A kind of fast successive permutation iterative algorithms with the relaxation factor for nonlinear radiation diffusion problem

Abstract

When the radiation is in equilibrium with matter, a nonlinear parabolic equation is formed by the approximation of single temperature diffusion equation. In the actual numerical simulation, most of the time is used to solve the linear equations by the implicit discretization so as to retain the stability. In this paper, the discretization of the nonlinear diffusion equation on time is still full-implicit, but we construct several new nonlinear iterative schemes for 1D, 2D and 3D radiation diffusion equation, and then a class of fast successive permutation iterative algorithms is proposed. The matrix analysis and convergence are presented. The numerical experiments are provided to examine the accuracy and superior between the Picard iteration method with the presented algorithms.