辐射扩散方程的非线性迭代方法  

Nonlinear Iterative Methods for Radiation Diffusion Equations

作　　者：安恒斌[1,2] 莫则尧 AN Hengbin;MO Zeyao(Institute of Applied Physics and Computational Mathematics,Beijing 100094,China;Software Center for High Performance Numerical Simulation,China Academy of Engineering Physics,Beijing 100088,China)

机构地区：[1]北京应用物理与计算数学研究所,北京100094 [2]中国工程物理研究院高性能数值模拟软件中心,北京100088

出　　处：《计算物理》2024年第1期75-86,共12页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(12171045)资助项目。

摘　　要：为了提高Newton方法和Picard方法求解辐射扩散方程组的健壮性和收敛速度,介绍应用这两类方法求解辐射扩散方程组的几方面工作,包括迭代初值的选取、迭代过程物理约束的处理、Picard迭代过程与Anderson加速的结合以及针对Anderson加速方法的改进等。通过应用相关的处理和改进策略,两类方法可有效应用于非线性辐射扩散方程的求解。To improve the robustness and convergence speed of the Newton method and Picard method of solving radiation diffusion equations,several work is introduced when they are used to solve the three temperature radiation diffusion equation system,including the selection of initial iteration value,the treatment of physical constraints in the iterative process,the combination of the Picard iterative method and Anderson acceleration,and the improvement of Anderson acceleration method.By applying application-driven treatments and improvements,the two methods can be used to solve the nonlinear radiation diffusion equations.

关 键 词：辐射扩散 非线性迭代 NEWTON迭代 Picard迭代 Anderson加速 

分 类 号：O241.7[理学—计算数学] O246[理学—数学]