<s>
Computational	B-Algorithm
mechanics	I-Algorithm
is	O
the	O
discipline	O
concerned	O
with	O
the	O
use	O
of	O
computational	O
methods	O
to	O
study	O
phenomena	O
governed	O
by	O
the	O
principles	O
of	O
mechanics	O
.	O
</s>
<s>
Before	O
the	O
emergence	O
of	O
computational	O
science	O
(	O
also	O
called	O
scientific	O
computing	O
)	O
as	O
a	O
"	O
third	O
way	O
"	O
besides	O
theoretical	O
and	O
experimental	O
sciences	O
,	O
computational	B-Algorithm
mechanics	I-Algorithm
was	O
widely	O
considered	O
to	O
be	O
a	O
sub-discipline	O
of	O
applied	O
mechanics	O
.	O
</s>
<s>
Computational	B-Algorithm
mechanics	I-Algorithm
(	O
CM	O
)	O
is	O
interdisciplinary	O
.	O
</s>
<s>
Its	O
three	O
pillars	O
are	O
mechanics	O
,	O
mathematics	O
,	O
and	O
computer	B-General_Concept
science	I-General_Concept
and	O
physics	O
.	O
</s>
<s>
Computational	O
fluid	O
dynamics	O
,	O
computational	B-Application
thermodynamics	I-Application
,	O
computational	O
electromagnetics	O
,	O
computational	O
solid	O
mechanics	O
are	O
some	O
of	O
the	O
many	O
specializations	O
within	O
CM	O
.	O
</s>
<s>
The	O
areas	O
of	O
mathematics	O
most	O
related	O
to	O
computational	B-Algorithm
mechanics	I-Algorithm
are	O
partial	O
differential	O
equations	O
,	O
linear	B-Language
algebra	I-Language
and	O
numerical	B-General_Concept
analysis	I-General_Concept
.	O
</s>
<s>
The	O
most	O
popular	O
numerical	B-General_Concept
methods	I-General_Concept
used	O
are	O
the	O
finite	B-Application
element	I-Application
,	O
finite	B-Algorithm
difference	I-Algorithm
,	O
and	O
boundary	B-Algorithm
element	I-Algorithm
methods	I-Algorithm
in	O
order	O
of	O
dominance	O
.	O
</s>
<s>
In	O
solid	O
mechanics	O
finite	B-Application
element	I-Application
methods	I-Application
are	O
far	O
more	O
prevalent	O
than	O
finite	B-Algorithm
difference	I-Algorithm
methods	I-Algorithm
,	O
whereas	O
in	O
fluid	O
mechanics	O
,	O
thermodynamics	O
,	O
and	O
electromagnetism	O
,	O
finite	B-Algorithm
difference	I-Algorithm
methods	I-Algorithm
are	O
almost	O
equally	O
applicable	O
.	O
</s>
<s>
The	O
boundary	B-Algorithm
element	I-Algorithm
technique	O
is	O
in	O
general	O
less	O
popular	O
,	O
but	O
has	O
a	O
niche	O
in	O
certain	O
areas	O
including	O
acoustics	O
engineering	O
,	O
for	O
example	O
.	O
</s>
<s>
With	O
regard	O
to	O
computing	O
,	O
computer	O
programming	O
,	O
algorithms	O
,	O
and	O
parallel	B-Operating_System
computing	I-Operating_System
play	O
a	O
major	O
role	O
in	O
CM	O
.	O
</s>
<s>
The	O
most	O
widely	O
used	O
programming	O
language	O
in	O
the	O
scientific	O
community	O
,	O
including	O
computational	B-Algorithm
mechanics	I-Algorithm
,	O
is	O
Fortran	B-Application
.	O
</s>
<s>
Recently	O
,	O
C++	B-Language
has	O
increased	O
in	O
popularity	O
.	O
</s>
<s>
The	O
scientific	O
computing	O
community	O
has	O
been	O
slow	O
in	O
adopting	O
C++	B-Language
as	O
the	O
lingua	O
franca	O
.	O
</s>
<s>
Because	O
of	O
its	O
very	O
natural	O
way	O
of	O
expressing	O
mathematical	O
computations	O
,	O
and	O
its	O
built-in	O
visualization	O
capacities	O
,	O
the	O
proprietary	O
language/environment	O
MATLAB	B-Language
is	O
also	O
widely	O
used	O
,	O
especially	O
for	O
rapid	O
application	O
development	O
and	O
model	O
verification	O
.	O
</s>
<s>
Scientists	O
within	O
the	O
field	O
of	O
computational	B-Algorithm
mechanics	I-Algorithm
follow	O
a	O
list	O
of	O
tasks	O
to	O
analyze	O
their	O
target	O
mechanical	O
process	O
:	O
</s>
<s>
This	O
step	O
is	O
called	O
discretization	B-Algorithm
because	O
it	O
involves	O
creating	O
an	O
approximate	O
discrete	O
model	O
from	O
the	O
original	O
continuous	O
model	O
.	O
</s>
<s>
The	O
processes	O
involved	O
in	O
this	O
step	O
are	O
studied	O
in	O
the	O
field	O
of	O
numerical	B-General_Concept
analysis	I-General_Concept
.	O
</s>
<s>
Computer	B-Application
programs	I-Application
are	O
made	O
to	O
solve	O
the	O
discretized	B-Algorithm
equations	O
using	O
direct	B-Algorithm
methods	I-Algorithm
(	O
which	O
are	O
single	O
step	O
methods	O
resulting	O
in	O
the	O
solution	O
)	O
or	O
iterative	B-Algorithm
methods	I-Algorithm
(	O
which	O
start	O
with	O
a	O
trial	O
solution	O
and	O
arrive	O
at	O
the	O
actual	O
solution	O
by	O
successive	O
refinement	O
)	O
.	O
</s>
<s>
Depending	O
on	O
the	O
nature	O
of	O
the	O
problem	O
,	O
supercomputers	B-Architecture
or	O
parallel	B-Operating_System
computers	I-Operating_System
may	O
be	O
used	O
at	O
this	O
stage	O
.	O
</s>
<s>
The	O
mathematical	O
model	O
,	O
numerical	O
procedures	O
,	O
and	O
the	O
computer	B-Application
codes	I-Application
are	O
verified	O
using	O
either	O
experimental	O
results	O
or	O
simplified	O
models	O
for	O
which	O
exact	O
analytical	O
solutions	O
are	O
available	O
.	O
</s>
<s>
Quite	O
frequently	O
,	O
new	O
numerical	O
or	O
computational	O
techniques	O
are	O
verified	O
by	O
comparing	O
their	O
result	O
with	O
those	O
of	O
existing	O
well-established	O
numerical	B-General_Concept
methods	I-General_Concept
.	O
</s>
<s>
Some	O
examples	O
where	O
computational	B-Algorithm
mechanics	I-Algorithm
have	O
been	O
put	O
to	O
practical	O
use	O
are	O
vehicle	O
crash	O
simulation	O
,	O
petroleum	O
reservoir	O
modeling	O
,	O
biomechanics	O
,	O
glass	O
manufacturing	O
,	O
and	O
semiconductor	O
modeling	O
.	O
</s>
<s>
Complex	O
systems	O
that	O
would	O
be	O
very	O
difficult	O
or	O
impossible	O
to	O
treat	O
using	O
analytical	O
methods	O
have	O
been	O
successfully	O
simulated	O
using	O
the	O
tools	O
provided	O
by	O
computational	B-Algorithm
mechanics	I-Algorithm
.	O
</s>
