Continuous Finite Element Methods of Molecular Dynamics Simulations

Qiong Tang,Luohua Liu,Yan Zheng

doi:10.1155/2015/904140

Abstract

Molecular dynamics simulations are necessary to perform very long integration times. In this paper, we discuss continuous finite element methods for molecular dynamics simulation problems. Our numerical results aboutABdiatomic molecular system andA2Btriatomic molecules show that linear finite element and quadratic finite element methods can better preserve the motion characteristics of molecular dynamics, that is, properties of energy conservation and long-term stability. So finite element method is also a reliable method to simulate long-time classical trajectory of molecular systems.

Highlights

Molecular dynamics (MD) simulations can provide detailed information on molecular fluctuations and conformational changes and are used to investigate the thermodynamics and structure of chemical and biological molecules
In numerical experiments of AB diatomic molecular and A2B triatomic molecules, the linear element and quadratic element methods can better preserve the motion characteristics of molecular system: conservation of energy and long-term stability properties, that reached the microscopic reaction need to be considered time. It is a reliable method for long-time classical trajectory simulations of MD
The continuous finite element methods cannot preserve the energy to nonautonomous Hamiltonian systems

Summary

Introduction

Molecular dynamics (MD) simulations can provide detailed information on molecular fluctuations and conformational changes and are used to investigate the thermodynamics and structure of chemical and biological molecules. Applying continuous finite element methods for Hamiltonian systems, there are two important advantages where finite element methods can preserve energy conservation and high accuracy approximation to symplectic structure. In numerical experiments of AB diatomic molecular and A2B triatomic molecules, the linear element and quadratic element methods can better preserve the motion characteristics of molecular system: conservation of energy and long-term stability properties, that reached the microscopic reaction need to be considered time. It is a reliable method for long-time classical trajectory simulations of MD

Continuous Finite Element Methods for Hamiltonian Systems

Numerical Experiments

Conclusion