<s>
A	O
discrete	B-Algorithm
element	I-Algorithm
method	I-Algorithm
(	O
DEM	O
)	O
,	O
also	O
called	O
a	O
distinct	O
element	O
method	O
,	O
is	O
any	O
of	O
a	O
family	O
of	O
numerical	B-General_Concept
methods	I-General_Concept
for	O
computing	O
the	O
motion	O
and	O
effect	O
of	O
a	O
large	O
number	O
of	O
small	O
particles	O
.	O
</s>
<s>
With	O
advances	O
in	O
computing	O
power	O
and	O
numerical	B-General_Concept
algorithms	I-General_Concept
for	O
nearest	O
neighbor	O
sorting	O
,	O
it	O
has	O
become	O
possible	O
to	O
numerically	B-General_Concept
simulate	O
millions	O
of	O
particles	O
on	O
a	O
single	O
processor	O
.	O
</s>
<s>
DEM	O
has	O
been	O
extended	O
into	O
the	O
Extended	B-Algorithm
Discrete	I-Algorithm
Element	I-Algorithm
Method	I-Algorithm
taking	O
heat	O
transfer	O
,	O
chemical	O
reaction	O
and	O
coupling	O
to	O
CFD	O
and	O
FEM	B-Application
into	O
account	O
.	O
</s>
<s>
Discrete	B-Algorithm
element	I-Algorithm
methods	I-Algorithm
are	O
relatively	O
computationally	O
intensive	O
,	O
which	O
limits	O
either	O
the	O
length	O
of	O
a	O
simulation	O
or	O
the	O
number	O
of	O
particles	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
solid-like	O
granular	O
behavior	O
as	O
in	O
soil	O
mechanics	O
,	O
the	O
continuum	O
approach	O
usually	O
treats	O
the	O
material	O
as	O
elastic	O
or	O
elasto-plastic	O
and	O
models	O
it	O
with	O
the	O
finite	B-Application
element	I-Application
method	I-Application
or	O
a	O
mesh	B-Algorithm
free	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
The	O
various	O
branches	O
of	O
the	O
DEM	O
family	O
are	O
the	O
distinct	O
element	O
method	O
proposed	O
by	O
Peter	O
A	O
.	O
Cundall	O
and	O
Otto	O
D	O
.	O
L	O
.	O
Strack	O
in	O
1979	O
,	O
the	O
generalized	O
discrete	B-Algorithm
element	I-Algorithm
method	I-Algorithm
,	O
the	O
discontinuous	B-Algorithm
deformation	I-Algorithm
analysis	I-Algorithm
(	O
DDA	O
)	O
and	O
the	O
finite-discrete	O
element	O
method	O
concurrently	O
developed	O
by	O
several	O
groups	O
(	O
e.g.	O
,	O
Munjiza	O
and	O
Owen	O
)	O
.	O
</s>
<s>
showed	O
that	O
DEM	O
could	O
be	O
viewed	O
as	O
a	O
generalized	O
finite	B-Application
element	I-Application
method	I-Application
.	O
</s>
<s>
Its	O
application	O
to	O
geomechanics	O
problems	O
is	O
described	O
in	O
the	O
book	O
Numerical	B-General_Concept
Methods	I-General_Concept
in	O
Rock	O
Mechanics	O
.	O
</s>
<s>
The	O
1st	O
,	O
2nd	O
and	O
3rd	O
International	O
Conferences	O
on	O
Discrete	B-Algorithm
Element	I-Algorithm
Methods	I-Algorithm
have	O
been	O
a	O
common	O
point	O
for	O
researchers	O
to	O
publish	O
advances	O
in	O
the	O
method	O
and	O
its	O
applications	O
.	O
</s>
<s>
Pauli	B-General_Concept
repulsion	I-General_Concept
,	O
when	O
two	O
atoms	O
approach	O
each	O
other	O
closely	O
;	O
</s>
<s>
An	O
integration	B-Algorithm
method	I-Algorithm
is	O
employed	O
to	O
compute	O
the	O
change	O
in	O
the	O
position	O
and	O
the	O
velocity	O
of	O
each	O
particle	O
during	O
a	O
certain	O
time	O
step	O
from	O
Newton	O
's	O
laws	O
of	O
motion	O
.	O
</s>
<s>
Typical	O
integration	O
methods	O
used	O
in	O
a	O
discrete	B-Algorithm
element	I-Algorithm
method	I-Algorithm
are	O
:	O
</s>
<s>
the	O
Verlet	B-Language
algorithm	I-Language
,	O
</s>
<s>
symplectic	B-Algorithm
integrators	I-Algorithm
,	O
</s>
<s>
the	O
leapfrog	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
The	O
discrete	B-Algorithm
element	I-Algorithm
method	I-Algorithm
is	O
widely	O
applied	O
for	O
the	O
consideration	O
of	O
mechanical	O
interactions	O
in	O
many-body	O
problems	O
,	O
particularly	O
granular	O
materials	O
.	O
</s>
<s>
Consider	O
as	O
an	O
example	O
the	O
interaction	O
between	O
a	O
star	O
and	O
a	O
distant	O
galaxy	B-Application
:	O
The	O
error	O
arising	O
from	O
combining	O
all	O
the	O
stars	O
in	O
the	O
distant	O
galaxy	B-Application
into	O
one	O
point	O
mass	O
is	O
negligible	O
.	O
</s>
<s>
These	O
algorithms	O
arrange	O
all	O
particles	O
in	O
a	O
tree	O
,	O
a	O
quadtree	B-Data_Structure
in	O
the	O
two-dimensional	O
case	O
and	O
an	O
octree	B-Data_Structure
in	O
the	O
three-dimensional	O
case	O
.	O
</s>
<s>
the	O
fast	B-Algorithm
multipole	I-Algorithm
method	I-Algorithm
.	O
</s>
