<s>
In	O
mathematics	O
,	O
Neumann	B-Algorithm
–	I-Algorithm
Neumann	I-Algorithm
methods	I-Algorithm
are	O
domain	O
decomposition	O
preconditioners	O
named	O
so	O
because	O
they	O
solve	O
a	O
Neumann	O
problem	O
on	O
each	O
subdomain	O
on	O
both	O
sides	O
of	O
the	O
interface	O
between	O
the	O
subdomains	O
.	O
</s>
<s>
Just	O
like	O
all	O
domain	O
decomposition	O
methods	O
,	O
so	O
that	O
the	O
number	O
of	O
iterations	O
does	O
not	O
grow	O
with	O
the	O
number	O
of	O
subdomains	O
,	O
Neumann	B-Algorithm
–	I-Algorithm
Neumann	I-Algorithm
methods	I-Algorithm
require	O
the	O
solution	O
of	O
a	O
coarse	O
problem	O
to	O
provide	O
global	O
communication	O
.	O
</s>
<s>
The	O
balancing	B-Algorithm
domain	I-Algorithm
decomposition	I-Algorithm
is	O
a	O
Neumann	B-Algorithm
–	I-Algorithm
Neumann	I-Algorithm
method	I-Algorithm
with	O
a	O
special	O
kind	O
of	O
coarse	O
problem	O
.	O
</s>
<s>
This	O
procedure	O
can	O
be	O
viewed	O
as	O
a	O
Richardson	B-Algorithm
iteration	I-Algorithm
for	O
the	O
iterative	O
solution	O
of	O
the	O
equations	O
arising	O
from	O
the	O
Schur	B-Algorithm
complement	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
This	O
continuous	O
iteration	O
can	O
be	O
discretized	O
by	O
the	O
finite	B-Application
element	I-Application
method	I-Application
and	O
then	O
solved	O
—	O
in	O
parallel	O
—	O
on	O
a	O
computer	O
.	O
</s>
