Selected Publications
Journal Publications

Y. Cheng and C.W. Shu, A discontinuous Galerkin finite element method for directly solving the HamiltonJacobi equations, Journal of Computational Physics, v223 (2007), pp.398415.

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.699730.

Y. Cheng, I. M. Gamba, A. Majorana and C.W. Shu, Discontinuous Galerkin solver for BoltzmannPoisson transients, Journal of Computational Electronics, v7 (2008), pp.119123.

Y. Cheng and C.W. Shu, Superconvergence and time evolution of discontinuous Galerkin finite element solutions, Journal of Computational Physics, v227 (2008), pp.96129627.

Y. Cheng and C.W. Shu, Superconvergence of local discontinuous Galerkin methods for onedimensional convectiondiffusion equations, Computers and Structures, v87 (2009), pp.630641.

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.31303150.

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. 40444072.

O. Bokanowski, Y. Cheng and C.W. Shu, A discontinuous Galerkin solver for front propagation, SIAM Journal on Scientific Computing, v33 (2011), pp.923938.

Y. Cheng, I. M. Gamba and J. Proft, Positivitypreserving discontinuous Galerkin schemes for linear VlasovBoltzmann transport equations, Mathematics of Computation, v81 (2012), pp. 153190.

Y. Cheng, I. M. Gamba, A. Majorana and C.W. Shu, A brief survey of the discontinuous Galerkin method for the BoltzmannPoisson equations, SEMA Journal, v54 (2011), pp.4764.

Y. Cheng, I. M. Gamba and K. Ren, Recovering doping profiles in semiconductor devices with the BoltzmannPoisson model, Journal of Computational Physics, v230 (2011), pp. 33913412.

Y. Cheng and I. M. Gamba, Numerical study of onedimensional VlasovPoisson 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. 20522061.

Y. Cheng, I. M. Gamba and P. J. Morrison, Study of conservation and recurrence of RungeKutta discontinuous Galerkin schemes for VlasovPoisson systems, Journal of Scientific Computing, v56 (2013), pp. 319349.

O. Bokanowski, Y. Cheng and C.W. Shu, A discontinuous Galerkin scheme for front propagation with obstacles, Numerische Mathematik, v126 (2014), pp. 131.

Y. Cheng, A. J. Christlieb and X. Zhong, Energyconserving discontinuous Galerkin methods for the VlasovAmpére system, Journal of Computational Physics, v256 (2014), pp. 630655.

R. Alonso, J. Young and Y. Cheng, A particle interaction model for the simulation of biological, crosslinked fiber networks inspired from flocking theory, Cellular and Molecular Bioengineering, v7 (2014), pp. 5872.

Y. Cheng, I. M. Gamba, F. Li and P. J. Morrison, Discontinuous Galerkin methods for the VlasovMaxwell equations, SIAM Journal on Numerical Analysis, v52 (2014), pp. 10171049.

Y. Cheng and Z. Wang, A new discontinuous Galerkin finite element method for directly solving the HamiltonJacobi equations, Journal of Computational Physics, v268 (2014), pp.134153.

Y. Cheng, A. J. Christlieb and X. Zhong, Energyconserving discontinuous Galerkin methods for the VlasovMaxwell system, Journal of Computational Physics, v279 (2014), pp. 145173.

Y. Cheng, A. J. Christlieb and X. Zhong, Energyconserving numerical simulations of electron holes in twospecies plasmas, European Physical Journal D, v69 (2015), 67.

Y. Cheng, A. J. Christlieb and X. Zhong, Numerical study of the twospecies VlasovAmpére system: energyconserving schemes and the currentdriven ionacoustic instability, Journal of Computational Physics, v288 (2015), pp.6685.

O. Bokanowski, Y. Cheng and C.W. Shu, Convergence of discontinuous Galerkin schemes for front propagation with obstacles, Mathematics of Computation, v85 (2016), pp.21312159.

Y. Cheng, C.S. Chou, F. Li and Y. Xing, L2 stable discontinuous Galerkin methods for onedimensional twoway wave equations, Mathematics of Computation, v86 (2017), pp.121155.

Z. Wang, Q. Tang, W. Guo and Y. Cheng, Sparse grid discontinuous Galerkin methods for highdimensional elliptic equations, Journal of Computational Physics, v314 (2016), pp. 244263.

W. Guo and Y. Cheng, A sparse grid discontinuous Galerkin method for highdimensional transport equations and its application to kinetic simulations, SIAM Journal on Scientific Computing, to appear.

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, to appear.
Conference Proceedings

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. 257260.

Y. Cheng, I. M. Gamba, A. Majorana and C.W. Shu, A discontinuous Galerkin solver for fullband BoltzmannPoisson models, Proceeding of IWCE13 (2009), pp. 211214.

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. 211214.

Y. Cheng, I. M. Gamba, A. Majorana and C.W. Shu, Discontinuous Galerkin methods for the BoltzmannPoisson systems in semiconductor device simulations , AIP Conference Proceedings, v1333 (2011), pp. 890895.

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.99136, Springer.
Preprints

R. J. Alonso, V. Bagland, Y. Cheng and B. Lods, Onedimensional dissipative Boltzmann equation: measure solutions, cooling rate, and selfsimilar profile, submitted, 2015.

J. MoralesEscalante, I. M. Gamba, Y. Cheng, A. Majorana, C.W Shu and J. Chelikowsky, Discontinuous Galerkin deterministic solvers for a BoltzmannPoisson model of hot electron transport by averaged empirical pseudopotential band structures, submitted, 2016.

Y. Liu, Y. Cheng and C.W. Shu, A simple boundpreserving sweeping technique for conservative numerical approximations, submitted, 2016.

W. Guo and Y. Cheng, An adaptive multiresolution discontinuous Galerkin method for timedependent transport equations in multidimensions, submitted, 2016.