\(\renewcommand{\AA}{\text{Å}}\)

4.7. How a timestep works

The first and most fundamental operation within LAMMPS to understand is how a timestep is structured. Timestepping is performed by calling methods of the Integrate class instance within the Update class. Since Integrate is a base class, it will point to an instance of a derived class corresponding to what is selected by the run_style input script command.

In this section, the timestep implemented by the Verlet class is described. A similar timestep protocol is implemented by the Respa class, for the r-RESPA hierarchical timestepping method.

The Min base class performs energy minimization, so does not perform a literal timestep. But it has logic similar to what is described here, to compute forces and invoke fixes at each iteration of a minimization. Differences between time integration and minimization are highlighted at the end of this section.

The Verlet class is encoded in the src/verlet.cpp and verlet.h files. It implements the velocity-Verlet timestepping algorithm. The workhorse method is Verlet::run(), but first we highlight several other methods in the class.

The init() method is called at the beginning of each dynamics run. It simply sets some internal flags, based on user settings in other parts of the code.
The setup() or setup_minimal() methods are also called before each run. The velocity-Verlet method requires current forces be calculated before the first timestep, so these routines compute forces due to all atomic interactions, using the same logic that appears in the timestepping described next. A few fixes are also invoked, using the mechanism described in the next section. Various counters are also initialized before the run begins. The setup_minimal() method is a variant that has a flag for performing less setup. This is used when runs are continued and information from the previous run is still valid. For example, if repeated short LAMMPS runs are being invoked, interleaved by other commands, via the pre no and every options of the run command, the setup_minimal() method is used.
The force_clear() method initializes force and other arrays to zero before each timestep, so that forces (torques, etc) can be accumulated.

Now for the Verlet::run() method. Its basic structure in hi-level pseudocode is shown below. In the actual code in src/verlet.cpp some of these operations are conditionally invoked.

loop over N timesteps:
  if timeout condition: break
  ev_set()

  fix->initial_integrate()
  fix->post_integrate()

  nflag = neighbor->decide()
  if nflag:
    fix->pre_exchange()
    domain->pbc()
    domain->reset_box()
    comm->setup()
    neighbor->setup_bins()
    comm->exchange()
    comm->borders()
    fix->pre_neighbor()
    neighbor->build()
    fix->post_neighbor()
  else:
    comm->forward_comm()

  force_clear()
  fix->pre_force()

  pair->compute()
  bond->compute()
  angle->compute()
  dihedral->compute()
  improper->compute()
  kspace->compute()

  fix->pre_reverse()
  comm->reverse_comm()

  fix->post_force()
  fix->final_integrate()
  fix->end_of_step()

  if any output on this step:
    output->write()

# after loop
fix->post_run()

The ev_set() method (in the parent Integrate class), sets two flags (eflag and vflag) for energy and virial computation. Each flag encodes whether global and/or per-atom energy and virial should be calculated on this timestep, because some fix or variable or output will need it. These flags are passed to the various methods that compute particle interactions, so that they either compute and tally the corresponding data or can skip the extra calculations if the energy and virial are not needed. See the comments for the Integrate::ev_set() method, which document the flag values.

At various points of the timestep, fixes are invoked, e.g. fix->initial_integrate(). In the code, this is actually done via the Modify class, which stores all the Fix objects and lists of which should be invoked at what point in the timestep. Fixes are the LAMMPS mechanism for tailoring the operations of a timestep for a particular simulation. As described elsewhere, each fix has one or more methods, each of which is invoked at a specific stage of the timestep, as show in the timestep pseudocode. All the active fixes defined in an input script, that are flagged to have an initial_integrate() method, are invoked at the beginning of each timestep. Examples are fix nve or fix nvt or fix npt which perform the start-of-timestep velocity-Verlet integration operations to update velocities by a half-step, and coordinates by a full step. The post_integrate() method is next for operations that need to happen immediately after those updates. Only a few fixes use this, e.g. to reflect particles off box boundaries in the FixWallReflect class.

The decide() method in the Neighbor class determines whether neighbor lists need to be rebuilt on the current timestep (conditions can be changed using the neigh_modify every/delay/check command). If not, coordinates of ghost atoms are acquired by each processor via the forward_comm() method of the Comm class. If neighbor lists need to be built, several operations within the inner if clause of the pseudocode are first invoked. The pre_exchange() method of any defined fixes is invoked first. Typically, this inserts or deletes particles from the system.

Periodic boundary conditions are then applied by the Domain class via its pbc() method to remap particles that have moved outside the simulation box back into the box. Note that this is not done every timestep, but only when neighbor lists are rebuilt. This is so that each processor’s subdomain will have consistent (nearby) atom coordinates for its owned and ghost atoms. It is also why dumped atom coordinates may be slightly outside the simulation box if not dumped on a step where the neighbor lists are rebuilt.

The box boundaries are then reset (if needed) via the reset_box() method of the Domain class, e.g. if box boundaries are shrink-wrapped to current particle coordinates. A change in the box size or shape requires internal information for communicating ghost atoms (Comm class) and neighbor list bins (Neighbor class) to be updated. The setup() method of the Comm class and setup_bins() method of the Neighbor class perform the update.

The code is now ready to migrate atoms that have left a processor’s geometric subdomain to new processors. The exchange() method of the Comm class performs this operation. The borders() method of the Comm class then identifies ghost atoms surrounding each processor’s subdomain and communicates ghost atom information to neighboring processors. It does this by looping over all the atoms owned by a processor to make lists of those to send to each neighbor processor. On subsequent timesteps, the lists are used by the Comm::forward_comm() method.

Fixes with a pre_neighbor() method are then called. These typically re-build some data structure stored by the fix that depends on the current atoms owned by each processor.

Now that each processor has a current list of its owned and ghost atoms, LAMMPS is ready to rebuild neighbor lists via the build() method of the Neighbor class. This is typically done by binning all owned and ghost atoms, and scanning a stencil of bins around each owned atom’s bin to make a Verlet list of neighboring atoms within the force cutoff plus neighbor skin distance.

In the next portion of the timestep, all interaction forces between particles are computed, after zeroing the per-atom force vector via the force_clear() method. If the newton flag is set to on by the newton command, forces are added to both owned and ghost atoms, otherwise only to owned (aka local) atoms.

Pairwise forces are calculated first, which enables the global virial (if requested) to be calculated cheaply (at O(N) cost instead of O(N**2) at the end of the Pair::compute() method), by a dot product of atom coordinates and forces. By including owned and ghost atoms in the dot product, the effect of periodic boundary conditions is correctly accounted for. Molecular topology interactions (bonds, angles, dihedrals, impropers) are calculated next (if supported by the current atom style). The final contribution is from long-range Coulombic interactions, invoked by the KSpace class.

The pre_reverse() method in fixes is used for operations that have to be done before the upcoming reverse communication (e.g. to perform additional data transfers or reductions for data computed during the force computation and stored with ghost atoms).

If the newton flag is on, forces on ghost atoms are communicated and summed back to their corresponding owned atoms. The reverse_comm() method of the Comm class performs this operation, which is essentially the inverse operation of sending copies of owned atom coordinates to other processor’s ghost atoms.

At this point in the timestep, the total force on each (local) atom is known. Additional force constraints (external forces, SHAKE, etc) are applied by Fixes that have a post_force() method. The second half of the velocity-Verlet integration, final_integrate() is then performed (another half-step update of the velocities) via fixes like nve, nvt, npt.

At the end of the timestep, fixes that contain an end_of_step() method are invoked. These typically perform a diagnostic calculation, e.g. the ave/time and ave/spatial fixes. The final operation of the timestep is to perform any requested output, via the write() method of the Output class. There are 3 kinds of LAMMPS output: thermodynamic output to the screen and log file, snapshots of atom data to a dump file, and restart files. See the thermo_style, dump, and restart commands for more details.

The flow of control during energy minimization iterations is similar to that of a molecular dynamics timestep. Forces are computed, neighbor lists are built as needed, atoms migrate to new processors, and atom coordinates and forces are communicated to neighboring processors. The only difference is what Fix class operations are invoked when. Only a subset of LAMMPS fixes are useful during energy minimization, as explained in their individual doc pages. The relevant Fix class methods are min_pre_exchange(), min_pre_force(), and min_post_force(). Each fix is invoked at the appropriate place within the minimization iteration. For example, the min_post_force() method is analogous to the post_force() method for dynamics; it is used to alter or constrain forces on each atom, which affects the minimization procedure.

After all iterations are completed, there is a cleanup step which calls the post_run() method of fixes to perform operations only required at the end of a calculation (like freeing temporary storage or creating final outputs).