  The thermal discrete dipole approximation (T-DDA) is a numerical approach for
modeling near-field radiative heat transfer in complex three-dimensional
geometries. In this work, the convergence of the T-DDA is investigated by
comparison against the exact results for two spheres separated by a vacuum gap.
The error associated with the T-DDA is reported for various sphere sizes,
refractive indices and vacuum gap thicknesses. The results reveal that for a
fixed number of subvolumes, the accuracy of the T-DDA degrades as the
refractive index and the sphere diameter to gap ratio increase. A converging
trend is observed as the number of subvolumes increases. The large
computational requirements associated with increasing the number of subvolumes,
and the shape error induced by large sphere diameter to gap ratios, are
mitigated by using a nonuniform discretization scheme. Nonuniform
discretization is shown to significantly accelerate the convergence of the
T-DDA, and is thus recommended for near-field thermal radiation simulations.
Errors less than 5% are obtained in 74% of the cases studied by using up to
82712 subvolumes. Additionally, the convergence analysis demonstrates that the
T-DDA is very accurate when dealing with surface polariton resonant modes
dominating radiative heat transfer in the near field.
