A High-Order Meshless Energy-Preserving Algorithm for the Beam Equation

Authors

  • Jialing Wang
  • Yali He

DOI:

https://doi.org/10.4208/cmr.2024-0018

Keywords:

Beam equation, meshless scheme, energy-preserving method, radial basis function, symplectic Runge-Kutta method.

Abstract

In this paper, a meshless energy-preserving algorithm which can be arbitrarily high-order in temporal direction for the beam equation has been proposed. Based on the method of lines, we first use the radial basis function quasi-interpolation method to discretize spatial variable and obtain a semi-discrete Hamiltonian system by using the premultiplication of a diagonal matrix. Then, symplectic Runge-Kutta method that can conserve quadratic invariants exactly has been used to discretize the temporal variable, which yields a fully discrete meshless scheme. Due to the specific quadratic energy expression of the beam equation, the proposed meshless scheme here is not only energy-preserving but also arbitrarily high-order in temporal direction. Besides uniform and nonuniform grids, numerical experiments on random grids are also conducted, which demonstrate the properties of the proposed scheme very well.

Published

2024-12-19

Issue

Section

Articles