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A novel numerical method called the Thermal Discrete Dipole Approximation(T-DDA) is proposed for modeling near-field radiative heat transfer inthree-dimensional arbitrary geometries. The T-DDA is conceptually similar tothe Discrete Dipole Approximation, except that the incident field originatesfrom thermal oscillations of dipoles. The T-DDA is described in details in thepaper, and the method is tested against exact results of radiative conductancebetween two spheres separated by a sub-wavelength vacuum gap. For all casesconsidered, the results calculated from the T-DDA are in good agreement withthose from the analytical solution. When considering frequency-independentdielectric functions, it is observed that the number of sub-volumes requiredfor convergence increases as the sphere permittivity increases. Additionally,simulations performed for two silica spheres of 0.5 micrometer-diameter showthat the resonant modes are predicted accurately via the T-DDA. For separationgaps of 0.5 micrometer and 0.2 micrometer, the relative differences between theT-DDA and the exact results are 0.35% and 6.4%, respectively, when 552sub-volumes are used to discretize a sphere. Finally, simulations are performedfor two cubes of silica separated by a sub-wavelength gap. The results revealedthat faster convergence is obtained when considering cubical objects ratherthan curved geometries. This work suggests that the T-DDA is a robust numericalapproach that can be employed for solving a wide variety of near-field thermalradiation problems in three-dimensional geometries.

The Thermal Discrete Dipole Approximation (T-DDA) for near-field radiative heat transfer simulations in three-dimensional arbitrary geometries