Particuology
9 (2011) 398–
405
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at
ScienceDirect
Particuology
j
our
nal
ho
me
p
ag
e:
www.elsevier.com/locate/partic
Parallel
computing
of
discrete
element
method
on
multi-core
processors
Yusuke
Shigeto
∗
,
Mikio
Sakai
Department
of
Systems
Innovation,
School
of
Engineering,
The
University
of
Tokyo,
7-3-1,
Hongo,
Bunkyo-ku,
Tokyo
113-8656,
Japan
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
10
November
2010
Received
in
revised
form
13
April
2011
Accepted
15
April
2011
Keywords:
Discrete
element
method
Parallel
computing
Multi-core
processor
GPGPU
a
b
s
t
r
a
c
t
This
paper
describes
parallel
simulation
techniques
for
the
discrete
element
method
(DEM)
on
multi-core
processors.
Recently,
multi-core
CPU
and
GPU
processors
have
attracted
much
attention
in
accelerating
computer
simulations
in
various
fields.
We
propose
a
new
algorithm
for
multi-thread
parallel
computa-
tion
of
DEM,
which
makes
effective
use
of
the
available
memory
and
accelerates
the
computation.
This
study
shows
that
memory
usage
is
drastically
reduced
by
using
this
algorithm.
To
show
the
practical
use
of
DEM
in
industry,
a
large-scale
powder
system
is
simulated
with
a
complicated
drive
unit.
We
compared
the
performance
of
the
simulation
between
the
latest
GPU
and
CPU
processors
with
optimized
programs
for
each
processor.
The
results
show
that
the
difference
in
performance
is
not
substantial
when
using
either
GPUs
or
CPUs
with
a
multi-thread
parallel
algorithm.
In
addition,
DEM
algorithm
is
shown
to
have
high
scalability
in
a
multi-thread
parallel
computation
on
a
CPU.
© 2011 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of
Sciences. Published by Elsevier B.V. All rights reserved.
1.
Introduction
Various
powder
devices
are
used
in
industrial
fields,
e.g.,
for
storage,
transportation
and
mixing.
In
designing
these
devices
or
investigating
their
operation,
numerical
simulation
is
a
promising
approach
from
the
viewpoint
of
minimizing
costs
and/or
optimiz-
ing
operating
conditions.
The
discrete
element
method
(DEM)
(Cundall
&
Strack,
1979)
is
widely
used
in
numerical
analyses
of
powder
processes
from
a
sci-
ence
and
engineering
perspective,
e.g.,
ball
mills
(Sakai,
Shibata,
&
Koshizuka,
2005,
2006),
fluidized
beds
(Tsuji,
Kawaguchi,
&
Tanaka,
1993;
Xu
&
Yu,
1997;
Ye,
van
der
Hoef,
&
Kuipers,
2004),
grinding
processes
(Cleary,
Sinnott,
&
Morrison,
2008),
and
the
investiga-
tion
of
particle
behavior
based
on
shape
(Latham,
Munjiza,
Garcia,
Xiang,
&
Guises,
2008).
DEM
is
a
Lagrangian
approach
where
indi-
vidual
particles
are
calculated
on
the
basis
of
Newton’s
second
law
of
motion.
DEM
enables
us
to
investigate
granular
flow
character-
istics
at
the
particle
level,
and
evaluate
particle
motion
precisely.
On
the
other
hand,
calculation
cost
becomes
excessive
when
the
number
of
particles
is
large,
thus
limiting
DEM
to
small-scale
sys-
tems.
The
development
of
novel
modeling
and
parallel
calculation
techniques
are
thus
urgently
needed
for
better
practical
implemen-
tation
of
DEM
in
complicated
and
large-scale
industrial
processes.
In
previous
studies,
a
coarse
grained
model
was
proposed
(Sakai
&
Koshizuka,
2009;
Sakai
et
al.,
2010)
to
solve
problems
of
dis-
∗
Corresponding
author.
Tel.:
+81
3
5841
7005;
fax:
+81
3
5841
7005.
E-mail
address:
shigeto@mps.q.t.u-tokyo.ac.jp
(Y.
Shigeto).
crete
element
modeling
of
large-scale
systems
by
using
a
coarse
grain
particle
to
represent
a
group
of
original
particles,
that
is,
cal-
culations
are
performed
using
the
coarse
grain
particles
instead
of
the
original
particles,
thus
drastically
reducing
the
number
of
calculated
particles.
However,
to
be
more
accurate,
the
number
of
calculated
particles
should
be
as
high
as
possible.
In
previous
studies,
PC
clusters
or
super
computers
were
used
to
simulate
the
large
number
of
calculated
particles
in
DEM
simulations
(Tsuji,
Nakamura,
Yabumoto,
&
Tanaka,
2007;
Ushijima
&
Nezu,
2001).
However,
because
of
excessive
initial
cost,
such
computer
systems
could
not
be
easily
promoted.
On
the
other
hand,
multi-thread
parallel
computing
could
be
introduced
at
low
cost.
The
recent
emergence
of
multi-core
proces-
sors
for
both
graphics
processing
unit
(GPU)
and
latest
multi-core
central
processing
unit
(CPU),
has
facilitated
multi-thread
paral-
lel
computations.
Nowadays,
a
GPU
is
a
common
component
in
all
types
of
PCs.
Of
course,
there
are
super
computers
(Chen
et
al.,
2009)
consisting
of
both
CPUs
and
GPUs.
Various
numerical
simu-
lations
in
general
scientific
fields
have
been
implemented
using
GPUs
(Harada,
Masaie,
Koshizuka,
&
Kawaguchi,
2008;
Harada,
Tanaka,
Koshizuka,
&
Kawaguchi,
2007;
Nguyen,
2007;
Nishiura
&
Sakaguchi,
2010;
NVIDIA,
in
press;
Ogawa
&
Aoki,
2009;
Pharr,
2005),
with
what
is
referred
to
as
general-purpose
computing
on
GPUs
(GPGPU),
while
DEM
has
also
been
implemented
on
a
GPU
(Shigeto,
Sakai,
Koshizuka,
&
Yamada,
2008).
The
performance
of
DEM
simulation
on
a
GPU
was
shown
to
be
several
dozen
times
faster
than
that
on
a
single-thread
CPU.
Similar
results
have
been
reported
for
other
simulations,
e.g.,
computational
fluid
dynam-
ics,
structural
analyses,
and
rigid
body
simulations.
The
number
of
1674-2001/$
–
see
front
matter ©
2011 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.partic.2011.04.002