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Volume 42 Issue 8
Aug.  2016
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Journal of Beijing University of Aeronautics and Astronautics  > 2016  >  42(8): 1682-1690.
ZHU Shuai, ZHOU Gang, LIU Xiaomei, et al. Symplectic weighted discontinuous Galerkin method with minimal phase-lag[J]. Journal of Beijing University of Aeronautics and Astronautics, 2016, 42(8): 1682-1690. doi: 10.13700/j.bh.1001-5965.2015.0523(in Chinese)
Citation: ZHU Shuai, ZHOU Gang, LIU Xiaomei, et al. Symplectic weighted discontinuous Galerkin method with minimal phase-lag[J]. Journal of Beijing University of Aeronautics and Astronautics, 2016, 42(8): 1682-1690. doi: 10.13700/j.bh.1001-5965.2015.0523(in Chinese)
shu

Symplectic weighted discontinuous Galerkin method with minimal phase-lag

doi: 10.13700/j.bh.1001-5965.2015.0523
  • 1.

    School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

  • 2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

  • 3. Department of Mathematics, Shanghai Second Polytechnic University, Shanghai 201209, China

  • Received Date: 10 Aug 2015
  • Publish Date: 20 Aug 2016
    Abstract
  • Symplectic finite difference method (FDM) can keep the symplectic structure, and finite element method (FEM) can keep the symplectic structure as well as energy conservation for linear Hamiltonian systems. However, symplectic FDM and FEM still have phase errors for the numerical solution, so, the computational accuracy is not very well in time domain analysis. Symplectic weighted discontinuous Galerkin method with minimal phase-lag (WDG-PF) is proposed for Hamiltonian systems. This method is symplectic and can highly decrease the phase error, compared to traditional method for Hamiltonian systems. Meanwhile, WDG-PF can keep the conservation of energy as well as the symplectic structure of Hamiltonian systems. WDG-PF can solve the phase-lag problem of continuous Galerkin method, and WDG is symplectic by the technique of weight. Compared to symmetric symplectic(FSJS) algorithm, Runge-Kutta-Nystrom(SRKN) and symplectic partitioned Runge-Kutta (SPRK) methods which are aimed at increasing the accuracy of phase error, WDG-PF ismuch more accurate and increase the energy accuracy of Hamiltonian systems, tremedously. The phase error and Hamiltonian function error almost achieve the accuracy of computer. WDG-PF has the ultraconvergence point in each element. Especially, for the systems with high and low frequency signals, and seldom has a method can simulate the high and low frequency signals with a fixed time step, WDG-PF can effectively simulate the high and low frequency signals with large time step. The numerical experiments show its validity.

     

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