Implicit - integration dynamics simulation with the GridPACK framework

2021 ◽  
Author(s):  
Shrirang Abhyankar ◽  
Renke Huang ◽  
Shuangshuang Jin ◽  
Bruce Palmer ◽  
William Perkins ◽  
...  
Keyword(s):  
Dynamics Simulation ◽  
Implicit Integration

A Quantitative Assessment of the Potential of Implicit Integration Methods for Molecular Dynamics Simulation

2010 ◽  
Vol 5 (3) ◽  
Author(s):  
Nick Schafer ◽  
Dan Negrut
Keyword(s):  
Molecular Dynamics ◽  
Md Simulation ◽  
Time Integration ◽  
Dynamics Simulation ◽  
Integration Step ◽  
Implicit Integration ◽  
Implicit Methods ◽  
Current Standard ◽  
Step Size ◽  
Computational Overhead

Implicit integration, unencumbered by numerical stability constraints, is attractive in molecular dynamics (MD) simulation due to its presumed ability to advance the simulation at large step sizes. It is not clear what step size values can be expected and if the larger step sizes will compensate for the computational overhead associated with an implicit integration method. The goal of this paper is to answer these questions and thereby assess quantitatively the potential of implicit integration in MD. Two implicit methods (midpoint and Hilber–Hughes–Taylor) are compared with the current standard for MD time integration (explicit velocity Verlet). The implicit algorithms were implemented in a research grade MD code, which used a first-principles interaction potential for biological molecules. The nonlinear systems of equations arising from the use of implicit methods were solved in a quasi-Newton framework. Aspects related to a Newton–Krylov type method are also briefly discussed. Although the energy conservation provided by the implicit methods was good, the integration step size lengths were limited by loss of convergence in the Newton iteration. Moreover, a spectral analysis of the dynamic response indicated that high frequencies present in the velocity and acceleration signals prevent a substantial increase in integration step size lengths. The overhead associated with implicit integration prevents this class of methods from having a decisive impact in MD simulation, a conclusion supported by a series of quantitative analyses summarized in the paper.

Implicit Integration in Molecular Dynamics Simulation

2008 ◽  
Author(s):  
Nicholas P. Schafer ◽  
Radu Serban ◽  
Dan Negrut
Keyword(s):  
Molecular Dynamics ◽  
Newton Method ◽  
Dynamics Simulation ◽  
Integration Scheme ◽  
Implicit Integration ◽  
Step Size ◽  
Time Step ◽  
Integration Methods ◽  
Size Limitation ◽  
Quasi Newton

Molecular Dynamics (MD) simulation is a versatile methodology that has found many applications in materials science, chemistry and biology. In biology, the models employed range from mixed quantum mechanical and fully atomistic to united atom and continuum mechanical. These systems are evolved in discrete time by solving Newton’s equations of motion at each time step. The numerical methods currently in use limit the step size of a typical all atom simulation to 1 femtosecond. This step size limitation means that many steps need to be taken in order to reach biologically relevant time scales. At each time step, an evaluation of the forces on each atom must be performed resulting in heavy computational loads. This work investigates the use of implicit integration methods in MD. Implicit integration methods have been proven superior to their explicit counterparts in classical mechanical simulation, with which MD has many similarities. Longer time steps reduce the number of force evaluations that must be performed and the corresponding computational load. Herein we present results that compare implicit integration techniques with the current standard for molecular dynamics, the explicit velocity Verlet integration scheme. Total energy conservation is used as a metric for evaluating the dependability of simulations in the microcanonical ensemble. In order to understand the nature of the problem, several long simulations were run and analyzed by performing a Fourier analysis on the position, velocity and acceleration signals. Lastly, several methods for improving the viability of implicit integration methods are considered including replacing the Jacobian used in the Quasi-Newton method with a constant, diagonal mass matrix, evaluating the Jacobian infrequently and finding a better prediction of the system configuration to improve the convergence of the Quasi-Newton method.

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