The thermal discrete dipole approximation and the discrete system Green's function methods for computational near-field radiative heat transfer

This chapter describes two-volume integral equation formulations, namely, the thermal discrete dipole approximation and the discrete system Green's function methods, for solving near-field radiative heat transfer problems in systems of three-dimensional thermal sources of arbitrary number, shape, size, and material. Both methods are derived from fluctuational electrodynamics and involve the discretization of thermal sources into cubic subvolumes. In the thermal discrete dipole approximation, the cubic subvolumes are conceptualized as electric point dipoles. Then, a system of linear equations is derived where dipole moment of each subvolume is unknown. In the discrete system Green's function method, a system of linear equations is obtained where the system Green's function between all cubic subvolumes is unknown. Both methods are based on same numerical approximations, and it is shown that they yield same results.