一维流动的Boussinesq方程渗流系数反演的变分伴随方法研究  

The Research on the Variational Adjoint Method for Percolation Coefficient Inversion for One-Dimensional Flowing Boussinesq Equation

作　　者：王兵贤[1] 徐定华[1] 胡康秀[1] 

机构地区：[1]东华理工大学数学与信息科学学院,江西抚州344000

出　　处：《数学的实践与认识》2008年第20期194-200,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10561001);东华理工大学校长基金(DHXK0702);浙江理工大学科研基金(0613263)

摘　　要：利用偏微分方程最优控制中的伴随方法讨论一维Boussinesq方程渗流系数反演问题的数值解法.吸收正则化思想改造最小二乘方法,利用变分伴随思想构造新迭代算法.迭代过程中首次搜索方向采用泛函下降最快的负梯度方向,第二次及以后搜索方向采用一种新的全局收敛的下降算法(Pan-Chen算法).与共轭梯度法比较,新算法具有更好的收敛性.数值模拟结果验证了理论算法的可靠性.This paper discusses a numerical method of percolation coefficient inversion for one- dimensional flowing Boussinesq equation. The paper improves the least squared method （LSM） by means of the idea of regularization, and derives a new iteration algorithm by means of variational adjoint method. The negative gradient direction is selected as the first search direction, and a newly globally convergent algorithm （Pan-Chen algorithm） is applied to determine the second search direction and later iteration direction. The new algorithm has better convergence than the conjugate gradient method. The algorithm＇s efficiency and feasibility are tested by the numerical simulation experiment.

关 键 词：BOUSSINESQ方程 反问题 变分伴随方法 系数识别 

分 类 号：O175[理学—数学]