辐射扩散方程的非线性迭代方法

doi:10.19596/j.cnki.1001-246x.8765

摘要/Abstract

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。

关键词: 辐射扩散, 非线性迭代, Newton迭代, Picard迭代, Anderson加速

Abstract:

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.

Key words: radiation diffusion, nonlinear iteration, Newton method, Picard method, Anderson acceleration

中图分类号:

O241.7
O246

安恒斌, 莫则尧. 辐射扩散方程的非线性迭代方法[J]. 计算物理, 2024, 41(1): 75-86.

Hengbin AN, Zeyao MO. Nonlinear Iterative Methods for Radiation Diffusion Equations[J]. Chinese Journal of Computational Physics, 2024, 41(1): 75-86.

图/表 3

图1 第n和n+1时间步以及预测的第n+1时间步的光子温度 (a) 未修正; (b) 修正

Fig.1 The photon temperatures at time steps n and n+1, and the predicted photon temperatures at n+1 time step with (a) unmodified and (b) modified

表1 三类方法开销

Table 1 The cost of three methods

	JFNK	PK	PK-AA(m)
NFE	NNI+NLI+1	NNI+1	NNI+1
NPS	NNI	NNI	NNI
NPA	NNI+NLI	NNI+NLI	NNI+NLI

表2 三类方法的迭代次数和时间

Table 2 Iteration numbers and computing time of three methods

方法	NNI	NLI	NFE	NPA	TIME
JFNK	2.88	12.90	16.78	15.78	28.77
PK	24.32	24.32	25.32	48.64	92.28
PK-AA(10)	9.11	9.11	10.11	18.22	34.78

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