Conservation of Hamiltonian using Continuous Galerkin Petrov time discretization scheme

TL;DR

This paper evaluates a fourth-order Continuous Galerkin Petrov time discretization scheme for Hamiltonian systems, demonstrating its superior efficiency and Hamiltonian conservation compared to existing symplectic methods.

Contribution

The paper introduces a fourth-order Continuous Galerkin Petrov scheme and shows it outperforms other methods in conserving Hamiltonian and computational efficiency.

Findings

Preserves Hamiltonian in tested systems.

Uses less CPU time than comparable methods.

Effective for various Hamiltonian systems.

Abstract

Continuous Galerkin Petrov time discretization scheme is tested on some Hamiltonian systems including simple harmonic oscillator, Kepler's problem with different eccentricities and molecular dynamics problem. In particular, we implement the fourth order Continuous Galerkin Petrov time discretization scheme and analyze numerically, the efficiency and conservation of Hamiltonian. A numerical comparison with some symplectic methods including Gauss implicit Runge-Kutta method and general linear method of same order is given for these systems. It is shown that the above mentioned scheme, not only preserves Hamiltonian but also uses the least CPU time compared with upto-date and optimized methods.