Discrete dipole approximation

For monochromatic incident waves the self-consistent solution for the oscillating dipole moments may be found; from these the absorption and scattering cross sections are computed.

If DDA solutions are obtained for two independent polarizations of the incident wave, then the complete amplitude scattering matrix can be determined.

[15] The DDA was also extended to employ rectangular or cuboid dipoles,[16] which are more efficient for highly oblate or prolate particles.

The Fast Fourier Transform (FFT) method was introduced in 1991 by Goodman, Draine, and Flatau[17] for the discrete dipole approximation.

Barrowes, Teixeira, and Kong[18] in 2001 developed a code that uses block reordering, zero padding, and a reconstruction algorithm, claiming minimal memory usage.

Other techniques to accelerate convolutions have been suggested in a general context[21][22] along with faster evaluations of Fast Fourier Transforms arising in DDA problem solvers.

Some of the early calculations of the polarization vector were based on direct inversion[3] and the implementation of the conjugate gradient method by Petravic and Kuo-Petravic.

[25] Thermal discrete dipole approximation is an extension of the original DDA to simulations of near-field heat transfer between 3D arbitrarily-shaped objects.

[14] These codes typically use regular grids (cubical or rectangular cuboid), conjugate gradient method to solve large system of linear equations, and FFT-acceleration of the matrix-vector products which uses convolution theorem.

In the discrete dipole approximation, a larger object is approximated in terms of discrete radiating electric dipoles.
Magnitude of the electric field strength (colored) and the Poynting vector (black arrows) in the near field of the vertically oriented dipole in the image plane. Blue/red colors indicate an electric field oriented downwards/upwards.