Computational efficiency of symplectic integration schemes: Application to multidimensional disordered Klein-Gordon lattices

TL;DR

This paper evaluates various symplectic integrators for simulating chaotic dynamics in multidimensional disordered Klein-Gordon lattices, highlighting the most efficient schemes for accurate energy conservation and dynamical analysis.

Contribution

It compares the performance of different symplectic integrators in modeling complex lattice dynamics, identifying the most efficient schemes for energy conservation and accurate chaos characterization.

Findings

Fourth order ABA864 scheme is most CPU-efficient for moderate accuracy.

Sixth order s11ABA82_6 scheme provides best energy conservation at higher accuracy.

Symplectic integrators effectively reproduce wave packet propagation features.

Abstract

We implement several symplectic integrators, which are based on two part splitting, for studying the chaotic behavior of one- and two-dimensional disordered Klein-Gordon lattices with many degrees of freedom and investigate their numerical performance. For this purpose, we perform extensive numerical simulations by considering many different initial energy excitations and following the evolution of the created wave packets in the various dynamical regimes exhibited by these models. We compare the efficiency of the considered integrators by checking their ability to correctly reproduce several features of the wave packets propagation, like the characteristics of the created energy distribution and the time evolution of the systems' maximum Lyapunov exponent estimator. Among the tested integrators the fourth order $ABA864$ scheme \cite{BCFLMM13} showed the best performance as it needed the least CPU time for capturing the correct dynamical behavior of all considered cases when a moderate accuracy in conserving the systems' total energy value was required. Among the higher order schemes used to achieve a better accuracy in the energy conservation, the sixth order scheme $s11ABA82\_6$ exhibited the best performance.