<s>
The	O
finite-difference	B-Algorithm
frequency-domain	I-Algorithm
(	O
FDFD	B-Algorithm
)	O
method	O
is	O
a	O
numerical	B-General_Concept
solution	I-General_Concept
method	O
for	O
problems	O
usually	O
in	O
electromagnetism	O
and	O
sometimes	O
in	O
acoustics	O
,	O
based	O
on	O
finite-difference	B-Algorithm
approximations	I-Algorithm
of	O
the	O
derivative	O
operators	O
in	O
the	O
differential	O
equation	O
being	O
solved	O
.	O
</s>
<s>
While	O
"	O
FDFD	B-Algorithm
"	O
is	O
a	O
generic	O
term	O
describing	O
all	O
frequency-domain	O
finite-difference	B-Algorithm
methods	I-Algorithm
,	O
the	O
title	O
seems	O
to	O
mostly	O
describe	O
the	O
method	O
as	O
applied	O
to	O
scattering	O
problems	O
.	O
</s>
<s>
The	O
method	O
shares	O
many	O
similarities	O
to	O
the	O
finite-difference	B-Algorithm
time-domain	I-Algorithm
(	O
FDTD	B-Algorithm
)	O
method	O
,	O
so	O
much	O
that	O
the	O
literature	O
on	O
FDTD	B-Algorithm
can	O
be	O
directly	O
applied	O
.	O
</s>
<s>
An	O
early	O
description	O
of	O
a	O
frequency-domain	O
response	O
FDTD	B-Algorithm
method	O
to	O
solve	O
scattering	O
problems	O
was	O
published	O
by	O
Christ	O
and	O
Hartnagel	O
(	O
1987	O
)	O
.	O
</s>
<s>
An	O
early	O
description	O
of	O
an	O
FDTD	B-Algorithm
method	O
to	O
solve	O
electromagnetic	O
eigenproblems	O
was	O
published	O
by	O
Albani	O
and	O
Bernardi	O
(	O
1974	O
)	O
.	O
</s>
<s>
Much	O
of	O
the	O
literature	O
on	O
finite-difference	B-Algorithm
time-domain	I-Algorithm
(	O
FDTD	B-Algorithm
)	O
methods	O
applies	O
to	O
FDFD	B-Algorithm
,	O
particularly	O
topics	O
on	O
how	O
to	O
represent	O
materials	O
and	O
devices	O
on	O
a	O
Yee	O
grid	O
.	O
</s>
<s>
The	O
FDFD	B-Algorithm
method	O
is	O
very	O
similar	O
to	O
the	O
finite	B-Application
element	I-Application
method	I-Application
(	O
FEM	O
)	O
,	O
though	O
there	O
are	O
some	O
major	O
differences	O
.	O
</s>
<s>
Unlike	O
the	O
FDTD	B-Algorithm
method	O
,	O
there	O
are	O
no	O
time	O
steps	O
that	O
must	O
be	O
computed	O
sequentially	O
,	O
thus	O
making	O
FDFD	B-Algorithm
easier	O
to	O
implement	O
.	O
</s>
<s>
This	O
might	O
also	O
lead	O
one	O
to	O
imagine	O
that	O
FDFD	B-Algorithm
is	O
less	O
computationally	O
expensive	O
;	O
however	O
,	O
this	O
is	O
not	O
necessarily	O
the	O
case	O
.	O
</s>
<s>
The	O
FDFD	B-Algorithm
method	O
requires	O
solving	O
a	O
sparse	O
linear	O
system	O
,	O
which	O
even	O
for	O
simple	O
problems	O
can	O
be	O
20,000	O
by	O
20,000	O
elements	O
or	O
larger	O
,	O
with	O
over	O
a	O
million	O
unknowns	O
.	O
</s>
<s>
In	O
this	O
respect	O
,	O
the	O
FDFD	B-Algorithm
method	O
is	O
similar	O
to	O
the	O
FEM	O
,	O
which	O
is	O
a	O
finite	O
differential	O
method	O
and	O
is	O
also	O
usually	O
implemented	O
in	O
the	O
frequency	O
domain	O
.	O
</s>
<s>
FDFD	B-Algorithm
,	O
and	O
FDTD	B-Algorithm
for	O
that	O
matter	O
,	O
does	O
not	O
lend	O
itself	O
well	O
to	O
complex	O
geometries	O
or	O
multiscale	O
structures	O
,	O
as	O
the	O
Yee	O
grid	O
is	O
restricted	O
mostly	O
to	O
rectangular	O
structures	O
.	O
</s>
<s>
The	O
FDFD	B-Algorithm
equations	O
can	O
be	O
rearranged	O
in	O
such	O
a	O
way	O
as	O
to	O
describe	O
a	O
second	O
order	O
equivalent	O
circuit	O
,	O
where	O
nodal	O
voltages	O
represent	O
the	O
E	O
field	O
components	O
and	O
branch	O
currents	O
represent	O
the	O
H	O
field	O
components	O
.	O
</s>
<s>
The	O
FDFD	B-Algorithm
method	O
has	O
been	O
used	O
to	O
provide	O
full	O
wave	O
simulation	O
for	O
modeling	O
interconnects	O
for	O
various	O
applications	O
in	O
electronic	O
packaging	O
.	O
</s>
<s>
FDFD	B-Algorithm
has	O
also	O
been	O
used	O
for	O
various	O
scattering	O
problems	O
at	O
optical	O
frequencies	O
.	O
</s>
