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sector command

Syntax:

sector flag keyword value ... 

Examples:

sector no
sector yes
sector 4
sector yes nstop 0.5
sector yes tstop 5.0 

Description:

This command partitions the portion of the simulation domain owned by each processor into sectors or sub-domains. It can only be used for on-lattice applications. Typically, it is used in a parallel simulation, to enable parallelism, but it can also be used on a single processor.

If sectoring is enabled via the yes setting, then for 1d lattices, each processor's sub-domain is partioned into 2 halves, for 2d lattices, each processor's sub-domain is partitioned into 4 quadrants, and for 3d lattices it is partitioned into 8 octants. If the N setting is used instead, then the number of sectors can be specified directly. This may be useful in some models to reduce communication. A 3d lattice can use 2 (x only) or 4 sectors (x and y), instead of the default 8 (x and y and z). A 2d lattice can use 2 sectors (x only), instead of the default 4 (x and y). Note that if no sectors are used in a dimension, then there must be only one processor assigned to that dimension of the simulation box (see the app_style procs command). For example, if "sector 2" is used for a 2d lattice, then the processor layout must be Px1, where P is the total number of processors.

If sectors are turned on, then a kinetic Monte Carlo (KMC) or rejection KMC (rKMC) algorithm is performed in the following manner. Events or sites are selected within the first sector on each processor, via a solver or sweeping method. Communication is then done between processors to update sector boundaries. Then all proecessors move to the next sector, and the process is repeated. Thus a single sweep over the entire lattice is performed in 2 (or 4 or 8) stages for 1d (of 2d or 3d) lattices, as sectors are processed one at a time, followed by the appropriate communication. This procedure insure events occurring on one processor do not conflict with events performed by other processors.

The optional keywords determine how much time is spent on each sector (i.e. how many events are performed) before moving to the next sector. See the discussion below for what they mean when sectoring is set to no.

Note that using sectors turns an exact KMC or rKMC algorithm into an approximate one, in the spirit of Amar. This is because events are occuring within a sector while the state of the system on the boundary of the sector is held frozen. If the time-per-sector is too large, this will require less communication but will induce incorrect dynamics at the sector boundaries. Conversely, if the time-per-sector is too small, the simulation will perform few events per sector and spend too much time communicating.

If the tstop keyword is set to a value > 0.0, it sets the time per sector to the specified value. For a KMC algorithm, events are performed until this time threshhold is reached. The final event, whose time >= tstop, is not accepted. For a rKMC algorithm, the time per attempted event = dt_sweep is defined by the application, and the number of attempted events in each sector is set to nsite*int(tstop/dt_sweep). Because of integer truncation, the simulation time increment in rKMC may differ slightly from the specified tstop.

If the nstop keyword is set to a value > 0.0, it sets the average number of events (or attempts) per site. For example, an nstop value of 2.0 means attempt 2 events per site for a rKMC algorithm. For a KMC algorithm, this is converted into a time using pmax = the maximum propensity per site. At the start of each visit to a sector, the per-site propensity for the sector = psect, is computed. Psect is the total propensity of the sector divided by the total number of active sites, which are those with propensity greater than zero. After all sectors have been visited, pmax is set to the largest value of psect across all processors and sectors, and the threshold time for the next visit to each sector is set to nstop/pmax.

In the KMC case, this means that if the total propensity of the system decreases as the simulation proceeds (e.g. grain growth occurs), then the effective time per sweep will increase in an adaptive way. Said another way, the number of events per sweep will remain roughly constant, as the time per event increases. In the rKMC case, the time per attempt is constant due to the use of a null-bin, so there is no adaptivity.

If neither the tstop or nstop keywords are specified, a default value of nstop = 1.0 is used, meaning one event per site is performed or attempted in the KMC or rKMC algorithm in each sector. This should give good behavior in many applications, meaning high accuracy is achieved with good parallel performance due to a modest amount of communication being performed.

Note that it makes no sense to specify both tstop and nstop since they define the time-per-sector in different ways. When tstop is specified, it sets nstop to 0.0. Likewise when nstop is specified, it sets tstop to 0.0. Thus if both are used, the last setting takes precedence.

If sectors are turned off via the no setting, then the nstop or tstop settings still have an effect for rKMC simulations where the sweep style is set to color. They determine how many times the sites associated with each color are looped over before moving to the next color. Normally, this should just be 1, which is the nstop default, but this can be changed if desired.

Restrictions:

This command can only be used as part of on-lattice applications as specified by the app_style command.

Related commands:

app_style, solve_style, sweep

Default:

The default for sectoring is no and the option defaults are nstop = 1.0 and tstop = 0.0.


(Amar) Shin and Amar, Phys Rev B, 71, 125432-1-125432-13 (2005).