U.S. patent application number 11/392405 was filed with the patent office on 2007-10-04 for reduced message count for interaction decomposition of n-body simulations.
This patent application is currently assigned to International Business Machines Corporation. Invention is credited to Blake G. Fitch, Robert S. Germain, Michael C. Pitman, Aleksandr Rayshubskiy.
Application Number | 20070233440 11/392405 |
Document ID | / |
Family ID | 38560446 |
Filed Date | 2007-10-04 |
United States Patent
Application |
20070233440 |
Kind Code |
A1 |
Fitch; Blake G. ; et
al. |
October 4, 2007 |
Reduced message count for interaction decomposition of N-body
simulations
Abstract
Disclosed are a method of and system for creating a load
balanced spatial partitioning of a structured, diffusing system of
particles with pairwise interactions that is scalable to a very
large number of nodes and has favorable communications
characteristics including well defined bounds on the number of hops
and the number of nodes to which a particle's position must be
sent. To deal with structural imbalance, we can assign a weight
corresponding to the computational cost for a particular pair
interaction of particles or locally clustered groups of particles
to simulation space at the midpoint of the distance between the
particles or centers of the clusters. We then carry out a spatial
partitioning of the simulation volume using a k-d tree or optimal
recursive bisection (ORB) to divide the volume into sections that
have approximately equal total weights. To deal with local
degradation of the load balance caused by changes in the
distribution of particles from that used to determine the original
spatial decomposition one can assign the actual computation of the
pair interaction between two particles to any node that has the
positions of both particles.
Inventors: |
Fitch; Blake G.; (White
Plaine, NY) ; Germain; Robert S.; (Larchmont, NY)
; Pitman; Michael C.; (Wappingers Falls, NY) ;
Rayshubskiy; Aleksandr; (Tarrytown, NY) |
Correspondence
Address: |
SCULLY SCOTT MURPHY & PRESSER, PC
400 GARDEN CITY PLAZA, SUITE 300
GARDEN CITY
NY
11530
US
|
Assignee: |
International Business Machines
Corporation
Armonk
NY
|
Family ID: |
38560446 |
Appl. No.: |
11/392405 |
Filed: |
March 29, 2006 |
Current U.S.
Class: |
703/6 |
Current CPC
Class: |
G16C 10/00 20190201 |
Class at
Publication: |
703/6 |
International
Class: |
G06G 7/48 20060101
G06G007/48 |
Claims
1. A method of creating a load balanced spatial partitioning of a
structured, diffusing system of particles, comprising the steps of:
providing a computer system having a plurality of processing nodes;
assigning computational weights to the particles; separating said
system of particles, based on the computational weights assigned to
the particles, into a number of voxels; mapping each voxel to one
of the processing nodes of the computer system; and for each voxel,
using said one of the processing nodes, to which said each voxel is
mapped, to perform a series of calculations for the particles in
said each voxel.
2. A method according to claim 1, wherein: the step of assigning
computational weights includes the step of assigning each of the
computational weights to a position in said system; and the
separating step includes the step of separating said system of
particles into said number of voxels based on the positions
assigned to the computational weights.
3. A method according to claim 2, wherein the voxels have an
approximately equal total of computational weights.
4. A method according to claim 2, wherein: each computational
weight is associated with a pair of the particles; and the step of
assigning each of the computational weights to a position includes
the step of assigning each computational weight to a position
between the pair of particles with which said each computational
weight is associated.
5. A method according to claim 1, wherein: the computer system has
a given number of said processing nodes; said given number of
voxels equals said given number; and the mapping step includes the
step of mapping each of the voxels to a respective one of the
processing nodes of the computer system.
6. A method according to claim 1, comprising the further step of,
over time, assigning said calculations for some of the particles
from one of the processing nodes to another of the processing nodes
to alleviate reduced load balance caused by changes in the
distribution of particles in said system.
7. A method according to claim 1, wherein: the using step includes
the step of using said one of the processing nodes to perform said
series of calculations at a first time for the particles in said
each voxel; and comprising the further steps of, for each of at
least some of the particles in the system: broadcasting the
position of the particle to a set of said processing nodes; and
using said one of said set of processing nodes to perform said
calculations, at a second time.
8. A system for creating a load balanced spatial partitioning of a
structured, diffusing system of particles, comprising the steps of:
a computer system having a plurality of processing nodes; means for
assigning computational weights to the particles; means for
separating said system of particles, based on the computational
weights assigned to the particles, into a number of voxels; and
means for mapping each voxel to one of the processing nodes of the
computer system; wherein said one of the processing nodes performs
a series of calculations for the particles in said each voxel.
9. A system according to claim 8, wherein: the means for assigning
computational weights includes means for assigning each of the
computational weights to a position in said system; and the means
for separating includes means for separating said system of
particles into said number of voxels based on the positions
assigned to the computational weights.
10. A system according to claim 9, wherein the voxels have an
approximately equal total of computational weights.
11. A system according to claim 9, wherein: each computational
weight is associated with a pair of the particles; and the
assigning means includes means for assigning each computational
weight to a position between the pair of particles with which said
each computational weight is associated.
12. A system according to claim 8, wherein: the computer system has
a given number of said processing nodes; said given number of
voxels equals said given number; and the means for mapping includes
means for mapping each of the voxels to a respective one of the
processing nodes of the computer system.
13. A system according to claim 8, wherein: said one of the
processing nodes performs said series of calculations at a first
time for the particles in said each voxel; and further comprising:
means for broadcasting the positions of at least some of the
particles to a set of said processing nodes; and wherein one of
said set of processing nodes performs said series of calculations
at a second time.
14. A program storage device readable by machine, tangibly
embodying a program of instructions executable by the machine to
perform method steps for creating a load balanced spatial
partitioning of a structured, diffusing system of particles, and
for use with a computer system having a plurality of processing
nodes, said method steps comprising: assigning computational
weights to the particles; separating said system of particles,
based on the computational weights assigned to the particles, into
a number of voxels; mapping each voxel to one of the processing
nodes of the computer system; and for each voxel, using said one of
the processing nodes, to which said each voxel is mapped, to
perform a series of calculations for the particles in said each
voxel.
15. A program storage device according to claim 14, wherein: the
step of assigning computational weights includes the step of
assigning each of the computational weights to a position in said
system; and the separating step includes the step of separating
said system of particles into said number of voxels based on the
positions assigned to the computational weights.
16. A program storage device according to claim 15, wherein the
voxels have an approximately equal total of computational
weights.
17. A program storage device according to claim 15, wherein: each
computational weight is associated with a pair of the particles;
and the step of assigning each of the computational weights to a
position includes the step of assigning each computational weight
to a position between the pair of particles with which said each
computational weight is associated.
18. A program storage device according to claim 14, wherein: the
computer system has a given number of said processing nodes; said
given number of voxels equals said given number; and the mapping
step includes the step of mapping each of the voxels to a
respective one of the processing nodes of the computer system.
19. A program storage device according to claim 14, wherein: the
using step includes the step of using said one of the processing
nodes to perform said series of calculations at a first time for
the particles in said each voxel; and said method steps comprise
the further steps of, for each of at least some of the particles in
the system: broadcasting the position of the particle to a set of
said processing nodes; and using said one of said set of processing
nodes to perform said calculations, at a second time.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] This invention generally relates to methods and systems for
solving N-body problems, such as classical molecular dynamics. More
specifically, the invention relates to methods and systems for
creating a load balanced spatial partitioning of a structured,
diffusing system of particles.
[0003] 2. Background Art
[0004] Over the last few years, unprecedented computational
resources have been developed, such as the Blue Gene family of
computers from the International Business Machines Corporation.
These resources may be used to attack, among other issues, grand
challenge life sciences problems such as advancing the
understanding of biologically important processes, in particular,
the mechanisms behind protein folding.
[0005] In order to address this goal, attention has been directed
to creating a classical molecular dynamics software package for
long-time and large-scale molecular simulations. Classical
molecular dynamics is predominantly an N-body problem. A standard
definition of an n-body problem is as follows: [0006] The n-body
problem is the problem of finding, given the initial positions,
masses, and velocities of n bodies, their subsequent motions as
determined by classical mechanics.
[0007] An N-body problem, for example molecular dynamics (MD),
proceeds as a sequence of simulation time steps. At each time step,
forces on particles, in MD atoms, are computed; and then the
equations of motion are integrated to update the velocities and
positions of the particles. In order to compute the forces on the
particles, nominally the force between each particle and every
other particle is computed, a computational burden of
O(n.sup.2).
[0008] Practically speaking, molecular dynamics programs reduce the
O(n.sup.2) by cutting off pair interactions at some distance.
However for many scientifically relevant molecular systems, the
computational burden due to the particle pair interactions remains
large. In order to reach scientifically relevant simulation times,
parallel computers are required to compute particle pair
interactions rapidly.
SUMMARY OF THE INVENTION
[0009] An object of this invention is to provide a method for
solving N-body problems such as classical molecular dynamics.
[0010] Another object of the present invention is to solve the
N-body problem by geometrically mapping simulation space to a
torus/mesh parallel computer's node space.
[0011] A further object of the invention is to enable the geometric
n-body problem to be efficiently mapped to a machine with a
fundamentally geometric processor space.
[0012] Another object of the invention is to create a load balanced
spatial partitioning of a structured, diffusing system of particles
with pairwise interactions that is scalable to a very large number
of nodes and has favorable communications characteristics,
including well defined bounds on the number of hops and the number
of nodes to which a particle's position must be sent.
[0013] These and other objectives are attained with a method of and
a system for creating a load balanced spatial partitioning of a
structured, diffusing system of particles. The method comprises the
steps of providing a computer system having a plurality of
processing nodes; assigning computational weights to the particles;
separating said system of particles, based on the computational
weights assigned to the particles, into a number of voxels; and
mapping each voxel to one of the processing nodes of the computer
system. For each voxel, the processing node, to which said each
voxel is mapped, performs a series of calculations for the
particles in said each voxel.
[0014] The preferred embodiment of the invention, described below
in detail, provides a method and system for creating a load
balanced spatial partitioning of a structured, diffusing system of
particles with pairwise interactions that is scalable to a very
large number of nodes and has favorable communications
characteristics including well defined bounds on the number of hops
and the number of nodes to which a particle's position must be
sent. To deal with structural imbalance, a weight corresponding to
the computational cost for a particular pair interaction of
particles or locally clustered groups of particles, is assigned to
simulation space at the midpoint of the distance between the
particles or centers of the clusters. Then a spatial partitioning
of the simulation volume is carried out using a k-d tree or optimal
recursive bisection (ORB) to divide the volume into sections that
have approximately equal total weights. To deal with local
degradation of the load balance caused by changes in the
distribution of particles from that used to determine the original
spatial decomposition one can assign the actual computation of the
pair interaction between two particles to any node that has the
positions of both particles.
[0015] Because pair interactions are cut-off beyond a defined
radius R.sub.c, one can broadcast the position of a particle to the
group of nodes containing a portion of the surface of a suitable
specified convex shape that contains the sphere of radius
R.sub.b.gtoreq.R.sub.c/2 centered about the position of original
particle in simulation space, ensuring the existence of at least
one node containing the positions of both particles required to
compute any interaction. An example of such a convex shape is the
spherical surface of radius R.sub.b itself. The locus of points
formed by the intersection of the two surfaces may be referred to
as the "interaction loop", and any node containing a portion of the
"interaction loop" can compute the specified interaction. This
provides an opportunity for eliminating imbalances caused by
short-term local fluctuations in interaction workload. Because the
load-balancing is carried out using interaction centers, there are
many more geometrically distinct work objects that can be
partitioned using an ORB strategy, and this decomposition allows
productive use of more nodes than there are particles in the
system.
[0016] Any suitable computer or computer system may be used to
implement the invention; and for instance, the above-mentioned Blue
Gene family of computers may be used. The Blue Gene/L parallel
computational platform does interprocessor communication primarily
using a 3D torus network. Processor space is defined by the
location of processors on the 3D torus network and communication
costs between processors increase with distance. The methods
described herein enable the geometric n-body problem to be
efficiently mapped to a machine with a fundamentally geometric
processor space, however these methods may be applied to other
network topologies with good results.
[0017] This invention addresses a method for solving N-body
problems such as classical molecular dynamics on preferably
mesh/torus machines such as Blue Gene/L.
[0018] In the discussion herein, the following
definitions/conventions are used: [0019] For some n-body
simulations, it is convenient to define a partitioning of the
particles into groups of one or more particles that are treated as
a unit for certain purposes. When this intended, the term
"fragment" will be used to indicate such an entity that consists of
one or more particles. [0020] The term "node" refers to the
computational element that form nodes in the graph defined by the
interconnection network. Any "node" may include one or more
processors. Any suitable processing unit or units may be used in
the node, and it is not necessary to describe the detail of the
processing units. [0021] The term "simulation space" refers to the
domain of the n-body simulation. [0022] The term "node space"
refers to the geometry of the interconnections between nodes of the
machine. Typically the discussion herein refers to a machine with a
three-dimensional torus/mesh interconnect geometry in which each
node is connected to its six nearest neighbors and is addressed by
a triple of integers that represent its coordinates within the
network. In a torus, periodic boundary conditions are implemented
physically by connecting the nodes on opposite "faces" of the
machine.
[0023] Further benefits and advantages of the invention will become
apparent from a consideration of the following detailed
description, given with reference to the accompanying drawings,
which specify and show preferred embodiments of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
[0024] FIG. 1 illustrates a part of a torus computer system that
may be used to practice this invention.
[0025] FIG. 2 is a flow chart showing a procedure for partitioning
simulation space.
[0026] FIG. 3 shows a series of data structures initialized with a
linked list of nodes.
[0027] FIG. 4 outlines a procedure to populate a table referred to
as the sparse skin table.
[0028] FIG. 5 illustrates the relationship of particle positions
and interaction centers in simulation space.
[0029] FIG. 6 shows broadcast zones for two nodes.
[0030] FIG. 7 shows an example of an algorithm that allows
deterministic, averaged interaction assignment.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0031] FIG. 1 illustrates a part of a computer system or structure
that may be used in the implementation of the present invention.
More specifically, FIG. 1 shows a part of a Massively Parallel
Supercomputer architecture in the form of a three-dimensional torus
designed to deliver processing power on the order of teraOPS
(trillion floating-point operations per second) for a wide range of
applications. The Massively Parallel supercomputer architecture, in
an exemplary embodiment, may comprise 65,536 processing nodes
organized as a 64.times.32.times.32 three-dimensional torus with
each processing node connected to six (6) neighboring nodes.
[0032] In particular, FIG. 1 shows a torus comprised of eight nodes
12 connected together by links or connections 13. It is clear to
see how this interconnect scales by increasing the number of nodes
12 along all three dimensions. With current technology, this
architecture can be leveraged to hundreds of teraOPS. As will be
understood by those of ordinary skill in the art, other computer
structures may also be used in the practice of this invention.
[0033] The present invention efficiently solves the N-body problem
by, in the preferred embodiment, geometrically mapping simulation
space to a torus/mesh parallel computer's node space, a spatial
decomposition. In the preferred embodiment, the mechanism for
distributing the work is a broadcast of particle positions followed
possibly by a reduction of forces on fragment home nodes.
[0034] A basic requirement of this method is the ability to
broadcast data from one node to a subset of all the nodes in the
system. The required collective operations can be constructed using
point-to-point communications however; hardware may offer features
to enhance the performance of these primitives such as
multi-cast.
[0035] In the preferred mapping of simulation space to node space,
simulation space is divided into the same number of sub-volumes as
there are nodes, and further, the simulation space preferably has
the same extents (measured in voxels) in each dimension as node
space (measured in nodes). The volume elements assigned to each
processor (or voxels) may be of non-uniform size.
[0036] The two communications operations of interest are: [0037]
Surface broadcast: given a convex shape in simulation space,
broadcast data from the node containing the center of such a shape
to each node managing a portion of the surface of that shape.
[0038] Ellipsoidal reduce: given a convex shape in simulation
space, theta-reduce data from each node managing a portion of the
surface of that shape 20 the root node containing the center of the
shape.
N-Body Spatial Decomposition for Load Balance
[0039] N-body problems in a periodic simulation space nominally
have a computational burden defined by the order O(N.sup.2)
pairwise particle interactions possible. In many applications, this
computational burden is reduced to O(N) by cutting off interactions
between particles separated by more than a specified distance in
periodic simulation space.
[0040] A natural way to map a spatial problem on a spatial
connected machine is with a direct mapping, where the simulation
space is uniformly assigned to processors space. For N-body systems
(assuming that all pair interactions have the same computational
cost) with a uniform density of particles or where no cut-offs are
imposed, this simple mapping will result in a balanced load across
the machine since each node or region of nodes will have roughly
the same interaction computation workload.
[0041] Where particles are not evenly distributed in the simulation
space and interaction cutoffs are in effect and/or interaction
computation costs are not the same, a direct mapping results in
load imbalance. There are techniques for locally averaging load
imbalance between nodes. However, if the imbalance is severe
enough, these regional averaging techniques will be
ineffective.
[0042] For any fixed distribution of particles, techniques such as
optimal recursive bisection (ORB) can be used to balance
computational burden on each node by assigning partitioning
simulation space into non-uniform sub-volumes that will be assigned
to nodes. One suitable spatial decomposition procedure is shown in
FIG. 2.
[0043] An ORB can be constructed from a distribution of points
representing particle or fragment centers, or as discussed below,
midpoints of pair interactions. Prior to ORB construction, a
function estimating the work associated with each point is
evaluated, at step 21, and stored with the point. In the case of
pair interaction midpoints, this corresponds to the work required
to evaluate the forces between the pair of particles or fragments.
ORB construction begins with the periodic boundaries of the
simulation cell as the initial volume, and the distribution of
points with their associated work values. Application of the ORB
technique partitions a unit cell into 2.sup.N smaller cells. For
cases where N is divisible by 3, the number of sub-volumes will be
equal in each dimension (number of sub-volumes=8, 64, 512, 4096, .
. . ).
[0044] The simulation cell volume is partitioned recursively in
cycles. Each cycle bisects a volume along each dimension in
succession giving eight sub-volumes at the end of the cycle. Each
bisection begins, at step 22 of FIG. 2, by sorting the distribution
of points within the volume along one of its dimensions and
locating the nearest point to the median of the distribution of
work values associated with each point. The volume, at step 23, is
then divided with a plane orthogonal to the sorted dimension
passing through the selected point. The points in the sub-volumes
on either side of the plane are, at step 24, then each separately
sorted along another dimension, and partitioned according to the
points near the median of the work distribution for their
respective work value distributions. At step 25, each of the four
resulting subvolumes is then sorted in the final dimension and
partitioned, giving eight partitions of the original volume. This
cycle repeats recursively for each of the eight sub-volumes until
the desired number of sub-volumes is reached, which is equal to the
number of nodes to be used in the simulation. For cases where N is
not divisible by three, the initial cycle partitions along either
one or two dimensions, rather than three. The remaining cycles will
then partition along each of the three dimensions.
[0045] The resulting ORB partitioning of simulation space greatly
reduces the variance of work needed to compute the forces
represented by the points in a given sub-volume. The assignment of
the work represented by the points in each sub-volume to a node
therefore provides an initial step in load balancing. A given
N-body problem may require multiple load balancing techniques. An
ORB may be required to balance the global imbalance caused by the
structure of the system being simulated and a local work exchange
scheme may be required for imbalances caused by diffusion.
Preferred Load Balancing Algorithm
[0046] In practice, a different scheme for load balancing has been
found to be more useful. In this algorithm, space is divided into
equally sized volume elements that map simulation space "naturally"
onto node space in the way that would be obtained via the ORB
technique if load were uniformly distributed throughout the
simulation volume. The algorithm begins with creation of a table,
the option table with an entry for every pair of nodes whose volume
elements have some region within cut-off. To this entry is attached
a list of nodes who are members of the interaction loop defined by
the intersection of the spherical surfaces with radius equal to
half the cut-off distance. The entries in the table are then sorted
by length of list with the entries possessing the shortest lists
coming first as shown in FIG. 3.
[0047] An additional table is created that consists of one entry
for every node where each entry has an attached list of nodes that
comprise the set of nodes to which the positions of particles homed
in the originating node is broadcast. However, the table is created
with these lists initialized to be empty. Because the lists in this
table will be subsets of the full broadcast skins defined by the
geometries of the simulation and node spaces, we refer to this as
the sparse skin table. Following the description in FIG. 4, we
iterate through the option table to populate the sparse skin table.
Many variants of the scheme outlined in FIG. 4 are possible
including the inclusion of a weighting field in the option table
that could be computed, for example, from the actual count of
particle pairs within range for each pair of nodes/volume elements.
Algorithms applicable to the "bin-packing" problem could be adapted
for use in this load-balancing problem.
Molecular Dynamics Decompositions Based on Ellipsoidal
Communications Primitives Optimal Interaction Assignment Using ORBs
and Dynamic Interaction Balancing
[0048] Molecular dynamics as applied to biomolecular simulation of
fixed sized problems on very large, geometric node spaces requires
a simulation space to node space mapping that, preferably,
maintains as much locality as possible while balancing workload.
This is so communication costs and computational costs are
minimized in balance. Since the n-body problem may have structural
imbalance caused by inhomogeneities in the system, create a
partition of simulation based on ORB that divides the workload
evenly assuming a nominal weight for each pair interaction and a
specified cutoff. In the limit that the ratio of the number of
particles to node count is small, it may be desirable to start
dividing simulation space using optimal recursive bisection and
then switch to a strict volumetric bisection near the leaves to
improve micro level balance of particle assignment. FIG. 5 contains
a view of a two-dimensional system with both particle positions and
interaction centers shown.
[0049] More specifically, FIG. 5 illustrates the relationship of
the particle positions (larger dots) and the interaction centers
(smaller dots) in simulation space. The interaction centers are
placed at the mid-point between each pair of particles that fall
within the cut-off radius. A dashed circle 34 with radius equal to
the cut-off radius chosen is drawn around one of the particles.
Static or "structural" load balancing is carried out by using
optimal recursive bisection to partition the simulation volume into
sub-volumes that contain approximately equal computational burdens.
The computational burden of a sub-volume is computed by summing the
computational burden of each interaction center contained within
within that sub-volume.
[0050] Next, the minimal set of communicating nodes for a
particular particle must be identified. The minimal set of
communicating nodes is defined as all those nodes which contain any
of the surface of a specified convex volume containing the
spherical volume of space (with radius greater than half the cutoff
radius) centered about the particle. This defines a minimal volume
in node space that ensures that there exists at least one node for
every pair of particles within cutoff that can calculate the
interaction between that pair.
[0051] During each simulation step, each node sends all its
particle positions to each of its communication partners and
receives from each a set of particle positions. A node may be
assigned to evaluate the interaction between any pair of particles
in the set of positions it has received.
[0052] Although pairs of particle positions in the simulation space
separated by close to the cutoff distance might be received by only
a single node creating a definitive assignment, generally the
positions of any given pair of particles will be received by
several nodes as shown in FIG. 6, any one of which may be assigned
that pair's interaction.
[0053] FIG. 6 shows the broadcast zones 41 and 42 for two nodes
superimposed on the spatial decomposition of the domain onto all
nodes (two-dimensional view for simplicity). The nodes that contain
portions of the surface in simulation space defined by the surface
of the volume defined by the set of points within radius R.sub.b of
any voxel assigned to Node A are shown in one type of hatching 43
with a different hatching 44 where the nodes also contain portions
of the surface in simulation space defined by the surface of the
volume defined by the set of points within R.sub.b of any voxel
assigned to Node B (which are marked with one type of hatching 45
except where overlap occurs). The broadcast radius
R.sub.b>R.sub.c/2 where R.sub.c is the cutoff radius. The
interaction between a particle stored on Node A and a particle
stored on Node B can be computed on any of the nodes with
cross-hatching.
[0054] Interaction assignment may be accomplished by any method,
which results in the interaction between a pair of particles being
done once on one node. An example of a suitable algorithm is to
specify that the interaction will be done on the node that has
received both particle positions and has the minimum node id
number. Such algorithms however have load balancing characteristics
which reflect the spatial mapping technique used.
[0055] In order to reduce micro load imbalance, dynamic
deterministic interaction assignment can be employed. These
techniques allow rapid overlapping regional averaging. To enable
these techniques, each node must measure its current computational
load and add this value to each message it sends to its
communication partners. When a node receives its set of [load,
position set] messages from its communicating partners, it now has
enough information to deterministically assign itself a set of
interactions. The set of interactions each node can contribute to
load averaging among its communication partners.
[0056] An example of an algorithm, illustrated in FIG. 7, which
allows deterministic, averaged interaction assignment is as
follows:
[0057] At step 51, receive a complete set of [load, position set]
messages from communicating partners. At step 52, for each pair of
received messages, create a canonical interaction list including
the effects of range cutoffs. At step 53, for each pair of messages
received, determine the set of nodes that also received this pair
of messages. At step 54, using a deterministic algorithm, assign
each interaction (appearing on the canonical interaction list) that
could be computed by the above set of nodes to one of those nodes.
Examples of such deterministic algorithms include: [0058] Using the
loads reported on each of those nodes, assign interactions (which
have been ordered in some canonical way) to attempt to equalize the
new loads on each of the nodes. [0059] Randomizing the assignment
of interactions to the node set using a hashing algorithm. [0060]
Assigning each interaction to the node owning the voxel that
contains the mid-point of the line connecting the interacting pair
of particles.
[0061] At step 55 of FIG. 7, do assigned particle pair
interactions. At step 56, send each computed interaction force back
to the pair of nodes that own the interacting particles.
[0062] Importantly, this algorithm costs only interaction
computation. The cost of returning the force should be added to
reflect lower communication cost of computing an interaction on a
node which owns one of the particles.
[0063] For the purposes of increased scope for load balancing or in
cases where communication costs are high relative to computation
costs, it may be advantageous to increase the simulation space
radius determining the communication partner set beyond R.sub.c/2
to increase the number of nodes available for load balancing.
[0064] It should be understood that the present invention can be
realized in hardware, software, or a combination of hardware and
software. Any kind of computer/server system(s)--or other apparatus
adapted for carrying out the methods described herein--is suited. A
typical combination of hardware and software could be a general
purpose computer system with a computer program that, when loaded
and executed, carries out the respective methods described herein.
Alternatively, a specific use computer, containing specialized
hardware for carrying out one or more of the functional tasks of
the invention, could be utilized.
[0065] The present invention, or aspects thereof, can also be
embedded in a computer program product, which comprises all the
respective features enabling the implementation of the methods
described herein, and which--when loaded in a computer system--is
able to carry out these methods. Computer program, software
program, program, or software, in the present context mean any
expression, in any language, code or notation, of a set of
instructions intended to cause a system having an information
processing capability to perform a particular function either
directly or after either or both of the following: (a) conversion
to another language, code or notation; and/or (b) reproduction in a
different material form.
[0066] While it is apparent that the invention herein disclosed is
well calculated to fulfill the objects stated above, it will be
appreciated that numerous modifications and embodiments may be
devised by those skilled in the art, and it is intended that the
appended claims cover all such modifications and embodiments as
fall within the true spirit and scope of the present invention.
* * * * *