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Table Of Contents
GPU-Accelerated Computing with Python 3 and CUDA
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The time integrator updates the positions and velocities of atoms as time in the simulation progresses. In principle, it numerically solves Newton's equations of motion for each atom in the system.
The Verlet algorithm is one of the simplest and most used time integrators in MD simulations, regarding its simplicity, computational efficiency, and numerical stability. In the Verlet integration, the new position
of a particle is computed as follows:

Where,
,
, and
are position, velocity, and the acceleration of the atom at the current time, and
is the time step. Acceleration
relates to Newton's law via
, where
is the force and
is the mass. For our particles, we will take
, which makes
.
The equation for the new velocity
is given by:

The new positions and velocities for all atoms are updated, and the algorithm proceeds to the next time step
. This process repeats, with forces recalculated at each step to gradually build the trajectory of the particles.