2012-02-10 00:12:43 +08:00
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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>
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<HR>
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<H3>balance command
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</H3>
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<P>NOTE: the fix balance command referred to here for dynamic load
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balancing has not yet been released.
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</P>
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<P><B>Syntax:</B>
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</P>
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<PRE>balance group-ID keyword args ...
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</PRE>
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<LI>group-ID = ID of group of atoms to balance across processors
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</UL>
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<LI>one or more keyword/arg pairs may be appended
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<LI>keyword = <I>x</I> or <I>y</I> or <I>z</I> or <I>dynamic</I>
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<PRE> <I>x</I> args = <I>uniform</I> or Px-1 numbers between 0 and 1
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<I>uniform</I> = evenly spaced cuts between processors in x dimension
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numbers = Px-1 ascending values between 0 and 1, Px - # of processors in x dimension
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<I>y</I> args = <I>uniform</I> or Py-1 numbers between 0 and 1
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<I>uniform</I> = evenly spaced cuts between processors in x dimension
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numbers = Py-1 ascending values between 0 and 1, Py - # of processors in y dimension
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<I>z</I> args = <I>uniform</I> or Pz-1 numbers between 0 and 1
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<I>uniform</I> = evenly spaced cuts between processors in x dimension
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numbers = Pz-1 ascending values between 0 and 1, Pz - # of processors in z dimension
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<I>dynamic</I> args = Nrepeat Niter dimstr thresh
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Nrepeat = # of times to repeat dimstr sequence
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Niter = # of times to iterate within each dimension of dimstr sequence
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dimstr = sequence of letters containing "x" or "y" or "z"
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thresh = stop balancing when this imbalance threshhold is reached
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</PRE>
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>balance x uniform y 0.4 0.5 0.6
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balance dynamic 1 5 xzx 1.1
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balance dynamic 5 10 x 1.0
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>This command adjusts the size of processor sub-domains within the
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simulation box, to attempt to balance the number of particles and thus
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the computational cost (load) evenly across processors. The load
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balancing is "static" in the sense that this command performs the
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balancing once, before or between simulations. The processor
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sub-domains will then remain static during the subsequent run. To
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perform "dynammic" balancing, see the <A HREF = "fix_balance.html">fix balance</A>
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command, which can adjust processor sub-domain sizes on-the-fly during
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a <A HREF = "run.html">run</A>.
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</P>
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<P>Load-balancing is only useful if the particles in the simulation box
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have a spatially-varying density distribution. E.g. a model of a
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vapor/liquid interface, or a solid with an irregular-shaped geometry
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containing void regions. In this case, the LAMMPS default of dividing
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the simulation box volume into a regular-spaced grid of processor
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sub-domain, with one equal-volume sub-domain per procesor, may assign
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very different numbers of particles per processor. This can lead to
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poor performance in a scalability sense, when the simulation is run in
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parallel.
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</P>
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<P>Note that the <A HREF = "processors.html">processors</A> command gives you some
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control over how the box volume is split across processors.
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Specifically, for a Px by Py by Pz grid of processors, it lets you
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choose Px, Py, and Pz, subject to the constraint that Px * Py * Pz =
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P, the total number of processors. This can be sufficient to achieve
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good load-balance for some models on some processor counts. However,
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all the processor sub-domains will still be the same shape and have
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the same volume.
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</P>
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<P>This command does not alter the topology of the Px by Py by Pz grid or
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processors. But it shifts the cutting planes between processors (in
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3d, or lines in 2d), which adjusts the volume (area in 2d) assigned to
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each processor, as in the following 2d diagram. The left diagram is
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the default partitioning of the simulation box across processors (one
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sub-box for each of 16 processors); the right diagram is after
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balancing.
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</P>
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<CENTER><IMG SRC = "JPG/balance.jpg">
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</CENTER>
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2012-02-10 02:04:37 +08:00
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<P>When the balance command completes, it prints out the final positions
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of all cutting planes in each of the 3 dimensions (as fractions of the
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box length). It also prints statistics about its results, including
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the change in "imbalance factor". This factor is defined as the
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maximum number of particles owned by any processor, divided by the
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average number of particles per processor. Thus an imbalance factor
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of 1.0 is perfect balance. For 10000 particles running on 10
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processors, if the most heavily loaded processor has 1200 particles,
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then the factor is 1.2, meaning there is a 20% imbalance. The change
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in the maximum number of particles (on any processor) is also printed.
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2012-02-10 00:12:43 +08:00
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</P>
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<P>IMPORTANT NOTE: This command attempts to minimize the imbalance
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factor, as defined above. But because of the topology constraint that
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only the cutting planes (lines) between processors are moved, there
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are many irregular distributions of particles, where this factor
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cannot be shrunk to 1.0, particuarly in 3d. Also, computational cost
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is not strictly proportional to particle count, and changing the
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relative size and shape of processor sub-domains may lead to
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additional computational and communication overheads, e.g. in the PPPM
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solver used via the <A HREF = "kspace_style.html">kspace_style</A> command. Thus
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you should benchmark the run times of your simulation before and after
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balancing.
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</P>
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<HR>
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<P>The <I>x</I>, <I>y</I>, and <I>z</I> keywords adjust the position of cutting planes
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between processor sub-domains in a specific dimension. The <I>uniform</I>
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argument spaces the planes evenly, as in the left diagram above. The
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<I>numeric</I> argument requires you to list Ps-1 numbers that specify the
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position of the cutting planes. This requires that you know Ps = Px
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or Py or Pz = the number of processors assigned by LAMMPS to the
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relevant dimension. This assignment is made (and the Px, Py, Pz
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values printed out) when the simulation box is created by the
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"create_box" or "read_data" or "read_restart" command and is
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influenced by the settings of the "processors" command.
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</P>
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<P>Each of the numeric values must be between 0 and 1, and they must be
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listed in ascending order. They represent the fractional position of
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the cutting place. The left (or lower) edge of the box is 0.0, and
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the right (or upper) edge is 1.0. Neither of these values is
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specified. Only the interior Ps-1 positions are specified. Thus is
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there are 2 procesors in the x dimension, you specify a single value
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such as 0.75, which would make the left processor's sub-domain 3x
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larger than the right processor's sub-domain.
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</P>
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<HR>
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<P>The <I>dynamic</I> keyword changes the cutting planes between processors in
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an iterative fashion, seeking to reduce the imbalance factor, similar
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to how the <A HREF = "fix_balance.html">fix balance</A> command operates. Note that
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this keyword begins its operation from the current processor
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partitioning, which could be uniform or the result of a previous
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balance command.
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</P>
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<P>The <I>dimstr</I> argument is a string of characters, each of which must be
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an "x" or "y" or "z". The characters can appear in any order, and can
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be repeated as many times as desired. These are all valid <I>dimstr</I>
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arguments: "x" or "xyzyx" or "yyyzzz".
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</P>
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<P>Balancing proceeds by adjusting the cutting planes in each of the
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dimensions listed in <I>dimstr</I>, one dimension at a time. The entire
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sequence of dimensions is repeated <I>Nrepeat</I> times. For a single
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dimension, the balancing operation (described below) is iterated on
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<I>Niter</I> times. After each dimension finishes, the imbalance factor is
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re-computed, and the balancing operation halts if the <I>thresh</I>
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criterion is met.
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</P>
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<P>The interplay between <I>Nrepeat</I>, <I>Niter</I>, and <I>dimstr</I> means that
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these commands do essentially the same thing, the only difference
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being how often the imbalance factor is computed and checked against
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the threshhold:
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</P>
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<PRE>balance y dynamic 5 10 x 1.2
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balance y dynamic 1 10 xxxxx 1.2
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balance y dynamic 50 1 x 1.2
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</PRE>
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<P>A rebalance operation in a single dimension is performed using an
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2012-02-10 02:04:37 +08:00
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iterative "diffusive" load-balancing algorithm <A HREF = "#Cybenko">(Cybenko)</A>.
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One iteration on a dimension (which is repeated <I>Niter</I> times), works
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as follows. Assume there are Px processors in the x dimension. This
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defines Px slices of the simulation, each of which contains Py*Pz
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processors. The task is to adjust the position of the Px-1 cuts
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between slices, leaving the end cuts unchanged (left and right edges
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of the simulation box).
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2012-02-10 00:12:43 +08:00
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</P>
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<P>The iteration beings by calculating the number of atoms within each of
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the Px slices. Then for each slice, its atom count is compared to its
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neighbors. If a slice has more atoms than its left (or right)
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neighbor, the cut is moved towards the center of the slice,
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effectively shrinking the width of the slice and migrating atoms to
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the other slice. The distance to move the cut is a function of the
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"density" of atoms in the donor slice and the difference in counts
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between the 2 slices. A damping factor is also applied to avoid
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oscillations in the position of the cutting plane as iterations
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proceed. Hence the "diffusive" nature of the algorithm as work
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(atoms) effectively diffuses from highly loaded processors to
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less-loaded processors.
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</P>
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<HR>
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<P><B>Restrictions:</B>
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</P>
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<P>The <I>dynamic</I> keyword cannot be used with the <I>x</I>, <I>y</I>, or <I>z</I>
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arguments.
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</P>
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<P>For 2d simulations, the <I>z</I> keyword cannot be used. Nor can a "z"
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appear in <I>dimstr</I> for the <I>dynamic</I> keyword.
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "processors.html">processors</A>, <A HREF = "fix_balance.html">fix balance</A>
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</P>
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<P><B>Default:</B> none
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</P>
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<HR>
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2012-02-10 02:04:37 +08:00
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<A NAME = "Cybenko"></A>
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<P><B>(Cybenko)</B> Cybenko, J Par Dist Comp, 7, 279-301 (1989).
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2012-02-10 00:12:43 +08:00
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</P>
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</HTML>
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