基于变限积分法数值求解二维逆热传导问题  

Solving numerically the 2D inverse heat conduction problem based on the variable limit integral method

作　　者：张燕 冯立新[1] ZHANG Yan;FENG Lixin(School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2022年第2期127-133,共7页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Natural Science Foundation of China(11871198)。

摘　　要：研究了一个二维逆热传导问题,即由最终时刻T>0的温度确定初始温度。对于这个问题,基于正则化技术和SOR迭代法构造了一种反演方案。在每个迭代步骤中,用所提出的变限积分法求解正问题。数值实验表明该方法是有效的。Consider a 2 D inverse heat conduction problem of determining the initial temperature from the temperature at the final time T>0. For the problem, an inversion method is constructed based on the regularization technique and the SOR iteration. At each iterative step, the direct problem is solved by using the proposed variable limit integral method. Numerical experiments show that this method is valid.

关 键 词：逆问题 热传导方程 正则化 SOR迭代 变限积分法 

分 类 号：O241[理学—计算数学]