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.

在惯性约束融合模拟和天体物理学应用中，应求解非线性辐射扩散方程。通常，仿真域由许多块组成，每个块都填充一种材料。由于材料的不同，扩散系数在块的界面处强烈不连续。通过隐式离散辐射扩散方程获得的代数方程很难求解。为了求解具有不连续系数的辐射扩散方程，提出了一种基于域分解的非线性显式-隐式迭代算法。该算法的关键是确定非线性显式-隐式迭代方案的加权系数。为了提高算法的鲁棒性，进一步校正非线性项，得到校正后的非线性显式-隐式迭代算法。分析了算法的收敛准则。通过数值实验验证了所提算法的有效性。