Examining the spectrum of radiative transfer systems

Abstract

The convergence of iterative methods used to solve the linear systems of equations arising from discretizing radiative transfer problems depends on the characteristics of the eigenvalues of the coefficient matrix of these systems. In this communication we examine the proof that all of these eigenvalues are real and positive and discuss its implications for the solution of problems in radiative heat and mass transfer by iterative methods. This proof, outlined initially by Baranoski [1] in the context of the radiative transfer of luminous energy, allows the use of more efficient methods to solve radiatve transfer systems. These methods, based on the knowledge about the set of eigenvalues of the radiative transfer coefficient matrix, may, in turn, provide faster solutions for these systems.