热传导系统初始温度和内部源项同时重建的变分伴随方法  

Simultaneous Recovery of Initial Field and Spatial Heat Source for Heat Conduction Process by Variational Adjoint Method

作　　者：王兵贤[1] 

机构地区：[1]东南大学数学系

出　　处：《江西科学》2017年第1期28-32,共5页Jiangxi Science

基　　金：江苏省普通高校研究生科研创新计划资助项目(KYLX-0082)

摘　　要：研究用变分伴随方法求解由抛物型方程描述的温度扩散系统的初始温度和和内部源项的同时反演问题。将此问题转化为一个二次泛函的优化问题。利用变分伴随思想构造交替迭代算法,迭代过程中首次搜索方向采用使得泛函下降最快的负梯度方向,后续的搜索方向对初始温度反演采用共轭梯度法,对源项反演采用一种全局收敛的下降算法。数值模拟结果显示用变分伴随方法求解此类反问题是可行的和有效的。This paper studies an inverse problem of simultaneous recovery for a spatial dependent heat source and the initial temperature field from a parabolic system by reformulating it as an optimization problem. An iteration algorithm is proposed by the variational adjoint method. The negative gradient direction is selected as the first search direction. For the succeed iterations,the conjugate gradient method is used for the initial temperature inversion and a globally convergent algorithm is used for the heat source identification. The efficiency of the proposed scheme is tested by the numerical simulation experiments.

关 键 词：抛物型方程 反问题 变分伴随方法 

分 类 号：O175[理学—数学]