Recent studies of interplanetary and interstellar dust provide evidenc
e that cosmic dust grains are fluffy, composite objects, highlighting
the need for models of the electromagnetic scattering by these grains.
Effective medium theory (EMT) with Mie-type series solutions has been
used to explore the effects of porosity which would be important in c
omposite dust particles. While this indirect approach is both flexible
and computationally efficient, it is not necessarily a good approxima
tion. The need for EMT and its rather restrictive assumptions may be c
ircumvented through a direct computation of the scattering properties
via finite element methods, such as the discrete dipole approximation
(DDA). Recently, the utility of the DDA method has been advanced signi
ficantly through improvements in theory, in numerical algorithms, and
in computer hardware. Extensive calculations with the DDA method are u
sed here to examine more directly the effects of porosity. A particula
r emphasis is placed upon developing a valid methodology. For both sol
id and porous targets we establish both numerical and physical converg
ence properties over the range of size parameter that is required for
our study. DDA cross sections for grains with a range of porosity are
compared to those computed by the EMT/series expansion technique to ex
amine the applicability of several mixing rules, including two extensi
ons of the Bruggeman rule. We show that for particles with Rayleigh va
cuum inclusions, the extension proposed by Rouleau & Martin is quite s
uccessful. We also investigate the effects of larger, non-Rayleigh vac
uum inclusions for various levels of porosity and find that they can b
e significant.