Research Interest

Numerical analysis, scientific computing, applied mathematics.

• Design and analysis of discontinuous Galerkin finite element methods.
• Design simple and compact WENO limiters for discontinuous Galerkin methods.
• Deterministic numerical simulations of kinetic transport, with applications in plasma physics.
• High order computational methods, including finite difference and finite volume WENO methods, spectral methods.
• Uncertainty quantification and stochastic computations.

Publications and Preprints

Publications in Refereed Journals (Appeared or Accepted)

1.    X.  Zhong and C.-W.  Shu, Numerical resolution of discontinuous Galerkin methods for time dependent wave equations, Computer Methods in Applied Mechanics and Engineering, v200 (2011), pp. 2814-2827.

2.    X.  Zhong and C.-W.  Shu, A simple weighted essentially nonoscillatory limiter for Runge-Kutta discontinuous Galerkin methods, Journal of Computational Physics, v232 (2012), pp. 397-415.

3.    W. Guo, X. Zhong and J.-M. Qiu,  Superconvergence of discontinuous Galerkin method: eigen-structures analysis based on Fourier approach, Journal of Computational Physics, v235 (2013), pp. 458-485.

4.    J. Zhu, X. Zhong, C.-W. Shu and J.X. Qiu, Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes,  Journal of Computational Physics, v248 (2013), pp. 200-220.

5.    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.

6.    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.

7.    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), pp. 1-19.

8.    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.

9.    W. Guo, R. D. Nair, X. Zhong*, An efficient WENO limiter for discontinuous Galerkin transport scheme on the cubed sphere, International Journal for Numerical Methods in Fluids, to appear.

10.  J. Zhu, X. Zhong, C.-W. Shu and J.X. Qiu, Runge-Kutta discontinuous Galerkin method with a simple and compact Hermite WENO limiter,  Communications in Computational Physics, accepted.

Technical Reports and Preprints

11. T. Chen, N. Gewecke, Z. Li, A.C. Rubiano, R. Shuttleworth, B. Yang and X. Zhong, Fast Computational Methods for Reservoir Flow Models, IMA Preprint Series 2286 (2009).

12. J. Zhu, X. Zhong, C.-W. Shu and J.X. Qiu, Runge-Kutta discontinuous Galerkin method with a simple and compact Hermite WENO limiter on unstructured meshes, submitted.