<s>
The	O
extended	B-Algorithm
finite	I-Algorithm
element	I-Algorithm
method	I-Algorithm
(	O
XFEM	B-Algorithm
)	O
,	O
is	O
a	O
numerical	O
technique	O
based	O
on	O
the	O
generalized	O
finite	B-Application
element	I-Application
method	I-Application
(	O
GFEM	O
)	O
and	O
the	O
partition	O
of	O
unity	O
method	O
(	O
PUM	O
)	O
.	O
</s>
<s>
It	O
extends	O
the	O
classical	O
finite	B-Application
element	I-Application
method	I-Application
(	O
FEM	B-Application
)	O
approach	O
by	O
enriching	O
the	O
solution	O
space	O
for	O
solutions	O
to	O
differential	O
equations	O
with	O
discontinuous	O
functions	O
.	O
</s>
<s>
The	O
extended	B-Algorithm
finite	I-Algorithm
element	I-Algorithm
method	I-Algorithm
(	O
XFEM	B-Algorithm
)	O
was	O
developed	O
in	O
1999	O
by	O
Ted	O
Belytschko	O
and	O
collaborators	O
,	O
</s>
<s>
to	O
help	O
alleviate	O
shortcomings	O
of	O
the	O
finite	B-Application
element	I-Application
method	I-Application
and	O
has	O
been	O
used	O
to	O
model	O
the	O
propagation	O
of	O
various	O
discontinuities	O
:	O
strong	O
(	O
cracks	B-Application
)	O
and	O
weak	O
(	O
material	O
interfaces	O
)	O
.	O
</s>
<s>
The	O
idea	O
behind	O
XFEM	B-Algorithm
is	O
to	O
retain	O
most	O
advantages	O
of	O
meshfree	O
methods	O
while	O
alleviating	O
their	O
negative	O
sides	O
.	O
</s>
<s>
The	O
extended	B-Algorithm
finite	I-Algorithm
element	I-Algorithm
method	I-Algorithm
was	O
developed	O
to	O
ease	O
difficulties	O
in	O
solving	O
problems	O
with	O
localized	O
features	O
that	O
are	O
not	O
efficiently	O
resolved	O
by	O
mesh	B-Algorithm
refinement	O
.	O
</s>
<s>
One	O
of	O
the	O
initial	O
applications	O
was	O
the	O
modelling	O
of	O
fractures	B-Application
in	O
a	O
material	O
.	O
</s>
<s>
A	O
key	O
advantage	O
of	O
XFEM	B-Algorithm
is	O
that	O
in	O
such	O
problems	O
the	O
finite	B-Application
element	I-Application
mesh	B-Algorithm
does	O
not	O
need	O
to	O
be	O
updated	O
to	O
track	O
the	O
crack	O
path	O
.	O
</s>
<s>
associated	O
with	O
conventional	O
finite	B-Application
element	I-Application
methods	I-Application
,	O
at	O
the	O
cost	O
of	O
restricting	O
the	O
discontinuities	O
to	O
mesh	B-Algorithm
edges	O
.	O
</s>
<s>
XFEM	B-Algorithm
has	O
also	O
been	O
implemented	O
in	O
code	O
like	O
Altair	O
Radioss	B-Algorithm
,	O
ASTER	O
,	O
Morfeo	O
,	O
and	O
Abaqus	B-Algorithm
.	O
</s>
<s>
It	O
is	O
increasingly	O
being	O
adopted	O
by	O
other	O
commercial	O
finite	B-Application
element	I-Application
software	O
,	O
with	O
a	O
few	O
plugins	O
and	O
actual	O
core	O
implementations	O
available	O
(	O
ANSYS	B-Application
,	O
SAMCEF	B-Algorithm
,	O
OOFELIE	O
,	O
etc	O
.	O
</s>
