A class of domain decomposition based nonlinear explicit–implicit iteration algorithms for solving diffusion equations with discontinuous coefficient

Abstract

In the simulation of inertial confinement fusion and astrophysics application, the nonlinear radiation diffusion equations should be solved. Usually, the simulation domain is consisted of many blocks, with each block filled with one material. The diffusion coefficient is strongly discontinuous at the interface of the blocks due to the different properties of materials. The algebraic equations obtained by implicit discretizing the radiation diffusion equations are very difficult to be solved. In this paper, for solving the radiation diffusion equations with discontinuous coefficient, a class of domain decomposition based nonlinear explicit–implicit iteration algorithm is proposed. The key of the algorithm is to determine the weighted coefficients for nonlinear explicit–implicit iteration schemes. To improve the robustness of the algorithm, the nonlinear terms are further corrected, and a corrected nonlinear explicit–implicit iteration algorithm is obtained. The convergence criteria for the algorithms are analyzed. The effectiveness of the presented algorithms are verified by some numerical experiments.