Long-time instability in the Runge-Kutta algorithm for a Nosé-Hoover heat bath of a harmonic chain and its stabilization

Long-time instability in the Runge-Kutta algorithm for a Nosé-Hoover heat bath of a harmonic... In this paper, we investigate the Runge-Kutta algorithm for the Nosé-Hoover heat bath of a harmonic chain. The Runge-Kutta algorithm is found to be unstable in long-time calculations, with the system temperature growing exponentially. The growth rate increases if time step size is chosen larger. By analyzing the Fourier spectra in both space (wave number) and time (frequency), we discover that the growth is caused by spurious energy accumulation, particularly at the largest wave number. Such accumulation may be explained by von Neumann analysis for an infinite chain, with the nonlinear heat bath being ignored. Furthermore, we propose to add a filter to remove excessive energy, which effectively stabilizes the algorithm. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review E American Physical Society (APS)

Long-time instability in the Runge-Kutta algorithm for a Nosé-Hoover heat bath of a harmonic chain and its stabilization

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Long-time instability in the Runge-Kutta algorithm for a Nosé-Hoover heat bath of a harmonic chain and its stabilization

Abstract

In this paper, we investigate the Runge-Kutta algorithm for the Nosé-Hoover heat bath of a harmonic chain. The Runge-Kutta algorithm is found to be unstable in long-time calculations, with the system temperature growing exponentially. The growth rate increases if time step size is chosen larger. By analyzing the Fourier spectra in both space (wave number) and time (frequency), we discover that the growth is caused by spurious energy accumulation, particularly at the largest wave number. Such accumulation may be explained by von Neumann analysis for an infinite chain, with the nonlinear heat bath being ignored. Furthermore, we propose to add a filter to remove excessive energy, which effectively stabilizes the algorithm.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1539-3755
eISSN
550-2376
D.O.I.
10.1103/PhysRevE.96.013308
Publisher site
See Article on Publisher Site

Abstract

In this paper, we investigate the Runge-Kutta algorithm for the Nosé-Hoover heat bath of a harmonic chain. The Runge-Kutta algorithm is found to be unstable in long-time calculations, with the system temperature growing exponentially. The growth rate increases if time step size is chosen larger. By analyzing the Fourier spectra in both space (wave number) and time (frequency), we discover that the growth is caused by spurious energy accumulation, particularly at the largest wave number. Such accumulation may be explained by von Neumann analysis for an infinite chain, with the nonlinear heat bath being ignored. Furthermore, we propose to add a filter to remove excessive energy, which effectively stabilizes the algorithm.

Journal

Physical Review EAmerican Physical Society (APS)

Published: Jul 13, 2017

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