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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
</CENTER>
<HR>
<H3>balance command
</H3>
<P>NOTE: the fix balance command referred to here for dynamic load
balancing has not yet been released.
</P>
<P><B>Syntax:</B>
</P>
<PRE>balance keyword args ...
</PRE>
<LI>one or more keyword/arg pairs may be appended
</UL>
<LI>keyword = <I>x</I> or <I>y</I> or <I>z</I> or <I>dynamic</I>
<PRE> <I>x</I> args = <I>uniform</I> or Px-1 numbers between 0 and 1
<I>uniform</I> = evenly spaced cuts between processors in x dimension
numbers = Px-1 ascending values between 0 and 1, Px - # of processors in x dimension
<I>y</I> args = <I>uniform</I> or Py-1 numbers between 0 and 1
<I>uniform</I> = evenly spaced cuts between processors in x dimension
numbers = Py-1 ascending values between 0 and 1, Py - # of processors in y dimension
<I>z</I> args = <I>uniform</I> or Pz-1 numbers between 0 and 1
<I>uniform</I> = evenly spaced cuts between processors in x dimension
numbers = Pz-1 ascending values between 0 and 1, Pz - # of processors in z dimension
<I>dynamic</I> args = Nrepeat Niter dimstr thresh
Nrepeat = # of times to repeat dimstr sequence
Niter = # of times to iterate within each dimension of dimstr sequence
dimstr = sequence of letters containing "x" or "y" or "z"
thresh = stop balancing when this imbalance threshhold is reached
</PRE>
</UL>
<P><B>Examples:</B>
</P>
<PRE>balance x uniform y 0.4 0.5 0.6
balance dynamic 1 5 xzx 1.1
balance dynamic 5 10 x 1.0
</PRE>
<P><B>Description:</B>
</P>
<P>This command adjusts the size of processor sub-domains within the
simulation box, to attempt to balance the number of particles and thus
the computational cost (load) evenly across processors. The load
balancing is "static" in the sense that this command performs the
balancing once, before or between simulations. The processor
sub-domains will then remain static during the subsequent run. To
perform "dynamic" balancing, see the <A HREF = "fix_balance.html">fix balance</A>
command, which can adjust processor sub-domain sizes on-the-fly during
a <A HREF = "run.html">run</A>.
</P>
<P>Load-balancing is only useful if the particles in the simulation box
have a spatially-varying density distribution. E.g. a model of a
vapor/liquid interface, or a solid with an irregular-shaped geometry
containing void regions. In this case, the LAMMPS default of dividing
the simulation box volume into a regular-spaced grid of processor
sub-domain, with one equal-volume sub-domain per procesor, may assign
very different numbers of particles per processor. This can lead to
poor performance in a scalability sense, when the simulation is run in
parallel.
</P>
<P>Note that the <A HREF = "processors.html">processors</A> command gives you some
control over how the box volume is split across processors.
Specifically, for a Px by Py by Pz grid of processors, it lets you
choose Px, Py, and Pz, subject to the constraint that Px * Py * Pz =
P, the total number of processors. This can be sufficient to achieve
good load-balance for some models on some processor counts. However,
all the processor sub-domains will still be the same shape and have
the same volume.
</P>
<P>This command does not alter the topology of the Px by Py by Pz grid or
processors. But it shifts the cutting planes between processors (in
3d, or lines in 2d), which adjusts the volume (area in 2d) assigned to
each processor, as in the following 2d diagram. The left diagram is
the default partitioning of the simulation box across processors (one
sub-box for each of 16 processors); the right diagram is after
balancing.
</P>
<CENTER><IMG SRC = "JPG/balance.jpg">
</CENTER>
<P>When the balance command completes, it prints out the final positions
of all cutting planes in each of the 3 dimensions (as fractions of the
box length). It also prints statistics about its results, including
the change in "imbalance factor". This factor is defined as the
maximum number of particles owned by any processor, divided by the
average number of particles per processor. Thus an imbalance factor
of 1.0 is perfect balance. For 10000 particles running on 10
processors, if the most heavily loaded processor has 1200 particles,
then the factor is 1.2, meaning there is a 20% imbalance. The change
in the maximum number of particles (on any processor) is also printed.
</P>
<P>IMPORTANT NOTE: This command attempts to minimize the imbalance
factor, as defined above. But because of the topology constraint that
only the cutting planes (lines) between processors are moved, there
are many irregular distributions of particles, where this factor
cannot be shrunk to 1.0, particuarly in 3d. Also, computational cost
is not strictly proportional to particle count, and changing the
relative size and shape of processor sub-domains may lead to
additional computational and communication overheads, e.g. in the PPPM
solver used via the <A HREF = "kspace_style.html">kspace_style</A> command. Thus
you should benchmark the run times of your simulation before and after
balancing.
</P>
<HR>
<P>The <I>x</I>, <I>y</I>, and <I>z</I> keywords adjust the position of cutting planes
between processor sub-domains in a specific dimension. The <I>uniform</I>
argument spaces the planes evenly, as in the left diagram above. The
<I>numeric</I> argument requires you to list Ps-1 numbers that specify the
position of the cutting planes. This requires that you know Ps = Px
or Py or Pz = the number of processors assigned by LAMMPS to the
relevant dimension. This assignment is made (and the Px, Py, Pz
values printed out) when the simulation box is created by the
"create_box" or "read_data" or "read_restart" command and is
influenced by the settings of the "processors" command.
</P>
<P>Each of the numeric values must be between 0 and 1, and they must be
listed in ascending order. They represent the fractional position of
the cutting place. The left (or lower) edge of the box is 0.0, and
the right (or upper) edge is 1.0. Neither of these values is
specified. Only the interior Ps-1 positions are specified. Thus is
there are 2 procesors in the x dimension, you specify a single value
such as 0.75, which would make the left processor's sub-domain 3x
larger than the right processor's sub-domain.
</P>
<HR>
<P>The <I>dynamic</I> keyword changes the cutting planes between processors in
an iterative fashion, seeking to reduce the imbalance factor, similar
to how the <A HREF = "fix_balance.html">fix balance</A> command operates. Note that
this keyword begins its operation from the current processor
partitioning, which could be uniform or the result of a previous
balance command.
</P>
<P>The <I>dimstr</I> argument is a string of characters, each of which must be
an "x" or "y" or "z". The characters can appear in any order, and can
be repeated as many times as desired. These are all valid <I>dimstr</I>
arguments: "x" or "xyzyx" or "yyyzzz".
</P>
<P>Balancing proceeds by adjusting the cutting planes in each of the
dimensions listed in <I>dimstr</I>, one dimension at a time. The entire
sequence of dimensions is repeated <I>Nrepeat</I> times. For a single
dimension, the balancing operation (described below) is iterated on
<I>Niter</I> times. After each dimension finishes, the imbalance factor is
re-computed, and the balancing operation halts if the <I>thresh</I>
criterion is met.
</P>
<P>The interplay between <I>Nrepeat</I>, <I>Niter</I>, and <I>dimstr</I> means that
these commands do essentially the same thing, the only difference
being how often the imbalance factor is computed and checked against
the threshhold:
</P>
<PRE>balance y dynamic 5 10 x 1.2
balance y dynamic 1 10 xxxxx 1.2
balance y dynamic 50 1 x 1.2
</PRE>
<P>A rebalance operation in a single dimension is performed using an
iterative "diffusive" load-balancing algorithm <A HREF = "#Cybenko">(Cybenko)</A>.
One iteration on a dimension (which is repeated <I>Niter</I> times), works
as follows. Assume there are Px processors in the x dimension. This
defines Px slices of the simulation, each of which contains Py*Pz
processors. The task is to adjust the position of the Px-1 cuts
between slices, leaving the end cuts unchanged (left and right edges
of the simulation box).
</P>
<P>The iteration beings by calculating the number of atoms within each of
the Px slices. Then for each slice, its atom count is compared to its
neighbors. If a slice has more atoms than its left (or right)
neighbor, the cut is moved towards the center of the slice,
effectively shrinking the width of the slice and migrating atoms to
the other slice. The distance to move the cut is a function of the
"density" of atoms in the donor slice and the difference in counts
between the 2 slices. A damping factor is also applied to avoid
oscillations in the position of the cutting plane as iterations
proceed. Hence the "diffusive" nature of the algorithm as work
(atoms) effectively diffuses from highly loaded processors to
less-loaded processors.
</P>
<HR>
<P><B>Restrictions:</B>
</P>
<P>The <I>dynamic</I> keyword cannot be used with the <I>x</I>, <I>y</I>, or <I>z</I>
arguments.
</P>
<P>For 2d simulations, the <I>z</I> keyword cannot be used. Nor can a "z"
appear in <I>dimstr</I> for the <I>dynamic</I> keyword.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "processors.html">processors</A>, <A HREF = "fix_balance.html">fix balance</A>
</P>
<P><B>Default:</B> none
</P>
<HR>
<A NAME = "Cybenko"></A>
<P><B>(Cybenko)</B> Cybenko, J Par Dist Comp, 7, 279-301 (1989).
</P>
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