New additions to the Computational Geometric Mechanics group

Over the next few months, we will be welcoming two new postdoctoral scholars, a visiting scholar, and a visiting graduate student to the Computational Geometric Mechanics group at UCSD.

• Dr. Joris Vankerschaver, Ph.D. in Mathematics, Ghent University, 2007.
  
• Dr. Tomoki Ohsawa, Ph.D. in Applied and Interdisciplinary Mathematics, University of Michigan, 2010.
  
• Dr. Wencheng Li, an assistant professor of computational mathematics at Northwestern Polytechnical University in Xian, China, who will be visiting on a one year fellowship from the Chinese Scholarship Council.
  
• Cuicui Liao, a Ph.D. student in Mathematics at the Harbin Institute of Technology, who will be visiting on a one year scholarship from the Chinese Scholarship Council.
  

Preprint: Discrete Hamiltonian Variational Integrators

[ PDF | arXiv:1001.1408 [math.NA] ]

(with J. Zhang)

We consider the continuous and discrete-time Hamilton's variational principle on phase space, and characterize the exact discrete Hamiltonian which provides an exact correspondence between discrete and continuous Hamiltonian mechanics. The variational characterization of the exact discrete Hamiltonian naturally leads to a class of generalized Galerkin Hamiltonian variational integrators, which include the symplectic partitioned Runge-Kutta methods. We also characterize the group invariance properties of discrete Hamiltonians which lead to a discrete Noether's theorem.