<s>
In	O
mathematics	O
,	O
in	O
particular	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
the	O
FETI	B-Algorithm
method	O
(	O
finite	B-Application
element	I-Application
tearing	O
and	O
interconnect	O
)	O
is	O
an	O
iterative	B-Algorithm
substructuring	I-Algorithm
method	O
for	O
solving	O
systems	O
of	O
linear	O
equations	O
from	O
the	O
finite	B-Application
element	I-Application
method	I-Application
for	O
the	O
solution	O
of	O
elliptic	O
partial	O
differential	O
equations	O
,	O
in	O
particular	O
in	O
computational	B-Algorithm
mechanics	I-Algorithm
In	O
each	O
iteration	O
,	O
FETI	B-Algorithm
requires	O
the	O
solution	O
of	O
a	O
Neumann	O
problem	O
in	O
each	O
substructure	O
and	O
the	O
solution	O
of	O
a	O
coarse	B-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
The	O
simplest	O
version	O
of	O
FETI	B-Algorithm
with	O
no	O
preconditioner	O
(	O
or	O
only	O
a	O
diagonal	O
preconditioner	O
)	O
in	O
the	O
substructure	O
is	O
scalable	O
with	O
the	O
number	O
of	O
substructures	O
but	O
the	O
condition	O
number	O
grows	O
polynomially	O
with	O
the	O
number	O
of	O
elements	O
per	O
substructure	O
.	O
</s>
<s>
FETI	B-Algorithm
with	O
a	O
(	O
more	O
expensive	O
)	O
preconditioner	O
consisting	O
of	O
the	O
solution	O
of	O
a	O
Dirichlet	O
problem	O
in	O
each	O
substructure	O
is	O
scalable	O
with	O
the	O
number	O
of	O
substructures	O
and	O
its	O
condition	O
number	O
grows	O
only	O
polylogarithmically	O
with	O
the	O
number	O
of	O
elements	O
per	O
substructure	O
.	O
</s>
<s>
The	O
coarse	B-Algorithm
space	I-Algorithm
in	O
FETI	B-Algorithm
consists	O
of	O
the	O
nullspace	B-Algorithm
on	O
each	O
substructure	O
.	O
</s>
<s>
Apart	O
from	O
FETI	B-Algorithm
Dual-Primal	O
(	O
FETI-DP	B-Algorithm
,	O
see	O
below	O
)	O
,	O
several	O
extensions	O
have	O
been	O
developed	O
to	O
solve	O
particular	O
physical	O
problems	O
,	O
as	O
FETI	B-Algorithm
Helmholtz	O
(	O
FETI-H	O
)	O
,	O
FETI	B-Algorithm
for	O
quasi-incompressible	O
problems	O
,	O
and	O
FETI	B-Algorithm
Contact	O
(	O
FETI-C	O
)	O
.	O
</s>
