hu yucheng
      Yucheng Hu's Homepage

      Department of Scientific & Engineering Computing
      School of Mathematical Sciences
      Peking University, 100871
      P.R. China

      Email : Huyc@pku.edu.cn

    Brief CV (pdf)
  • 2001-2005 B.S. at Beijing University
  • 2005-present Ph.D. program at Beijing University, Adviser Dr. Tiejun Li

    • Thesis (in Chinese): 化学反应随机动力学的数值模拟方法 (pdf, defence ppt)
    Research
  • Stochastic Chemical Kinetic Systems
  • Stochastic Modeling and Simulation
    Activities
  • Singapore Summer School, July 24 - Augest 15
  • China Meeting of Numerical Mathematics, in Gui Yang, July 19-23
  • EASIAM 2009, in Brunei, June 7-12
    Publications
  • Yucheng Hu, Tiejun Li and Bin Min Local truncation error analysis of tau-leaping methods: revisited, Submitted.
  • Assyr Abdulle, Yucheng Hu and Tiejun Li, Chebyshev methods with discrete noise: the tau -ROCK methods, Submitted.
  • Yucheng Hu and Tiejun Li, Highly Accurate Tau-leaping Methods with Random Corrections, J. Chem. Phys., Vol.130, Issue 12., 2009 (PDF)
      • Abstract: We aim to construct higher order tau-leaping methods for numerically simulating stochastic chemical kinetic systems in this paper. By adding a random correction to the primitive tau-leaping scheme in each time step, we greatly improve the accuracy of the tau-leaping approximations. This gain in accuracy actually comes from the reduction of the local truncation error of the scheme by order of τ, the marching time stepsize. While the local truncation error of the primitive tau-leaping method is O(τ2) for all moments, our Poisson random correction tau-leaping method, in which the correction term is a Poisson random variable, can reduce the local truncation error for the mean to O(τ3), and both Gaussian random correction tau-leaping methods, in which the correction term is a Gaussian random variable, can reduce the local truncation error for both the mean and covariance to O(τ3). Numerical results demonstrate that these novel methods more accurately capture crucial properties such as the mean and variance than existing methods for simulating chemical reaction systems. This work constitutes a first step to construct high order numerical methods for simulating jump processes. With further refinement and appropriately modified step-size selection procedures, the random correction methods should provide a viable way of simulating chemical reaction systems accurately and efficiently.
  • Yucheng Hu, Xiang Peng, Tiejun Li and Hong Guo, On the Poisson Approximation to Photon Distribution for Faint Lasers, Phys. Lett. A, 367, 173-176, 2007. (PDF)
      • Abstract: The photon number statistics for attenuated faint laser pulses is quantitatively studied. It confirms that, even for a non-Poissonian laser source, after being attenuated into faint laser with ultra-low mean photon number, the photon number distribution would approximately be a Poisson distribution. The error of such an approximation is estimated, and numerical tests verify our theoretical analysis. This work lays a sound mathematical foundation for the well-known intuitive idea which has been widely used in quantum cryptography.
  • Wang Ming, Xu Jinchao and Hu Yucheng, Modified Morley Element Method for a Fourth Order Elliptic Singular Perturbation Problem, J COMPUT MATH, 24, 2, 113-120, 2006.
      • Abstract: This paper proposes a modified Morley element method for a fourth order elliptic singular perturbation problem. The method also uses Morley element or rectangle Morley element, but linear or bilinear approximation of finite element functions is used in the lower part of the bilinear form. It is shown that the modified method converges uniformly in the perturbation parameter.
    Links