A class of domain decomposition based nonlinear explicit–implicit iteration algorithms for solving diffusion equations with discontinuous coefficient
A class of domain decomposition based nonlinear explicit–implicit iteration algorithms for solving diffusion equations with discontinuous coefficient
复制标题
一类基于域分解的非线性显隐迭代算法求解间断系数扩散方程
DOI：
10.1016/j.cam.2020.113232
复制
发表时间：
2020
影响因子：
2.4
通讯作者：
安恒斌
中科院分区：
文献类型：
--
作者：
许秋燕;安恒斌
在惯性约束聚变模拟和天体物理应用中，需要求解非线性辐射扩散方程。通常，模拟域由多个块组成，每个块填充一种材质。由于材料性质的不同，块体界面处的扩散系数具有很强的不连续性。对辐射扩散方程进行隐式离散得到的代数方程很难求解。针对具有间断系数的辐射扩散方程，提出了一类基于区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-隐式迭代格式的加权系数。为了提高算法的鲁棒性，对非线性项进行了进一步修正，得到了修正后的非线性显式-隐式迭代算法。分析了算法的收敛准则。数值实验验证了所提算法的有效性。
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.