Discrete Dipole Approximation of Volume Integral Equations: A perfect method for perfect equations ?

In this talk, the numerical solution of a strongly singular volume integral equation which models the scattering of time-harmonic electromagnetic waves with a penetrable obstacle is discussed. Discrete Dipole Approximation (DDA) as an easy method for the discretization of the volume integral equation is introduced. Then we follow the questions of consistency and stability of the numerical method and try to find an affirmative answer to them.