  A new numerical method is introduced for calculating the polarizability of an
arbitrary dielectric object with position dependent complex permittivity. Three
separate numerical approaches are provided to calculate the dipole moment of a
nanoparticle embedded in a dielectric matrix in the presence of an applied
electric field. Numerical tests confirm the accuracy of this method when
applied to several cases for which an exact solution is available. This method
is especially well suited for the calculation of absolute Raman scattering
intensities due to acoustic phonons in metallic and dielectric nanoparticles
embedded in transparent matrices.
