<s>
In	O
mathematics	O
,	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
and	O
numerical	B-Algorithm
partial	I-Algorithm
differential	I-Algorithm
equations	I-Algorithm
,	O
domain	B-Algorithm
decomposition	I-Algorithm
methods	I-Algorithm
solve	O
a	O
boundary	O
value	O
problem	O
by	O
splitting	O
it	O
into	O
smaller	O
boundary	O
value	O
problems	O
on	O
subdomains	O
and	O
iterating	O
to	O
coordinate	O
the	O
solution	O
between	O
adjacent	O
subdomains	O
.	O
</s>
<s>
A	O
coarse	B-Algorithm
problem	I-Algorithm
with	O
one	O
or	O
few	O
unknowns	O
per	O
subdomain	O
is	O
used	O
to	O
further	O
coordinate	O
the	O
solution	O
between	O
the	O
subdomains	O
globally	O
.	O
</s>
<s>
The	O
problems	O
on	O
the	O
subdomains	O
are	O
independent	O
,	O
which	O
makes	O
domain	B-Algorithm
decomposition	I-Algorithm
methods	I-Algorithm
suitable	O
for	O
parallel	B-Operating_System
computing	I-Operating_System
.	O
</s>
<s>
Domain	B-Algorithm
decomposition	I-Algorithm
methods	I-Algorithm
are	O
typically	O
used	O
as	O
preconditioners	O
for	O
Krylov	O
space	O
iterative	B-Algorithm
methods	I-Algorithm
,	O
such	O
as	O
the	O
conjugate	B-Algorithm
gradient	I-Algorithm
method	I-Algorithm
,	O
GMRES	O
,	O
and	O
LOBPCG	B-Application
.	O
</s>
<s>
In	O
overlapping	O
domain	B-Algorithm
decomposition	I-Algorithm
methods	I-Algorithm
,	O
the	O
subdomains	O
overlap	O
by	O
more	O
than	O
the	O
interface	O
.	O
</s>
<s>
Overlapping	O
domain	B-Algorithm
decomposition	I-Algorithm
methods	I-Algorithm
include	O
the	O
Schwarz	O
alternating	O
method	O
and	O
the	O
additive	B-Algorithm
Schwarz	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
Many	O
domain	B-Algorithm
decomposition	I-Algorithm
methods	I-Algorithm
can	O
be	O
written	O
and	O
analyzed	O
as	O
a	O
special	O
case	O
of	O
the	O
abstract	B-Algorithm
additive	I-Algorithm
Schwarz	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
In	O
primal	O
methods	O
,	O
such	O
as	O
Balancing	B-Algorithm
domain	I-Algorithm
decomposition	I-Algorithm
and	O
BDDC	B-Algorithm
,	O
the	O
continuity	O
of	O
the	O
solution	O
across	O
subdomain	O
interface	O
is	O
enforced	O
by	O
representing	O
the	O
value	O
of	O
the	O
solution	O
on	O
all	O
neighboring	O
subdomains	O
by	O
the	O
same	O
unknown	O
.	O
</s>
<s>
In	O
dual	O
methods	O
,	O
such	O
as	O
FETI	B-Algorithm
,	O
the	O
continuity	O
of	O
the	O
solution	O
across	O
the	O
subdomain	O
interface	O
is	O
enforced	O
by	O
Lagrange	O
multipliers	O
.	O
</s>
<s>
The	O
FETI-DP	B-Algorithm
method	O
is	O
hybrid	O
between	O
a	O
dual	O
and	O
a	O
primal	O
method	O
.	O
</s>
<s>
Non-overlapping	O
domain	B-Algorithm
decomposition	I-Algorithm
methods	I-Algorithm
are	O
also	O
called	O
iterative	B-Algorithm
substructuring	I-Algorithm
methods	I-Algorithm
.	O
</s>
<s>
Mortar	B-Algorithm
methods	I-Algorithm
are	O
discretization	O
methods	O
for	O
partial	O
differential	O
equations	O
,	O
which	O
use	O
separate	O
discretization	O
on	O
nonoverlapping	O
subdomains	O
.	O
</s>
<s>
Several	O
hours	O
per	O
time	O
step	O
is	O
an	O
average	O
sequential	O
run	O
time	O
,	O
therefore	O
,	O
parallel	B-Operating_System
computing	I-Operating_System
is	O
a	O
necessity	O
.	O
</s>
<s>
Domain	B-Algorithm
decomposition	I-Algorithm
methods	I-Algorithm
embody	O
large	O
potential	O
for	O
a	O
parallelization	B-Operating_System
of	O
the	O
finite	O
element	O
methods	O
,	O
and	O
serve	O
a	O
basis	O
for	O
distributed	O
,	O
parallel	B-Operating_System
computations	I-Operating_System
.	O
</s>
