| Books
1. Numerical Methods in Applied Sciences, W. Cai, Z.-C. Shi, C.-W. Shu and J. Xu, editors, Science Press, New York and Beijing, 1996.
2. Advanced Numerical Approximation of Nonlinear Hyperbolic Equations , B. Cockburn, C. Johnson, C.-W. Shu and E. Tadmor (Editor: A. Quarteroni), Lecture Notes in Mathematics, volume 1697, Springer, 1998.
3. Discontinuous Galerkin Methods: Theory, Computation and Applications , B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000.
4. High Order Numerical Methods for the Problems of Aerodynamics (in Russian) , V.I. Pinchukov and C.-W. Shu, Publishing House of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia, 2000.
5. Recent Advances in Scientific Computing and Partial Differential Equations , S.Y. Cheng, C.-W. Shu and T. Tang, editors, Contemporary Mathematics, volume 330, American Mathematical Society, 2003.
6. Selected New Numerical Methods for Computational Fluid Dynamics (in Chinese) , R.-X. Liu and C.-W. Shu, Science Press, Beijing, 2003. Publications in Refereed Journals (Appeared or Accepted)
1. C.-W. Shu, TVB uniformly high order schemes for conservation laws, Mathematics of Computation, v49 (1987), pp.105-121.
2. C.-W. Shu, TVB boundary treatment for numerical solutions of conservation laws, Mathematics of Computation, v49 (1987), pp.123-134.
3. C.-W. Shu, Total-Variation-Diminishing time discretizations, SIAM Journal on Scientific and Statistical Computing, v9 (1988), pp.1073-1084.
4. C.-W. Shu and S. Osher, Efficient implementation of... Books
1. Numerical Methods in Applied Sciences, W. Cai, Z.-C. Shi, C.-W. Shu and J. Xu, editors, Science Press, New York and Beijing, 1996.
2. Advanced Numerical Approximation of Nonlinear Hyperbolic Equations , B. Cockburn, C. Johnson, C.-W. Shu and E. Tadmor (Editor: A. Quarteroni), Lecture Notes in Mathematics, volume 1697, Springer, 1998.
3. Discontinuous Galerkin Methods: Theory, Computation and Applications , B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000.
4. High Order Numerical Methods for the Problems of Aerodynamics (in Russian) , V.I. Pinchukov and C.-W. Shu, Publishing House of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia, 2000.
5. Recent Advances in Scientific Computing and Partial Differential Equations , S.Y. Cheng, C.-W. Shu and T. Tang, editors, Contemporary Mathematics, volume 330, American Mathematical Society, 2003.
6. Selected New Numerical Methods for Computational Fluid Dynamics (in Chinese) , R.-X. Liu and C.-W. Shu, Science Press, Beijing, 2003. Publications in Refereed Journals (Appeared or Accepted)
1. C.-W. Shu, TVB uniformly high order schemes for conservation laws, Mathematics of Computation, v49 (1987), pp.105-121.
2. C.-W. Shu, TVB boundary treatment for numerical solutions of conservation laws, Mathematics of Computation, v49 (1987), pp.123-134.
3. C.-W. Shu, Total-Variation-Diminishing time discretizations, SIAM Journal on Scientific and Statistical Computing, v9 (1988), pp.1073-1084.
4. C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics, v77 (1988), pp.439-471.
5. B. Cockburn and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework, Mathematics of Computation, v52 (1989), pp.411-435.
6. C.-W. Shu and S. Osher, Efficient implementation of essentially non- oscillatory shock capturing schemes II, Journal of Computational Physics, v83 (1989), pp.32-78.
7. B. Cockburn, S.-Y. Lin and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one dimensional systems, Journal of Computational Physics, v84 (1989), pp.90-113.
8. W. Cai, D. Gottlieb and C.-W. Shu, Essentially non-oscillatory spectral Fourier methods for shock wave calculations, Mathematics of Computation, v52 (1989), pp.389-410.
9. B. Cockburn, S. Hou and C.-W. Shu, The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case, Mathematics of Computation, v54 (1990), pp.545-581.
10. C.-W. Shu, Numerical experiments on the accuracy of ENO and modified ENO schemes, Journal of Scientific Computing, v5 (1990), pp.127-149.
11. B. Cockburn and C.-W. Shu, The Runge-Kutta local projection P1-discontinuous Galerkin finite element method for scalar conservation laws, Mathematical Modelling and Numerical Analysis (M^2 AN), v25 (1991), pp.337-361.
12. S. Osher and C.-W. Shu, High order essentially non-oscillatory schemes for Hamilton-Jacobi equations, SIAM Journal on Numerical Analysis, v28 (1991), pp.907-922.
13. C.-W. Shu, A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting, Journal of Computational Physics v100 (1992), pp.424-429.
14. C.-W. Shu, T.A. Zang, G. Erlebacher, D. Whitaker and S. Osher, High order ENO schemes applied to two and three dimensional compressible flow, Applied Numerical Mathematics, v9 (1992), pp.45-71.
15. W. Cai, D. Gottlieb and C.-W. Shu, On one-sided filters for spectral Fourier approximations of discontinuous functions, SIAM Journal on Numerical Analysis v29 (1992), pp.905-916.
16. D. Chen, E. Kan, U. Ravaioli, C.-W. Shu and W. Dutton, An improved energy transport model including nonparabolicity and non-Maxwellian distribution effects, IEEE Electron Device Letters, v13 (1992), pp.26-28.
17. D. Gottlieb, C.-W. Shu, A. Solomonoff and H. Vandeven, On the Gibbs phenomenon I: recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function, Journal of Computational and Applied Mathematics, v43 (1992), pp.81-98.
18. W. Cai and C.-W. Shu, Uniform high order spectral methods for one and two dimensional Euler equations, Journal of Computational Physics, v104 (1993), pp.427-443.
19. W. E and C.-W. Shu, Effective equations and the inverse cascade theory for Kolmogorov flows, Physics of Fluids A, v5 (1993), pp.998-1010.
20. W. E and C.-W. Shu, A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow, Journal of Computational Physics, v110 (1994), pp.39-46.
21. B. Cockburn and C.-W. Shu, Nonlinearly stable compact schemes for shock calculations, SIAM Journal on Numerical Analysis, v31 (1994), pp.607-627.
22. G.-S. Jiang and C.-W. Shu, On cell entropy inequality for discontinuous Galerkin methods, Mathematics of Computation, v62 (1994), pp.531-538.
23. W. E and C.-W. Shu, Small scale structures in Boussinesq convection, Physics of Fluids A, v6 (1994), pp.49-58.
24. J. Casper, C.-W. Shu and H.L. Atkins, Comparison of two formulations for high-order accurate essentially non-oscillatory schemes, AIAA Journal, v32 (1994), pp.1970-1977.
25. D. Gottlieb and C.-W. Shu, Resolution properties of the Fourier method for discontinuous waves, Computer Methods in Applied Mechanics and Engineering, v116 (1994), pp.27-37.
26. Z. Chen, B. Cockburn, J. Jerome and C.-W. Shu, Mixed-RKDG finite element methods for the 2-D hydrodynamic model for semiconductor device simulation, VLSI Design, v3 (1995), pp.145-158.
27. J. Jerome and C.-W. Shu, The response of the hydrodynamic model to heat conduction, mobility, and relaxation expressions, VLSI Design, v3 (1995), pp.131-143.
28. D. Gottlieb and C.-W. Shu, On the Gibbs phenomenon IV: recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function, Mathematics of Computation, v64 (1995), pp.1081-1095.
29. C.-W. Shu and P. Wong, A note on the accuracy of spectral method applied to nonlinear conservation laws, Journal of Scientific Computing, v10 (1995), pp.357-369.
30. J. Jerome and C.-W. Shu, Transport effects and characteristic modes in the modeling and simulation of submicron devices, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, v14 (1995), pp.917-923.
31. D. Gottlieb and C.-W. Shu, On the Gibbs phenomenon V: recovering exponential accuracy from collocation point values of a piecewise analytic function, Numerische Mathematik, v71 (1995), pp.511-526.
32. D. P. Chen, R. Eisenberg, J. Jerome and C.-W. Shu,1 A hydrodynamic model of temperature change in open ionic channels, Biophysical Journal, v69 (1995), pp.2304-2322.
33. D. Gottlieb and C.-W. Shu, On the Gibbs phenomenon III: recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function, SIAM Journal on Numerical Analysis, v33 (1996), pp.280-290.
34. B. Perthame and C.-W. Shu, On positive preserving finite volume schemes for compressible Euler equations, Numerische Mathematik, v73 (1996), pp.119-130.
35. E. Harabetian, S. Osher and C.-W. Shu, An Eulerian approach for vortex motion using a level set regularization procedure, Journal of Computational Physics, v127 (1996), pp.15-26.
36. G.-S. Jiang and C.-W. Shu, Efficient implementation of weighted ENO schemes, Journal of Computational Physics, v126 (1996), pp.202-228.
37. C.-W. Shu and Y. Zeng, High order essentially non-oscillatory scheme for viscoelasticity with fading memory, Quarterly of Applied Mathematics, v55 (1997), pp.459-484.
38. G. Erlebacher, M.Y. Hussaini and C.-W. Shu, Interaction of a shock with a longitudinal vortex, with Journal of Fluid Mechanics, v337 (1997), pp.129-153.
39. D. Gottlieb and C.-W. Shu, On the Gibbs phenomenon and its resolution,, SIAM Review, v30 (1997), pp.644-668.
40. K. Siddiqi, B. Kimia and C.-W. Shu, Geometric shock-capturing ENO schemes for subpixel interpolation, computation and curve evolution,, Computer Vision Graphics and Image Processing: Graphical Models and Image Processing (CVGIP:GMIP), v59 (1997), pp.278-301.
41. S. Gottlieb and C.-W. Shu, Total variation diminishing Runge-Kutta schemes, Mathematics of Computation, v67 (1998), pp.73-85.
42. B. Cockburn and C.-W. Shu, The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems, Journal of Computational Physics, v141 (1998), pp.199-224.
43. H. Atkins and C.-W. Shu, Quadrature-free implementation of the discontinuous Galerkin method for hyperbolic equations, AIAA Journal, v36 (1998), pp.775-782.
44. G.-Q. Chen, J. Jerome and C.-W. Shu, Analysis and simulation of extended hydrodynamic models: the multi-valley Gunn oscillator and MESFET symmetries, VLSI Design, v6 (1998), pp.277-282.
45. C. Cercignani, I. Gamba, J. Jerome and C.-W. Shu, Applicability of the high field model: an analytical study via asymptotic parameters defining domain decomposition, VLSI Design, v8 (1998), pp.135-141.
46. C. Cercignani, I. Gamba, J. Jerome and C.-W. Shu, Applicability of the high field model: a preliminary numerical study, VLSI Design, v8 (1998), pp.275-282.
47. B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems, SIAM Journal on Numerical Analysis, v35 (1998), pp.2440-2463.
48. P. Montarnal and C.-W. Shu, Real gas computation using an energy relaxation method and high order WENO schemes, Journal of Computational Physics, v148 (1999), pp.59-80.
49. C. Hu and C.-W. Shu, Weighted essentially non-oscillatory schemes on triangular meshes, Journal of Computational Physics, v150 (1999), pp.97-127.
50. C. Hu and C.-W. Shu, A discontinuous Galerkin finite element method for Hamilton-Jacobi equations, SIAM Journal on Scientific Computing, v21 (1999), pp.666-690.
51. O. Lepsky, C. Hu and C.-W. Shu, The Analysis of the discontinuous Galerkin method for Hamilton-Jacobi equations, Applied Numerical Mathematics, v33 (2000), pp.423-434.
52. C. Cercignani, I. Gamba, J. Jerome and C.-W. Shu, Device benchmark comparisons via kinetic, hydrodynamic, and high-field models, Computer Methods in Applied Mechanics and Engineering, v181 (2000), pp.381-392.
53. D. Balsara and C.-W. Shu, Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy , Journal of Computational Physics , v160 (2000), pp.405-452.
54. J.-G. Liu and C.-W. Shu, A high order discontinuous Galerkin method for 2D incompressible flows , Journal of Computational Physics , v160 (2000), pp.577-596.
55. C. Cercignani, I. Gamba, J. Jerome and C.-W. Shu, A domain decomposition method for silicon devices , Transport Theory and Statistical Physics , v29 (2000), pp.525-536.
56. J.A. Carrillo, I. Gamba and C.-W. Shu, Computational macroscopic approximations to the 1-D relaxation-time kinetic system for semiconductors , Physica D , v146 (2000), pp.289-306.
57. S. Gottlieb, C.-W. Shu and E. Tadmor, Strong stability preserving high order time discretization methods , SIAM Review, v43 (2001), pp.89-112.
58. T. Zhou, Y. Guo and C.-W. Shu, Numerical study on Landau damping , Physica D, v157 (2001), pp.322-333.
59. A. Arnold, J.A. Carrillo, I. Gamba and C.-W. Shu, Low and high field scaling limits for the Vlasov and Wigner-Poisson-Fokker-Planck systems , Transport Theory and Statistical Physics, v30 (2001), pp.121-153.
60. T. Zhou, Y. Li and C.-W. Shu, Numerical comparison of WENO finite volume and Runge-Kutta discontinuous Galerkin methods , Journal of Scientific Computing, v16 (2001), pp.145-171.
61. B. Cockburn and C.-W. Shu, Runge-Kutta Discontinuous Galerkin methods for convection-dominated problems , Journal of Scientific Computing, v16 (2001), pp.173-261.
62. M. Anile, J. Carrillo, I. Gamba and C.-W. Shu, Approximation of the BTE by a relaxation-time operator: simulations for a 50nm-channel Si diode , VLSI Design , v13 (2001), pp.349-354.
63. K. Banoo, J.-H. Rhew, M. Lundstrom, C.-W. Shu and J. Jerome, Simulating quasi-ballistic transport in Si nanotransistors , VLSI Design , v13 (2001), pp.5-13.
64. J. Shi, C. Hu and C.-W. Shu, A technique of treating negative weights in WENO schemes , Journal of Computational Physics, v175 (2002), pp.108-127.
65. J. Yan and C.-W. Shu, A local discontinuous Galerkin method for KdV type equations , SIAM Journal on Numerical Analysis, v40 (2002), pp.769-791.
66. J. Yan and C.-W. Shu, Local discontinuous Galerkin methods for partial differential equations with higher order derivatives , Journal of Scientific Computing, v17 (2002), pp.27-47.
67. J. Carrillo, I. Gamba, A. Majorana and C.-W. Shu, A WENO-solver for the 1D non-stationary Boltzmann-Poisson system for semiconductor devices , Journal of Computational Electronics, v1 (2002), pp.365-370.
68. P. Lin and C.-W. Shu, Numerical solution of a virtual internal bond model for material fracture , Physica D, v167 (2002), pp.101-121.
69. J. Qiu and C.-W. Shu, On the construction, comparison, and local characteristic decomposition for high order central WENO schemes , Journal of Computational Physics, v183 (2002), pp.187-209.
70. C.-W. Shu, High order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD , International Journal of Computational Fluid Dynamics, v17 (2003), pp.107-118.
71. B. Cockburn, M. Luskin, C.-W. Shu and E. Suli, Enhanced accuracy by post-processing for finite element methods for hyperbolic equations , Mathematics of Computation, v72 (2003), pp.577-606.
72. M. Carpenter, D. Gottlieb and C.-W. Shu, On the conservation and convergence to weak solutions of global schemes , Journal of Scientific Computing, v18 (2003), pp.111-132.
73. Y.-T. Zhang and C.-W. Shu, High order WENO schemes for Hamilton-Jacobi equations on triangular meshes , SIAM Journal on Scientific Computing, v24 (2003), pp.1005-1030.
74. J.A. Carrillo, I.M. Gamba, A. Majorana and C.-W. Shu, A WENO-solver for the transients of Boltzmann--Poisson system for semiconductor devices. Performance and comparisons with Monte Carlo methods , Journal of Computational Physics, v184 (2003), pp.498-525.
75. R. Fedkiw, G. Sapiro and C.-W. Shu, Shock capturing, level sets and PDE based methods in computer vision and image processing: a review of Osher's contributions , Journal of Computational Physics, v185 (2003), pp.309-341.
76. K. Sebastian and C.-W. Shu, Multi domain WENO finite difference method with interpolation at sub-domain interfaces , Journal of Scientific Computing, v19 (2003), pp.405-438.
77. M. Zhang and C.-W. Shu, An analysis of three different formulations of the discontinuous Galerkin method for diffusion equations , Mathematical Models and Methods in Applied Sciences, v13 (2003), pp.395-413.
78. J. Shi, Y.-T. Zhang and C.-W. Shu, Resolution of high order WENO schemes for complicated flow structures , Journal of Computational Physics, v186 (2003), pp.690-696.
79. J. Qiu and C.-W. Shu, Finite difference WENO schemes with Lax-Wendroff type time discretization , SIAM Journal on Scientific Computing, v24 (2003), pp.2185-2198.
80. M. Zhang, C.-W. Shu, G.C.K. Wong and S.C. Wong, A weighted essentially non-oscillatory numerical scheme for a multi-class Lighthill-Whitham-Richards traffic flow model , Journal of Computational Physics, v191 (2003), pp.639-659.
81. Y.-T. Zhang, J. Shi, C.-W. Shu and Y. Zhou, Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high Reynolds numbers , Physical Review E, v68 (2003), article number 046709, pp.1-16.
82. J. Qiu and C.-W. Shu, Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: one dimensional case , Journal of Computational Physics, v193 (2003), pp.115-135.
83. J. Carrillo, I. Gamba, A. Majorana and C.-W. Shu, A direct solver for 2D non-stationary Boltzmann-Poisson systems for semiconductor devices: a MESFET simulation by WENO-Boltzmann schemes , Journal of Computational Electronics, v2 (2003), pp.375-380.
84. J. Ryan and C.-W. Shu, On a one-sided post-processing technique for the discontinuous Galerkin methods , Methods and Applications of Analysis, v10 (2003), pp.295-307.
85. Q. Zhang, M. Zhang, G. Jin, D. Liu and C.-W. Shu, Modeling, numerical methods and simulation for particle-fluid two phase flow problems , Computers and Mathematics with Applications, v47 (2004), pp.1437-1462.
86. Y. Guo, C.-W. Shu and T. Zhou, The dynamics of a plane diode , SIAM Journal on Mathematical Analysis, v35 (2004), pp.1617-1635.
87. B. Cockburn, F. Li and C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for the Maxwell equations , Journal of Computational Physics, v194 (2004), pp.588-610.
88. F. Li and C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for MHD equations , Journal of Scientific Computing, to appear.
89. Q. Zhang and C.-W. Shu, Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws , SIAM Journal on Numerical Analysis, v42 (2004), pp.641-666.
90. M. Zhang and C.-W. Shu, An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods , Computers and Fluids, to appear.
91. D. Levy, C.-W. Shu and J. Yan, Local discontinuous Galerkin methods for nonlinear dispersive equations , Journal of Computational Physics, v196 (2004), pp.751-772.
92. Y. Ha, C. Gardner, A. Gelb and C.-W. Shu, Numerical simulation of high Mach number astrophysical jets with radiative cooling , Journal of Scientific Computing, to appear.
93. W.-S. Don, D. Gottlieb, C.-W. Shu, O. Schilling and L. Jameson, Numerical convergence study of nearly-incompressible, inviscid Taylor-Green vortex flow , Journal of Scientific Computing, to appear.
94. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for three classes of nonlinear wave equations , Journal of Computational Mathematics, v22 (2004), pp.250-274.
95. J. Ryan, C.-W. Shu and H. Atkins, Extension of a post-processing technique for the discontinuous Galerkin method for hyperbolic equations with application to an aeroacoustic problem , SIAM Journal on Scientific Computing, to appear.
96. J. Qiu and C.-W. Shu, Runge-Kutta discontinuous Galerkin method using WENO limiters , SIAM Journal on Scientific Computing, to appear.
97. L.-L. Feng, C.-W. Shu and M. Zhang, A hybrid cosmological hydrodynamic/N-body code based on a weighted essentially non-oscillatory scheme , Astrophysical Journal, v612 (2004), pp.1-13.
98. J. Qiu and C.-W. Shu, Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method II: two dimensional case , Computers and Fluids, to appear.
99. J. Qiu and C.-W. Shu, Hermite WENO schemes for Hamilton-Jacobi equations , Journal of Computational Physics, to appear.
100. F. Li and C.-W. Shu, Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations , Applied Mathematics Letters, to appear. Publications in Refereed Book Chapters, Proceedings and Lecture Notes
1. B. Cockburn and C.-W. Shu, A new class of non-oscillatory discontinuous Galerkin finite element methods for conservation laws, Proceedings of the 7th International Conference of Finite Element Methods in Flow Problems, UAH Press, 1989, pp.977-986.
2. S. Osher and C.-W. Shu, Recent progress on non-oscillatory shock capturing schemes, in Recent Advances in Computational Fluid Dynamics, C. C. Chao, S. A. Orszag and W. Shyy, Editors, Lecture Notes in Engineering, v43 (1989), Springer-Verlag. pp.316-333.
3. S. Osher and C.-W. Shu, Recent developments in non-oscillatory shock capturing methods, in The Numerical Modelling of Nonlinear Stellar Pulsations, J.R. Buchler, editor, Kluwer Academic Publishers, 1989. pp.263- 267.
4. C. Quillen and C.-W. Shu, Parallel implementation and application of high order ENO schemes, in Modeling and Simulation Volume 23, Part 5, Proceedings of the 23rd Annual Pittsburgh Conference on Modeling and Simulation, W. Vogt and M. Mickle, editors, University of Pittsburgh, 1992. pp.2739-2746.
5. J. Jerome and C.-W. Shu, Essentially Non-Oscillatory methods for two-dimensional hydrodynamic models, in Proceedings of the International Workshop on Computational Electronics, Beckman Institute, University of Illinois, May 1992, pp.83-86.
6. C. Gardner, J. Jerome and C.-W. Shu, The ENO method for the hydrodynamic model for semiconductor devices, in High Performance Computing, 1993: Grand Challenges in Computer Simulation, Adrian Tentner, editor, the Society for Computer Simulation, San Diego, 1993. pp.96-101.
7. G.-S. Jiang and C.-W. Shu, Stability of discontinuous Galerkin methods for general triangulations, In Developments in Theoretical and Applied Mechanics, Volume XVII, edited by I.C. Jong and F.A. Akl, Louisiana Tech University and University of Arkanas, 1994, pp.227-234.
8. J. Jerome and C.-W. Shu, Energy models for one-carrier transport in semiconductor devices, in IMA Volumes in Mathematics and Its Applications, v59, W. Coughran, J. Cole, P. Lloyd and J. White, editors, Springer-Verlag, 1994, pp.185-207.
9. J. Jerome and C.-W. Shu, Transport effect, hyperbolicity, and shock capturing algorithms for device simulations, in Proceedings of the Third International Workshop on Computational Electronics, Portland, Oregon, May 18-20, 1994, pp.252-255.
10. D. Gottlieb and C.-W. Shu, The resolution of the Gibbs phenomenon, ICASE Research Quarterly, Vol. 3, No. 2, June 1994, pp.5-7.
11. C.-W. Shu, Essentially non-oscillatory finite difference, finite volume and discontinuous Galerkin finite element methods for conservation laws, in Proceedings of the Third International Colloquium on Numerical Analysis, Plovdiv, Bulgaria, August 1994. D. Bainov and V. Covachev, editors, VSP International Science Publishers, the Netherlands, 1995, pp.171-180.
12. C.-W. Shu, On finite difference and finite element shock capturing methods for conservation laws, in Numerical Methods in Applied Sciences, W. Cai, Z.-C. Shi, C.-W. Shu and J. Xu, editors, Science Press, New York and Beijing, 1996, pp.169-187.
13. J. Jerome and C.-W. Shu, Energy transport systems for semiconductors: Analysis and simulation, in World Congress of Nonlinear Analysts '92, V. Lakshmikantham, Editor, Walter de Gruyter, Berlin and New York, 1996, pp. 3835-3846.
14. C.-W. Shu and P. Wong, A numerical study on the accuracy of Fourier spectral methods applied to the nonlinear Burgers equation, in Proceedings of the Third International Conference on Spectral and High Order Methods, A.V. Ilin and L.R. Scott, Editors, Houston Journal of Mathematics, 1996, pp. 131-138.
15. C. Hu and C.-W. Shu, High order weighted ENO schemes for unstructured meshes: preliminary results, Computational Fluid Dynamics 98, Invited Lectures, Minisymposia and Special Technological Sessions of the Fourth European Computational Fluid Dynamics Conference, K. Papailiou, D. Tsahalis, J. Periaux and D. Knorzer, Editors, John Wiley and Sons, v2, September 1998, pp.356-362.
16. C. Cercignani, I. Gamba, J. Jerome and C.-W. Shu, A domain decomposition method: a simulation study, in Proceedings of 1998 Sixth International Workshop on Computational Electronics (IWCE-6), Osaka University, Japan, October 19-21, 1998, IEEE Catalog Number 98EX116.
17. C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, B. Cockburn, C. Johnson, C.-W. Shu and E. Tadmor (Editor: A. Quarteroni), Lecture Notes in Mathematics, volume 1697, Springer, 1998, pp.325-432.
18. G.-Q. Chen, J. Jerome, C.-W. Shu and D. Wang, Two carrier semiconductor device models with geometric structure, Modeling and Computation for Applications in Mathematics, Science, and Engineering, J. Jerome, editor, Oxford University Press, 1998, pp.103-140.
19. C.-W. Shu, High order ENO and WENO schemes for computational fluid dynamics, in High-Order Methods for Computational Physics, T.J. Barth and H. Deconinck, editors, Lecture Notes in Computational Science and Engineering, volume 9, Springer, 1999, pp.439-582.
20. B. Cockburn, G. Karniadakis and C.-W. Shu, The development of discontinuous Galerkin methods , in Discontinuous Galerkin Methods: Theory, Computation and Applications, B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000, Part I: Overview, pp.3-50.
21. B. Cockburn, J. Jerome and C.-W. Shu, The utility of modeling and simulation in determining transport performance properties of semiconductors , in Discontinuous Galerkin Methods: Theory, Computation and Applications, B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000, Part II: Invited Papers, pp.147-156.
22. B. Cockburn, M. Luskin, C.-W. Shu and E. Suli, Post-processing of Galerkin methods for hyperbolic problems , in Discontinuous Galerkin Methods: Theory, Computation and Applications, B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000, Part III: Contributed Papers, pp.291-300.
23. C. Hu, O. Lepsky and C.-W. Shu, The effect of least square procedure for discontinuous Galerkin methods for Hamilton-Jacobi equations , in Discontinuous Galerkin Methods: Theory, Computation and Applications, B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000, Part III: Contributed Papers, pp.343-348.
24. J.-G. Liu and C.-W. Shu, A numerical example on the performance of high order discontinuous Galerkin method for 2D incompressible flows , in Discontinuous Galerkin Methods: Theory, Computation and Applications, B. Cockburn, G. Karniadakis and C.-W. Shu, editors, Lecture Notes in Computational Science and Engineering, volume 11, Springer, 2000, Part III: Contributed Papers, pp.369-374.
25. C.-W. Shu, Different formulations of the discontinuous Galerkin method for the viscous terms , in Advances in Scientific Computing, Z.-C. Shi, M. Mu, W. Xue and J. Zou, editors, Science Press, 2001, pp.144-155.
26. C.-W. Shu, A survey of strong stability preserving high order time discretizations , in Collected Lectures on the Preservation of Stability under Discretization, D. Estep and S. Tavener, editors, SIAM, 2002, pp.51-65.
27. J.A. Carrillo, I. Gamba, O. Muscato and C.-W. Shu, Comparison of Monte Carlo and deterministic simulations of a silicon diode , in Transport in Transition Regimes, N.B. Ben Abdallah, A. Arnold, P. Degond, I. Gamba, R. Glassey, C. Levermore and C. Ringhofer, editors, IMA Volumes in Mathematics and Its Applications, v135, Springer-Verlag, New York, 2003, pp.75-84.
28. C.-W. Shu, An overview on high order numerical methods for convection dominated PDEs , in Hyperbolic Problems: Theory, Numerics, Applications, T.Y. Hou and E. Tadmor, editors, Springer-Verlag, Berlin, 2003, pp.79-88.
29. Y.-T. Zhang and C.-W. Shu, Third and fourth order weighted ENO schemes for Hamilton-Jacobi equations on 2D unstructured meshes , in Hyperbolic Problems: Theory, Numerics, Applications, T.Y. Hou and E. Tadmor, editors, Springer-Verlag, Berlin, 2003, pp.941-950.
30. L.-L. Feng, C.-W. Shu and M. Zhang, A hybrid cosmological hydrodynamic/N-body code based on the weighted essentially non-oscillatory scheme , Proceedings of the Fifth Sino-Germany Workshop on Cosmology and Galaxy Formation: The Formation, Evolution and Distribution of Galaxies, Y.P. Jing and G. Borner, editors, Prog. in Astro. (Suppl) vol 21, (2003) p18-23.
31. Y.-T. Zhang, J. Shi, C.-W. Shu and Y. Zhou, Resolution of high order WENO schemes and Navier-Stokes simulation of the Rayleigh-Taylor instability problem , in Computational Fluid and Solid Mechanics 2003, K.J. Bathe, Editor, the Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, June 17-20, 2003, volume 1, pp.1216-1218, Elsevier Science.
32. B. Cockburn, F. Li and C.-W. Shu, Discontinuous Galerkin methods for equations with divergence-free solutions: preliminary results , in Computational Fluid and Solid Mechanics 2003, K.J. Bathe, Editor, the Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, June 17-20, 2003, volume 2, pp.1900-1902, Elsevier Science. Preprints
1. S. Gottlieb, D. Gottlieb and C.-W. Shu, Recovering high order accuracy in WENO computations of steady state hyperbolic systems , preprint.
2. J. Qiu, M. Dumbser and C.-W. Shu, The discontinuous Galerkin method with Lax-Wendroff type time discretizations , submitted to Computer Methods in Applied Mechanics and Engineering.
3. F. Filbet and C.-W. Shu, Approximation of hyperbolic models for chemosensitive movement , submitted to SIAM Journal on Scientific Computing.
4. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations , submitted to Computer Methods in Applied Mechanics and Engineering.
5. D. Levy, S. Nayak, C.-W. Shu and Y.-T. Zhang, Central WENO schemes for Hamilton-Jacobi equations on triangular meshes , submitted to SIAM Journal on Scientific Computing.
6. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for nonlinear Schrodinger equations , submitted to Journal of Computational Physics.
7. Y. Xing and C.-W. Shu, High order finite difference WENO schemes with the exact conservation property for the shallow water equations , submitted to Journal of Computational Physics.
8. S. Chen, W. E and C.-W. Shu, The heterogeneous multi-scale method based on the discontinuous Galerkin method for hyperbolic and parabolic problems , submitted to Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal.
9. H. Atkins and C.-W. Shu, Analysis of preconditioning and relaxation operators for the discontinuous Galerkin method applied to diffusion , submitted to AIAA Journal.
10. J. Qiu and C.-W. Shu, A comparison of troubled cell indicators for Runge-Kutta discontinuous Galerkin methods using WENO limiters , submitted to SIAM Journal on Scientific Computing.
11. S. Chen, W. E and C.-W. Shu, The heterogeneous multi-scale method based on the discontinuous Galerkin and the finite volume methods for hyperbolic problems , submitted to the Proceedings of the Third MIT Conference on Computational Fluid and Solid Mechanics.
12. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for two classes of two dimensional nonlinear wave equations , submitted to Physica D.
13. Z. Xu and C.-W. Shu, Anti-diffusive flux corrections for high order finite difference WENO schemes , submitted to Journal of Computational Physics. |