On choice of relaxation parameter for Anderson acceleration method

DUAN Xiaoyu; AN Hengbin

doi:10.13471/j.cnki.acta.snus.2021B109

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On choice of relaxation parameter for Anderson acceleration method

Research articles | 更新时间：2023-11-01

- On choice of relaxation parameter for Anderson acceleration method
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 61, Issue 6, Pages: 113-122(2022)
- 作者机构：
  
  1.中国工程物理研究院研究生院，北京 100088
  2.北京应用物理与计算数学研究所，北京 100094
  3.中国工程物理研究院高性能数值模拟软件中心，北京 100088
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2021B109
  CLC： O241.7
- Published：25 November 2022，
  
  Published Online：07 May 2022，
  
  Received：19 November 2021，
  
  Accepted：21 December 2021
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段晓宇,安恒斌.Anderson加速方法中的松弛参数选取[J].中山大学学报(自然科学版),2022,61(06):113-122.

DUAN Xiaoyu,AN Hengbin.On choice of relaxation parameter for Anderson acceleration method[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(06):113-122.
段晓宇,安恒斌.Anderson加速方法中的松弛参数选取[J].中山大学学报(自然科学版),2022,61(06):113-122. DOI： 10.13471/j.cnki.acta.snus.2021B109.

DUAN Xiaoyu,AN Hengbin.On choice of relaxation parameter for Anderson acceleration method[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(06):113-122. DOI： 10.13471/j.cnki.acta.snus.2021B109.

摘要

Anderson加速方法是提高不动点迭代收敛速度的一类方法。该方法中的松弛参数一般在区间（0，1］内，且大多数选取为1。考虑扩大Anderson加速方法中松弛参数的选取范围，以求解非线性扩散方程的Picard迭代过程为例，比较了不同松弛参数选取方法的效果。数值结果表明，合适的松弛参数可以有效提高Anderson加速方法的效果。

Abstract

Anderson acceleration method is a kind of method to improve the convergence speed of fixed-point iteration. The relaxation parameter is generally in the interval （0，1］， and is selected as 1 in most cases. This paper expanded the selection range of the relaxation parameter. Taking the Picard iteration of solving the nonlinear diffusion equation as an example， the effect of the relaxation parameter selection method was compared. The numerical results show that the appropriate relaxation parameter can effectively improve the convergence speed of the Anderson acceleration method.

关键词

迭代方法Anderson加速非线性扩散方程参数选取

Keywords

iterative methodsAnderson accelerationnonlinear diffusion equationsparameter selection

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