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., 2012, 69, 1584–1613.
  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, 2010
  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, 2008
  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 Cheby-shev 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