<s>
Parallel	B-Operating_System
mesh	I-Operating_System
generation	I-Operating_System
in	O
numerical	B-General_Concept
analysis	I-General_Concept
is	O
a	O
new	O
research	O
area	O
between	O
the	O
boundaries	O
of	O
two	O
scientific	O
computing	O
disciplines	O
:	O
computational	O
geometry	O
and	O
parallel	B-Operating_System
computing	I-Operating_System
.	O
</s>
<s>
Parallel	B-Operating_System
mesh	I-Operating_System
generation	I-Operating_System
methods	O
decompose	O
the	O
original	O
mesh	B-Architecture
generation	I-Architecture
problem	O
into	O
smaller	O
subproblems	O
which	O
are	O
solved	O
(	O
meshed	O
)	O
in	O
parallel	O
using	O
multiple	O
processors	O
or	O
threads	O
.	O
</s>
<s>
The	O
existing	O
parallel	B-Operating_System
mesh	I-Operating_System
generation	I-Operating_System
methods	O
can	O
be	O
classified	O
in	O
terms	O
of	O
two	O
basic	O
attributes	O
:	O
</s>
<s>
One	O
of	O
the	O
challenges	O
in	O
parallel	B-Operating_System
mesh	I-Operating_System
generation	I-Operating_System
is	O
to	O
develop	O
parallel	O
meshing	O
software	O
using	O
off-the-shelf	O
sequential	O
meshing	O
codes	O
.	O
</s>
<s>
Parallel	B-Operating_System
mesh	I-Operating_System
generation	I-Operating_System
procedures	O
in	O
general	O
decompose	O
the	O
original	O
2-dimensional	O
(	O
2D	O
)	O
or	O
3-dimensional	O
(	O
3D	O
)	O
mesh	B-Architecture
generation	I-Architecture
problem	O
into	O
N	O
smaller	O
subproblems	O
which	O
are	O
solved	O
(	O
i.e.	O
,	O
meshed	O
)	O
concurrently	O
using	O
P	O
processors	O
or	O
threads	O
.	O
</s>
<s>
The	O
challenges	O
in	O
parallel	B-Operating_System
mesh	I-Operating_System
generation	I-Operating_System
methods	O
are	O
:	O
to	O
maintain	O
stability	O
of	O
the	O
parallel	O
mesher	O
(	O
i.e.	O
,	O
retain	O
the	O
quality	O
of	O
finite	O
elements	O
generated	O
by	O
state-of-the-art	O
sequential	O
codes	O
)	O
and	O
at	O
the	O
same	O
time	O
achieve	O
100%	O
code	O
re-use	O
(	O
i.e.	O
,	O
leverage	O
the	O
continuously	O
evolving	O
and	O
fully	O
functional	O
off-the-shelf	O
sequential	O
meshers	O
)	O
without	O
substantial	O
deterioration	O
of	O
the	O
scalability	O
of	O
the	O
parallel	O
mesher	O
.	O
</s>
<s>
There	O
is	O
a	O
difference	O
between	O
parallel	B-Operating_System
mesh	I-Operating_System
generation	I-Operating_System
and	O
parallel	O
triangulation	O
.	O
</s>
<s>
A	O
very	O
efficient	O
algorithm	O
for	O
parallel	O
Delaunay	B-Algorithm
triangulations	I-Algorithm
appears	O
in	O
Blelloch	O
et	O
al	O
.	O
</s>
<s>
This	O
algorithm	O
is	O
extended	O
in	O
Clemens	O
and	O
Walkington	O
for	O
parallel	B-Operating_System
mesh	I-Operating_System
generation	I-Operating_System
.	O
</s>
<s>
While	O
many	O
solvers	O
have	O
been	O
ported	O
to	O
parallel	B-Operating_System
machines	I-Operating_System
,	O
grid	O
generators	O
have	O
left	O
behind	O
.	O
</s>
<s>
Still	O
the	O
preprocessing	O
step	O
of	O
mesh	B-Architecture
generation	I-Architecture
remains	O
a	O
sequential	O
bottleneck	O
in	O
the	O
simulation	O
cycle	O
.	O
</s>
<s>
It	O
includes	O
parallel	O
implementations	O
of	O
surface	O
,	O
volume	O
and	O
boundary	O
layer	O
mesh	B-Architecture
generation	I-Architecture
as	O
well	O
as	O
parallel	O
mesh	O
adaptivity	O
.	O
</s>
<s>
It	O
takes	O
substantial	O
time	O
to	O
develop	O
the	O
algorithmic	O
and	O
software	O
infrastructure	O
for	O
commercial	O
sequential	O
mesh	B-Architecture
generation	I-Architecture
libraries	O
.	O
</s>
<s>
ended	O
which	O
makes	O
the	O
task	O
of	O
creating	O
leading	O
edge	O
parallel	B-Operating_System
mesh	I-Operating_System
generation	I-Operating_System
codes	O
challenging	O
.	O
</s>
<s>
An	O
area	O
with	O
immediate	O
high	O
benefits	O
to	O
parallel	B-Operating_System
mesh	I-Operating_System
generation	I-Operating_System
is	O
domain	O
decomposition	O
.	O
</s>
<s>
The	O
DD	O
problem	O
as	O
it	O
is	O
posed	O
in	O
is	O
still	O
open	O
for	O
3D	O
geometries	O
and	O
its	O
solution	O
will	O
help	O
to	O
deliver	O
stable	O
and	O
scalable	O
methods	O
that	O
rely	O
on	O
off-the-shelf	O
mesh	B-Architecture
generation	I-Architecture
codes	O
for	O
Delaunay	O
and	O
Advancing	O
Front	O
Techniques	O
.	O
</s>
<s>
Finally	O
,	O
a	O
long	O
term	O
investment	O
to	O
parallel	B-Operating_System
mesh	I-Operating_System
generation	I-Operating_System
is	O
to	O
attract	O
the	O
attention	O
of	O
mathematicians	O
with	O
open	O
problems	O
in	O
mesh	B-Architecture
generation	I-Architecture
and	O
broader	O
impact	O
in	O
mathematics	O
.	O
</s>
