Non-iterative and exact method for constraining particles in a linear geometry

TL;DR

This paper introduces a non-iterative, exact numerical method for maintaining linear constraints in particle simulations, eliminating drift and improving stability in molecular dynamics of rigid molecules or non-spherical grains.

Contribution

A practical, non-iterative method for calculating Lagrange multipliers to enforce linear constraints in particle dynamics, enhancing accuracy and stability.

Findings

No drift in constrained geometry during simulations

Method is exact within numerical accuracy

Applicable to molecular dynamics of rigid molecules

Abstract

We present a practical numerical method for evaluating the Lagrange multipliers necessary for maintaining a constrained linear geometry of particles in dynamical simulations. The method involves no iterations, and is limited in accuracy only by the numerical methods for solving small systems of linear equations. As a result of the non-iterative and exact (within numerical accuracy) nature of the procedure there is no drift in the constrained geometry, and the method is therefore readily applied to molecular dynamics simulations of, e.g., rigid linear molecules or materials of non-spherical grains. We illustrate the approach through implementation in the commonly used second-order velocity explicit Verlet method.