of Mapped Spectral Chebyshev Methods, Proceeding of 2005 International Conference on Scientific Computing and Partial Differential Equations (SCPDF05), Recent Progress in Scientific Computing, eds. Wenbin Liu, Michael Ng, Zhong-Ci Shi, Science press, Beijing, pp. 179-188, 2007
  31. O. Schilling, M. Latini, W.S. Don, Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability, Phys. Rev. E 76 (026319): 1-18, 2007
  32. M. Latini, O. Schilling, W.S. Don, High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability. Comparison to experimental data and to amplitude growth model predictions, Phys. Fluids 19, 024104: 1-19, 2007
  33. M. Latini, O. Schilling, W.S. Don, Effects of order of WENO flux reconstruction and spatial resolution on reshocked two-dimensional Richtmyer-Meshkov instability, J. Comput. Phys. 221 (2): 805-836, 2007
  34. B. Costa, W.S. Don, Multi-Domain Hybrid Spectral-WENO Methods for Hyperbolic Conservation Laws, J. Comput. Phys. 224 (2): 970-991, 2007
  35. B. Costa, W.S. Don, High Order Hybrid Central-WENO Finite Difference Methods for Conservation Laws, J. Comput. Appl. Math. 204 (2): 209-218, 2007
  36. M.S. Min, M.S. Kaber, W.S. Don, Fourier-Pade approximations and filtering for the spectral simulations of incompressible Boussinesq convection problem, Publications du Laboratorie Jacques-Louis Lions, R03021, Math. Comput. 76: 1275-1290, 2007