<s>
Discrete	B-Algorithm
dipole	I-Algorithm
approximation	I-Algorithm
(	O
DDA	O
)	O
,	O
also	O
known	O
as	O
coupled	B-Algorithm
dipole	I-Algorithm
approximation	I-Algorithm
,	O
is	O
a	O
method	O
for	O
computing	O
scattering	O
of	O
radiation	O
by	O
particles	O
of	O
arbitrary	O
shape	O
and	O
by	O
periodic	O
structures	O
.	O
</s>
<s>
This	O
technique	O
is	O
used	O
in	O
a	O
variety	O
of	O
applications	O
including	O
nanophotonics	B-Algorithm
,	O
radar	B-Application
scattering	O
,	O
aerosol	O
physics	O
and	O
astrophysics	O
.	O
</s>
<s>
The	O
dipoles	O
interact	O
with	O
one	O
another	O
via	O
their	O
electric	O
fields	O
,	O
so	O
the	O
DDA	O
is	O
also	O
sometimes	O
referred	O
to	O
as	O
the	O
coupled	B-Algorithm
dipole	I-Algorithm
approximation	I-Algorithm
.	O
</s>
<s>
Alternatively	O
,	O
the	O
DDA	O
can	O
be	O
derived	O
from	O
volume	B-Algorithm
integral	I-Algorithm
equation	I-Algorithm
for	I-Algorithm
the	I-Algorithm
electric	I-Algorithm
field	I-Algorithm
.	O
</s>
<s>
The	O
method	O
was	O
improved	O
by	O
Draine	O
,	O
Flatau	O
,	O
and	O
Goodman	O
who	O
applied	O
fast	O
Fourier	O
transform	O
to	O
calculate	O
convolution	B-Language
problem	O
arising	O
in	O
the	O
DDA	O
which	O
allowed	O
to	O
calculate	O
scattering	O
by	O
large	O
targets	O
.	O
</s>
<s>
They	O
distributed	O
discrete	B-Algorithm
dipole	I-Algorithm
approximation	I-Algorithm
open	O
source	O
code	O
DDSCAT	O
.	O
</s>
<s>
Other	O
aspects	O
such	O
as	O
the	O
validity	O
criteria	O
of	O
the	O
discrete	B-Algorithm
dipole	I-Algorithm
approximation	I-Algorithm
was	O
published	O
.	O
</s>
<s>
These	O
codes	O
typically	O
use	O
regular	O
grids	O
(	O
cubical	O
or	O
rectangular	O
cuboid	O
)	O
,	O
conjugate	B-Algorithm
gradient	I-Algorithm
method	I-Algorithm
to	O
solve	O
large	O
system	O
of	O
linear	O
equations	O
,	O
and	O
FFT-acceleration	O
of	O
the	O
matrix-vector	O
products	O
which	O
uses	O
convolution	B-Language
theorem	O
.	O
</s>
<s>
Uses	O
OpenMP	B-Application
acceleration	O
.	O
</s>
<s>
Uses	O
Message	B-Application
Passing	I-Application
Interface	I-Application
(	O
MPI	O
)	O
parallelization	O
and	O
can	O
run	O
on	O
GPU	O
(	O
OpenCL	B-Application
)	O
.	O
</s>
<s>
OpenDDA	O
McDonald	O
C	O
2009	O
(	O
v.0.4.1	O
)	O
Uses	O
both	O
OpenMP	B-Application
and	O
MPI	O
parallelization	O
.	O
</s>
<s>
DDA-GPU	O
Kieß	O
C++	O
2016	O
Runs	O
on	O
GPU	O
(	O
OpenCL	B-Application
)	O
.	O
</s>
<s>
Uses	O
OpenMP	B-Application
and	O
HDF5	O
.	O
</s>
<s>
Uses	O
OpenMP	B-Application
and	O
MPI	O
parallelization	O
.	O
</s>
