Publications

 

  1. 1.Y. Cheng and C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics, v223 (2007), pp.398-415.

  2. 2.Y. Cheng and C.-W. Shu, A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives, Mathematics of Computation, v77 (2008), pp.699-730.

  3. 3.Y. Cheng, I. M. Gamba, A. Majorana and C.-W. Shu, Discontinuous Galerkin solver for Boltzmann-Poisson transients, Journal of Computational Electronics, v7 (2008), pp.119-123.

  4. 4.Y. Cheng and C.-W. Shu, Superconvergence and time evolution of discontinuous Galerkin finite element solutions, Journal of Computational Physics, v227 (2008), pp.9612-9627.

  5. 5.Y. Cheng and C.-W. Shu, Superconvergence of local discontinuous Galerkin methods for one-dimensional convection-diffusion equations, Computers and Structures, v87 (2009), pp.630-641.

  6. 6.Y. Cheng, I. M. Gamba, A. Majorana and C.-W. Shu, A discontinuous Galerkin solver for Boltzmann Poisson systems in nano devices, Computer Methods in Applied Mechanics and Engineering, v198 (2009), pp.3130-3150.

  7. 7.Y. Cheng and C.-W. Shu, Superconvergence of discontinuous Galerkin and local discontinuous Galerkin schemes for linear hyperbolic and convection diffusion equations in one space dimension, SIAM Journal on Numerical Analysis, v47 (2010), pp. 4044-4072.

  8. 8.O. Bokanowski, Y. Cheng and C.-W. Shu, A discontinuous Galerkin solver for front propagation, SIAM Journal on Scientific Computing, v33 (2011), pp.923-938.

  9. 9.Y. Cheng, I. M. Gamba and J. Proft, Positivity-preserving discontinuous Galerkin schemes for linear Vlasov-Boltzmann transport equations, Mathematics of Computation, v81 (2012), pp. 153-190.

  10. 10.Y. Cheng, I. M. Gamba, A. Majorana and C.-W. Shu, A brief survey of the discontinuous Galerkin method for the Boltzmann-Poisson equations, SEMA Journal, v54 (2011), pp.47-64.

  11. 11.Y. Cheng, I. M. Gamba and K. Ren, Recovering doping profiles in semiconductor devices with the Boltzmann-Poisson model, Journal of Computational Physics, v230 (2011), pp. 3391-3412.

  12. 12.Y. Cheng and I. M. Gamba, Numerical study of one-dimensional Vlasov-Poisson equations in the simulation for infinite homogeneous stellar systems, Communications in Nonlinear Science and Numerical Simulation (Special Issue dedicated to P. J. Morrison’s 60th Birthday), v17 (2011), pp. 2052-2061.

  13. 13.Y. Cheng, I. M. Gamba and P. J. Morrison, Study of conservation and recurrence of Runge-Kutta discontinuous Galerkin schemes for Vlasov-Poisson systems, Journal of Scientific Computing, v56 (2013), pp. 319-349.

  14. 14.O. Bokanowski, Y. Cheng and C.-W. Shu, A discontinuous Galerkin scheme for front propagation with obstacles, Numerische Mathematik, v126 (2014), pp. 1-31.

  15. 15.Y. Cheng, A. J. Christlieb and X. Zhong, Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampére system, Journal of Computational Physics, v256 (2014), pp. 630-655.

  16. 16.R. Alonso, J. Young and Y. Cheng, A particle interaction model for the simulation of biological, cross-linked fiber networks inspired from flocking theory, Cellular and Molecular Bioengineering, v7 (2014), pp. 58-72.

  17. 17.Y. Cheng, I. M. Gamba, F. Li and P. J. Morrison, Discontinuous Galerkin methods for the Vlasov-Maxwell equations, SIAM Journal on Numerical Analysis, v52 (2014), pp. 1017-1049.

  18. 18.Y. Cheng and Z. Wang, A new discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics, v268 (2014), pp.134-153.

  19. 19.Y. Cheng, A. J. Christlieb and X. Zhong, Energy-conserving discontinuous Galerkin methods for the Vlasov-Maxwell system, Journal of Computational Physics, v279 (2014), pp. 145-173.

  20. 20.Y. Cheng, A. J. Christlieb and X. Zhong, Energy-conserving numerical simulations of electron holes in two-species plasmas, European Physical Journal D, v69 (2015), 67.

  21. 21.Y. Cheng, A. J. Christlieb and X. Zhong, Numerical study of the two-species Vlasov-Ampére system: energy-conserving schemes and the current-driven ion-acoustic instability, Journal of Computational Physics, v288 (2015), pp.66-85.

  22. 22.O. Bokanowski, Y. Cheng and C.-W. Shu, Convergence of discontinuous Galerkin schemes for front propagation with obstacles, Mathematics of Computation, v85 (2016), pp.2131-2159.

  23. 23.Y. Cheng, C.-S. Chou, F. Li and Y. Xing, L2 stable discontinuous Galerkin methods for one-dimensional two-way wave equations, Mathematics of Computation, v86 (2017), pp.121-155.

  24. 24.Z. Wang, Q. Tang, W. Guo and Y. Cheng, Sparse grid discontinuous Galerkin methods for high-dimensional elliptic equations, Journal of Computational Physics, v314 (2016), pp. 244-263.

  25. 25.W. Guo and Y. Cheng, A sparse grid discontinuous Galerkin method for high-dimensional transport equations and its application to kinetic simulations, SIAM Journal on Scientific Computing, v38 (2016), pp. A3381-A3409.

  26. 26.Y. Cheng, A. J. Christlieb, W. Guo and B. Ong, An asymptotic preserving Maxwell solver resulting in Darwin limit of electrodynamics, Journal of Scientific Computing, v71 (2017), pp. 959-993.

  27. 27.Y. Liu, Y. Cheng and C.-W. Shu, A simple bound-preserving sweeping technique for conservative numerical approximations, Journal of Scientific Computing, v73 (2017), pp. 1028-1071.

  28. 28.J. Morales-Escalante, I. M. Gamba, Y. Cheng, A. Majorana, C.-W Shu and J. Chelikowsky, Discontinuous Galerkin deterministic solvers for a Boltzmann-Poisson model of hot electron transport by averaged empirical pseudopotential band structures, Computer Methods in Applied Mechanics and Engineering, v321 (2017), pp. 209-234.

  29. 29.W. Guo and Y. Cheng, An adaptive multiresolution discontinuous Galerkin method for time-dependent transport equations in multi-dimensions, SIAM Journal on Scientific Computing, v39 (2017), pp. A2962–A2992.

  30. 30.V. A. Bokil, Y. Cheng, Y. Jiang and F. Li, Energy stable discontinuous Galerkin methods for Maxwell’s equations in nonlinear optical media, Journal of Computational Physics, v350 (2017), pp. 420-452.

  31. 31.R. J. Alonso, V. Bagland, Y. Cheng and B. Lods, One-dimensional dissipative Boltzmann equation: measure solutions, cooling rate, and self-similar profile, SIAM Journal on Mathematical Analysis, v50 (2018), pp. 1278-1321.

  32. 32.V. A. Bokil, Y. Cheng, Y. Jiang, F. Li and P. Sakkaplangkul, High spatial order energy stable FDTD methods for Maxwell’s equations in nonlinear optical media, Journal of Scientific Computing, v77 (2018), pp. 330-371.

  33. 33.A. Chen, F. Li and Y. Cheng, An ultra-weak discontinuous Galerkin method for Schrodinger equation in one dimension, Journal of Scientific Computing, v78 (2019), pp. 772-815.

  34. 34.P. Fu, Y. Cheng, F. Li and Y. Xu, Discontinuous Galerkin methods with optimal $L^2$ accuracy for PDEs with high order spatial derivatives, Journal of Scientific Computing, v78 (2019), pp. 816-863.

  35. 35.Z. Tao, W. Guo and Y. Cheng, Sparse grid discontinuous Galerkin methods for the Vlasov-Maxwell system, Journal of Computational Physics, to appear.

  36. 36.Y. Liu, Y. Cheng, S. Chen and Y.-T. Zhang, Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations, Journal of Computational Physics, to appear.

  37. 37.Z. Tao, A. Chen, M. Zhang and Y. Cheng, Sparse grid central discontinuous Galerkin method for linear hyperbolic systems in high dimensions, SIAM Journal on Scientific Computing, to appear.

  38. 38.Y. Jiang, P. Sakkaplangkul, V. A. Bokil, Y. Cheng and F. Li, Dispersion analysis of finite difference and discontinuous Galerkin schemes for Maxwell's equations in linear Lorentz media, Journal of Computational Physics, to appear.

  1. 1.Y. Cheng, I. M. Gamba, A. Majorana and C.-W. Shu, Discontinuous Galerkin solver for the semiconductor Boltzmann equation, SISPAD 07, T. Grasser and S. Selberherr, editors, Springer (2007) pp. 257-260.

  2. 2.Y. Cheng, I. M. Gamba, A. Majorana and C.-W. Shu, A discontinuous Galerkin solver for full-band Boltzmann-Poisson models, Proceeding of IWCE13 (2009), pp. 211-214.

  3. 3.Y. Cheng, I. M. Gamba, A. Majorana and C.-W. Shu, Performance of Discontinuous Galerkin Solvers for Semiconductor Boltzmann Equations, Proceeding of IWCE14 (2010), pp. 211-214.

  4. 4.Y. Cheng, I. M. Gamba, A. Majorana and C.-W. Shu, Discontinuous Galerkin methods for the Boltzmann-Poisson systems in semiconductor device simulations , AIP Conference Proceedings, v1333 (2011), pp. 890-895.

  5. 5.Y. Chen, Z. Chen, Y. Cheng, A. Gillman and F. Li, Study of discrete scattering operators for some linear kinetic models, the IMA Volumes in Mathematics and its Applications, v160 (2016), Susanne Brenner Ed): Topics in Numerical Partial Differential Equations and Scientific Computing, pp.99-136, Springer.

Journal Publications

Conference Proceedings

Preprints: Preprints on Arxiv


  1. 1.Z. Peng, Y. Cheng, J.-M. Qiu and F. Li, Stability-enhanced AP IMEX-LDG schemes for linear kinetic transport equations under a diffusive scaling, 2018.

  2. 2.Y. Cheng, J. Huang, X. Li and L. Xu, An interior penalty discontinuous Galerkin method for the time-domain acoustic-elastic wave interaction problem, 2019.

  3. 3.Z. Peng, V. Bokil, Y. Cheng and F. Li, Asymptotic and positivity preserving methods for Kerr-Debye model with Lorentz dispersion in one dimension, 2019.

  4. 4.A. Chen, Y. Cheng, Y. Liu and M. Zhang, Superconvergence of ultra-weak discontinuous Galerkin methods for the linear Schrodinger equation in one dimension, 2019.

  5. 5.J. Huang and Y. Cheng, An adaptive multiresolution discontinuous Galerkin method with artificial viscosity for scalar hyperbolic conservation laws in multidimensions, 2019.

  6. 6.M. Jiao, Y. Cheng, Y. Liu and M. Zhang, Central discontinuous Galerkin methods for the generalized Korteweg-de Vries equations, 2019.


 

Last update: 2019