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<p>In this paper, a symplectic finite element method (SFEM) for linear Hamiltonian system is proposed. First, the SFEM is derived by applying the finite element method to the linear Hamiltonian equation, and it is shown to strictly preserve the symplectic structure. Furthermore, the implementation of the high-order iterative scheme is achieved through mathematical software. In addition, the flexibility of SFEM for linear Hamiltonian system is analyzed. Several numerical examples verify the excellent performance of SFEM in structural dynamic response problems and prove that SFEM offers significant advantages over traditional numerical methods due to its ability to maintain energy conservation during long-term dynamic simulation, as well as its superior stability.</p>

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High order symplectic finite element method for linear Hamiltonian system and its applications in structural dynamic systems

  • 期刊论文

  • 发表日期：

    2026年2月12日

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  • Zhiping Qiu,
  • Peixuan Zhang

摘要

In this paper, a symplectic finite element method (SFEM) for linear Hamiltonian system is proposed. First, the SFEM is derived by applying the finite element method to the linear Hamiltonian equation, and it is shown to strictly preserve the symplectic structure. Furthermore, the implementation of the high-order iterative scheme is achieved through mathematical software. In addition, the flexibility of SFEM for linear Hamiltonian system is analyzed. Several numerical examples verify the excellent performance of SFEM in structural dynamic response problems and prove that SFEM offers significant advantages over traditional numerical methods due to its ability to maintain energy conservation during long-term dynamic simulation, as well as its superior stability.