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NVE ensemble

Time integration in exaStamp is performed using the velocity form of the Störmer-Verlet algorithm, better known as velocity-Verlet. It's a good fit for atomistic simulations because it's symplectic (it preserves the system's energy over long trajectories) and second-order accurate in both time and energy, at the cost of only one force evaluation per step:

Velocity-Verlet steps

  1. Position at the full step:
\[ \mathbf{x}(t + \Delta t) = \mathbf{x}(t) + \mathbf{v}(t) \Delta t + \mathbf{a}(t) \frac{\Delta t^2}{2} \]
  1. Velocity at the half step:
\[ \mathbf{v}\left(t + \frac{\Delta t}{2}\right) = \mathbf{v}(t) + \mathbf{a}(t) \frac{\Delta t}{2} \]

  1. Recompute the acceleration \(\mathbf{a}(t + \Delta t)\) from the interatomic potential, using the position from step 1.

  2. Velocity at the full step:

\[ \mathbf{v}(t + \Delta t) = \mathbf{v}\left(t + \frac{\Delta t}{2}\right) + \mathbf{a}(t + \Delta t) \frac{\Delta t}{2} \]

The verlet_nve scheme

verlet_nve is exaStamp's default value for numerical_scheme — plain velocity-Verlet, no thermostat or barostat attached:

Usage example
numerical_scheme: verlet_nve

verlet_nve (exaStamp/data/config/config_numerical_schemes.msp) expands to:

Usage example
verlet_nve:
  name: NVE_scheme
  body:
    - verlet_first_half
    - check_and_update_particles
    - load_balance_auto_tune_start
    - compute_all_forces_energy
    - verlet_second_half
    - load_balance_auto_tune_end

verlet_first_half:
  - push_f_v_r: { dt_scale: 1.0, xform_mode: INV_XFORM }
  - push_f_v: { dt_scale: 0.5, xform_mode: IDENTITY }

verlet_second_half:
  - push_f_v: { dt_scale: 0.5, xform_mode: IDENTITY }

verlet_first_half/verlet_second_half are themselves named body: lists — the same batch-label mechanism as verlet_nve itself, just one level down, wrapping the generic push operators; check_and_update_particles and compute_all_forces_energy are conventional batch labels (not standalone operators) that decide whether ghost cells/domain decomposition need rebuilding, and run the potential-specific force computation, respectively. Every other ensemble/thermostat/barostat on this site works by pointing numerical_scheme at a different named scheme instead of verlet_nve — see the full list of schemes.

This is steps 1–2 and step 4 of the velocity-Verlet steps above, expressed directly in terms of the generic push operators:

  • verlet_first_half calls push_f_v_r at dt_scale: 1.0 — step 1, the full position update from \(\mathbf{v}(t)\) and \(\mathbf{a}(t)\) — immediately followed by push_f_v at dt_scale: 0.5 — step 2, the half-step velocity kick.
  • compute_all_forces_energy (step 3) then recomputes \(\mathbf{a}(t + \Delta t)\) at the new position.
  • verlet_second_half calls push_f_v again, at dt_scale: 0.5 — step 4, completing the velocity kick with the freshly recomputed acceleration.