Convergence analysis of the thermal discrete dipole approximation

TL;DR

This paper analyzes the convergence behavior of the thermal discrete dipole approximation (T-DDA) for near-field radiative heat transfer, demonstrating that nonuniform discretization significantly improves accuracy and efficiency in complex geometries.

Contribution

The study provides a detailed convergence analysis of T-DDA, introducing nonuniform discretization to enhance accuracy and reduce computational costs in near-field thermal radiation modeling.

Findings

Errors less than 5% in 74% of cases with up to 82,712 subvolumes

Nonuniform discretization accelerates convergence significantly

T-DDA is highly accurate for surface polariton resonant modes

Abstract

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.