Deterministic Formulation of the Thermal Discrete Dipole Approximation for Computational Modeling of Near-Field Thermal Radiation in Arbitrary Geometries

As micro/nanotechnologies advance and become more pervasive in common consumer products, robust and efficient modeling techniques for near-field thermal radiation are needed.  While analytical approaches based on fluctuational electrodynamics have been used to describe near-field radiative heat transfer between simple, highly-symmetric geometries (e.g., spheres, layered media), these approaches are not generalizable to the complex, three-dimensional structures seen in practical real-world design.  In response to this limitation, various numerical approaches have been developed to solve the relevant stochastic Maxwell equations.  One such approach is the thermal discrete dipole approximation (TDDA) (S. Edalatpour et al., Phys. Rev. E. 91, 063307, 2015).  While better convergence toward exact analytical solutions using the TDDA approach has been generally observed with finer discretization, the computational demands for such large discretization schemes cannot be satisfied with a standard desktop computer.  This hinderance stems from the formulation’s required inversion of a large 3N-by-3N matrix, where N is the number of discretized subvolumes in the system.  The goal of the work presented here is therefore to reformulate the TDDA to be compatible with iterative approaches for solving large systems of linear equations and thereby avoid direct calculation of the matrix inverse.  Iterative approaches, such as the quasi-minimal residual method, the biconjugate gradient stabilized method, and the generalized minimal residual method, have already been integrated into similar light-scattering algorithms (M. A. Yurkin and A. G. Hoekstra, J. Quant. Spectrosc. Radiat. Transf. 106, 558, 2007), and so reformulating the TDDA in this way lends itself to cross-reference of iterative procedures commonly used within the light-scattering community.  Construction of the TDDA to avoid direct matrix inversion is achieved by deriving a system of linear equations in terms of an unknown deterministic system Green’s function which contains all information of the environment (i.e., both thermal and scattering effects).  Previously, the TDDA was based on the free-space Green’s function solution, and scattering effects were accounted for in the source function of the defining wave equation.  Knowledge of the system Green’s function allows calculation of quantities of interest such as the radiative flux, thermal conductance, and energy density.  This work applies the system Green’s function approach to the study of near-field radiative heat transfer in new geometries that more closely resemble the asymmetric and distorted shapes found in manufactured structures.  This technique, which lends itself to desktop computation rather than supercomputing facilities, makes application-driven design, experimental validation, and troubleshooting of near-field thermal radiation effects more accessible.