<s>
A	O
frontal	B-Application
solver	I-Application
,	O
conceived	O
by	O
Bruce	O
Irons	O
,	O
is	O
an	O
approach	O
to	O
solving	O
sparse	B-Algorithm
linear	I-Algorithm
systems	I-Algorithm
which	O
is	O
used	O
extensively	O
in	O
finite	B-Application
element	I-Application
analysis	I-Application
.	O
</s>
<s>
It	O
is	O
a	O
variant	O
of	O
Gauss	B-Algorithm
elimination	I-Algorithm
that	O
automatically	O
avoids	O
a	O
large	O
number	O
of	O
operations	O
involving	O
zero	O
terms	O
.	O
</s>
<s>
A	O
frontal	B-Application
solver	I-Application
builds	O
a	O
LU	O
or	O
Cholesky	O
decomposition	O
of	O
a	O
sparse	B-Algorithm
matrix	I-Algorithm
given	O
as	O
the	O
assembly	O
of	O
element	O
matrices	O
by	O
assembling	O
the	O
matrix	O
and	O
eliminating	O
equations	O
only	O
on	O
a	O
subset	O
of	O
elements	O
at	O
a	O
time	O
.	O
</s>
<s>
The	O
whole	O
sparse	B-Algorithm
matrix	I-Algorithm
is	O
never	O
created	O
explicitly	O
.	O
</s>
<s>
Processing	O
the	O
front	O
involves	O
dense	B-Algorithm
matrix	I-Algorithm
operations	O
,	O
which	O
use	O
the	O
CPU	B-Device
efficiently	O
.	O
</s>
<s>
In	O
a	O
typical	O
implementation	O
,	O
only	O
the	O
front	O
is	O
in	O
memory	B-General_Concept
,	O
while	O
the	O
factors	O
in	O
the	O
decomposition	O
are	O
written	O
into	O
files	B-Operating_System
.	O
</s>
<s>
The	O
element	O
matrices	O
are	O
read	O
from	O
files	B-Operating_System
or	O
created	O
as	O
needed	O
and	O
discarded	O
.	O
</s>
<s>
A	O
multifrontal	B-Application
solver	I-Application
of	O
Duff	O
and	O
Reid	O
is	O
an	O
improvement	O
of	O
the	O
frontal	B-Application
solver	I-Application
that	O
uses	O
several	O
independent	O
fronts	O
at	O
the	O
same	O
time	O
.	O
</s>
<s>
The	O
fronts	O
can	O
be	O
worked	O
on	O
by	O
different	O
processors	B-Device
,	O
which	O
enables	O
parallel	B-Operating_System
computing	I-Operating_System
.	O
</s>
