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362 lines
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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>fix balance command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>fix ID group-ID balance Nfreq thresh style args keyword value ...
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
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<LI>balance = style name of this fix command
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<LI>Nfreq = perform dynamic load balancing every this many steps
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<LI>thresh = imbalance threshhold that must be exceeded to perform a re-balance
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<LI>style = <I>shift</I> or <I>rcb</I>
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<PRE> shift args = dimstr Niter stopthresh
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dimstr = sequence of letters containing "x" or "y" or "z", each not more than once
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Niter = # of times to iterate within each dimension of dimstr sequence
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stopthresh = stop balancing when this imbalance threshhold is reached
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rcb args = none
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</PRE>
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<LI>zero or more keyword/value pairs may be appended
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<LI>keyword = <I>out</I>
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<PRE> <I>out</I> value = filename
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filename = write each processor's sub-domain to a file, at each re-balancing
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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>fix 2 all balance 1000 1.05 shift x 10 1.05
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fix 2 all balance 100 0.9 shift xy 20 1.1 out tmp.balance
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fix 2 all balance 1000 1.1 rcb
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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 and shape of processor sub-domains
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within the simulation box, to attempt to balance the number of
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particles and thus the computational cost (load) evenly across
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processors. The load balancing is "dynamic" in the sense that
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rebalancing is performed periodically during the simulation. To
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perform "static" balancing, before or between runs, see the
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<A HREF = "balance.html">balance</A> command.
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</P>
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<P>Load-balancing is typically only useful if the particles in the
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simulation box have a spatially-varying density distribution. E.g. a
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model of a vapor/liquid interface, or a solid with an irregular-shaped
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geometry containing void regions. In this case, the LAMMPS default of
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dividing the simulation box volume into a regular-spaced grid of 3d
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bricks, with one equal-volume sub-domain per processor, may assign
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very different numbers of particles per processor. This can lead to
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poor performance when the simulation is run in parallel.
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</P>
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<P>Note that the <A HREF = "processors.html">processors</A> command allows some control
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over how the box volume is split across processors. Specifically, for
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a Px by Py by Pz grid of processors, it allows choice of Px, Py, and
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Pz, subject to the constraint that Px * Py * Pz = P, the total number
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of processors. This is sufficient to achieve good load-balance for
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some problems on some processor counts. However, all the processor
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sub-domains will still have the same shape and same volume.
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</P>
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<P>On a particular timestep, a load-balancing operation is only performed
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if the current "imbalance factor" in particles owned by each processor
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exceeds the specified <I>thresh</I> parameter. The imbalance factor is
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defined as the maximum number of particles owned by any processor,
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divided by the average number of particles per processor. Thus an
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imbalance factor of 1.0 is perfect balance.
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</P>
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<P>As an example, for 10000 particles running on 10 processors, if the
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most heavily loaded processor has 1200 particles, then the factor is
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1.2, meaning there is a 20% imbalance. Note that re-balances can be
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forced even if the current balance is perfect (1.0) be specifying a
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<I>thresh</I> < 1.0.
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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 depending on the method a perfect
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balance (1.0) may not be achieved. For example, "grid" methods
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(defined below) that create a logical 3d grid cannot achieve perfect
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balance for many irregular distributions of particles. Likewise, if a
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portion of the system is a perfect lattice, e.g. the initial system is
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generated by the <A HREF = "create_atoms.html">create_atoms</A> command, then "grid"
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methods may be unable to achieve exact balance. This is because
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entire lattice planes will be owned or not owned by a single
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processor.
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</P>
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<P>IMPORTANT NOTE: The imbalance factor is also an estimate of the
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maximum speed-up you can hope to achieve by running a perfectly
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balanced simulation versus an imbalanced one. In the example above,
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the 10000 particle simulation could run up to 20% faster if it were
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perfectly balanced, versus when imbalanced. However, computational
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cost 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 a 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 method used to perform a load balance is specified by one of the
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listed styles, which are described in detail below. There are 2 kinds
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of styles.
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</P>
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<P>The <I>shift</I> style is a "grid" method which produces a logical 3d grid
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of processors. It operates by changing the cutting planes (or lines)
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between processors in 3d (or 2d), to adjust the volume (area in 2d)
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assigned to each processor, as in the following 2d diagram where
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processor sub-domains are shown and atoms are colored by the processor
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that owns them. The leftmost diagram is the default partitioning of
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the simulation box across processors (one sub-box for each of 16
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processors); the middle diagram is after a "grid" method has been
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applied.
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</P>
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<CENTER><A HREF = "balance_uniform.jpg"><IMG SRC = "JPG/balance_uniform_small.jpg"></A><A HREF = "balance_nonuniform.jpg"><IMG SRC = "JPG/balance_nonuniform_small.jpg"></A><A HREF = "balance_rcb.jpg"><IMG SRC = "JPG/balance_rcb_small.jpg"></A>
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</CENTER>
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<P>The <I>rcb</I> style is a "tiling" method which does not produce a logical
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3d grid of processors. Rather it tiles the simulation domain with
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rectangular sub-boxes of varying size and shape in an irregular
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fashion so as to have equal numbers of particles in each sub-box, as
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in the rightmost diagram above.
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</P>
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<P>The "grid" methods can be used with either of the
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<A HREF = "comm_style.html">comm_style</A> command options, <I>brick</I> or <I>tiled</I>. The
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"tiling" methods can only be used with <A HREF = "comm_style.html">comm_style
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tiled</A>.
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</P>
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<P>When a "grid" method is specified, the current domain partitioning can
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be either a logical 3d grid or a tiled partitioning. In the former
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case, the current logical 3d grid is used as a starting point and
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changes are made to improve the imbalance factor. In the latter case,
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the tiled partitioning is discarded and a logical 3d grid is created
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with uniform spacing in all dimensions. This is the starting point
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for the balancing operation.
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</P>
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<P>When a "tiling" method is specified, the current domain partitioning
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("grid" or "tiled") is ignored, and a new partitioning is computed
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from scratch.
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</P>
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<HR>
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<P>The <I>group-ID</I> is currently ignored. In the future it may be used to
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determine what particles are considered for balancing. Normally it
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would only makes sense to use the <I>all</I> group. But in some cases it
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may be useful to balance on a subset of the particles, e.g. when
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modeling large nanoparticles in a background of small solvent
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particles.
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</P>
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<P>The <I>Nfreq</I> setting determines how often a rebalance is performed. If
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<I>Nfreq</I> > 0, then rebalancing will occur every <I>Nfreq</I> steps. Each
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time a rebalance occurs, a reneighboring is triggered, so <I>Nfreq</I>
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should not be too small. If <I>Nfreq</I> = 0, then rebalancing will be
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done every time reneighboring normally occurs, as determined by the
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the <A HREF = "neighbor.html">neighbor</A> and <A HREF = "neigh_modify.html">neigh_modify</A>
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command settings.
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</P>
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<P>On rebalance steps, rebalancing will only be attempted if the current
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imbalance factor, as defined above, exceeds the <I>thresh</I> setting.
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</P>
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<HR>
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<P>The <I>shift</I> style invokes a "grid" method for balancing, as described
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above. It changes the positions of cutting planes between processors
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in an iterative fashion, seeking to reduce the imbalance factor.
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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". Eacn character can appear zero or one time,
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since there is no advantage to balancing on a dimension more than
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once. You should normally only list dimensions where you expect there
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to be a density variation in the particles.
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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. For a single
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dimension, the balancing operation (described below) is iterated on up
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to <I>Niter</I> times. After each dimension finishes, the imbalance factor
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is re-computed, and the balancing operation halts if the <I>stopthresh</I>
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criterion is met.
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</P>
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<P>A rebalance operation in a single dimension is performed using a
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density-dependent recursive multisectioning algorithm, where the
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position of each cutting plane (line in 2d) in the dimension is
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adjusted independently. This is similar to a recursive bisectioning
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for a single value, except that the bounds used for each bisectioning
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take advantage of information from neighboring cuts if possible, as
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well as counts of particles at the bounds on either side of each cuts,
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which themselves were cuts in previous iterations. The latter is used
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to infer a density of pariticles near each of the current cuts. At
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each iteration, the count of particles on either side of each plane is
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tallied. If the counts do not match the target value for the plane,
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the position of the cut is adjusted based on the local density. The
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low and high bounds are adjusted on each iteration, using new count
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information, so that they become closer together over time. Thus as
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the recursion progresses, the count of particles on either side of the
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plane gets closer to the target value.
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</P>
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<P>The density-dependent part of this algorithm is often an advantage
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when you rebalance a system that is already nearly balanced. It
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typically converges more quickly than the geometric bisectioning
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algorithm used by the <A HREF = "balance.html">balance</A> command. However, if can
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be a disadvantage if you attempt to rebalance a system that is far
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from balanced, and converge more slowly. In this case you probably
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want to use the <A HREF = "balance.html">balance</A> command before starting a run,
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so that you begin the run with a balanced system.
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</P>
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<P>Once the rebalancing is complete and final processor sub-domains
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assigned, particles migrate to their new owning processor as part of
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the normal reneighboring procedure.
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</P>
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<P>IMPORTANT NOTE: At each rebalance operation, the bisectioning for each
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cutting plane (line in 2d) typcially starts with low and high bounds
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separated by the extent of a processor's sub-domain in one dimension.
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The size of this bracketing region shrinks based on the local density,
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as described above, which should typically be 1/2 or more every
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iteration. Thus if <I>Niter</I> is specified as 10, the cutting plane will
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typically be positioned to better than 1 part in 1000 accuracy
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(relative to the perfect target position). For <I>Niter</I> = 20, it will
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be accurate to better than 1 part in a million. Thus there is no need
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to set <I>Niter</I> to a large value. This is especially true if you are
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rebalancing often enough that each time you expect only an incremental
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adjustement in the cutting planes is necessary. LAMMPS will check if
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the threshold accuracy is reached (in a dimension) is less iterations
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than <I>Niter</I> and exit early.
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</P>
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<HR>
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<P>The <I>rcb</I> style invokes a "tiled" method for balancing, as described
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above. It performs a recursive coordinate bisectioning (RCB) of the
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simulation domain. The basic idea is as follows.
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</P>
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<P>The simulation domain is cut into 2 boxes by an axis-aligned cut in
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the longest dimension, leaving one new box on either side of the cut.
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All the processors are also partitioned into 2 groups, half assigned
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to the box on the lower side of the cut, and half to the box on the
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upper side. (If the processor count is odd, one side gets an extra
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processor.) The cut is positioned so that the number of atoms in the
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lower box is exactly the number that the processors assigned to that
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box should own for load balance to be perfect. This also makes load
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balance for the upper box perfect. The positioning is done
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iteratively, by a bisectioning method. Note that counting atoms on
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either side of the cut requires communication between all processors
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at each iteration.
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</P>
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<P>That is the procedure for the first cut. Subsequent cuts are made
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recursively, in exactly the same manner. The subset of processors
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assigned to each box make a new cut in the longest dimension of that
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box, splitting the box, the subset of processsors, and the atoms in
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the box in two. The recursion continues until every processor is
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assigned a sub-box of the entire simulation domain, and owns the atoms
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in that sub-box.
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</P>
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<HR>
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<P>The <I>out</I> keyword writes a text file to the specified <I>filename</I> with
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the results of each rebalancing operation. The file contains the
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bounds of the sub-domain for each processor after the balancing
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operation completes. The format of the file is compatible with the
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<A HREF = "pizza">Pizza.py</A> <I>mdump</I> tool which has support for manipulating and
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visualizing mesh files. An example is shown here for a balancing by 4
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processors for a 2d problem:
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</P>
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<PRE>ITEM: TIMESTEP
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0
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ITEM: NUMBER OF NODES
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16
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ITEM: BOX BOUNDS
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0 10
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0 10
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0 10
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ITEM: NODES
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1 1 0 0 0
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2 1 5 0 0
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3 1 5 5 0
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4 1 0 5 0
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5 1 5 0 0
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6 1 10 0 0
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7 1 10 5 0
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8 1 5 5 0
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9 1 0 5 0
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10 1 5 5 0
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11 1 5 10 0
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12 1 10 5 0
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13 1 5 5 0
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14 1 10 5 0
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15 1 10 10 0
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16 1 5 10 0
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ITEM: TIMESTEP
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0
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ITEM: NUMBER OF SQUARES
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4
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ITEM: SQUARES
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1 1 1 2 3 4
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2 1 5 6 7 8
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3 1 9 10 11 12
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4 1 13 14 15 16
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</PRE>
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<P>The coordinates of all the vertices are listed in the NODES section, 5
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per processor. Note that the 4 sub-domains share vertices, so there
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will be duplicate nodes in the list.
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</P>
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<P>The "SQUARES" section lists the node IDs of the 4 vertices in a
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rectangle for each processor (1 to 4).
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</P>
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<P>For a 3d problem, the syntax is similar with 8 vertices listed for
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each processor, instead of 4, and "SQUARES" replaced by "CUBES".
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</P>
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<HR>
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<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
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</P>
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<P>No information about this fix is written to <A HREF = "restart.html">binary restart
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files</A>. None of the <A HREF = "fix_modify.html">fix_modify</A> options
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are relevant to this fix.
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</P>
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<P>This fix computes a global scalar which is the imbalance factor
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after the most recent rebalance and a global vector of length 3 with
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additional information about the most recent rebalancing. The 3
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values in the vector are as follows:
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</P>
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<UL><LI>1 = max # of particles per processor
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<LI>2 = total # iterations performed in last rebalance
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<LI>3 = imbalance factor right before the last rebalance was performed
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</UL>
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<P>As explained above, the imbalance factor is the ratio of the maximum
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number of particles on any processor to the average number of
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particles per processor.
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</P>
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<P>These quantities can be accessed by various <A HREF = "Section_howto.html#howto_15">output
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commands</A>. The scalar and vector values
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calculated by this fix are "intensive".
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</P>
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<P>No parameter of this fix can be used with the <I>start/stop</I> keywords of
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the <A HREF = "run.html">run</A> command. This fix is not invoked during <A HREF = "minimize.html">energy
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minimization</A>.
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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>For 2d simulations, a "z" cannot appear in <I>dimstr</I> for the <I>shift</I>
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style.
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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 = "balance.html">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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</HTML>
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