二维热传导方程源强识别反问题的数值求解  

THE STRENGTH ESTIMATION OF THE HEAT SOURCE IN THE 2-D HEAT CONDUCTION PROBLEMS BY NUMERICAL SOLUTION

作　　者：闵涛[1] 淮永涛[1] 符巍敏 

机构地区：[1]西安理工大学理学院,陕西西安710054

出　　处：《数学杂志》2015年第3期601-607,共7页Journal of Mathematics

基　　金：国家自然科学基金重大项目基金资助(51190093);国家自然科学基金(50979088);国家自然科学基金(51179151)

摘　　要：本文研究了一类含有时间变量热源的二维热传导方程.利用有限元方法给出了数值求解过程,并在已知热源位置的前提下,根据某点的温度观测值,利用插值方法,将源强识别问题转化为参数反演问题,通过微分进化方法结合最佳摄动量法对源强识别反问题进行了数值模拟,结果表明所提出的方法是可行有效的.A class of the two-dimensional heat conduction equation with the time-varying strength of the heat source is studied, and a numerical solution of finite element process is given. In the case of the known heat source location, according to the temperature observation of a certain point, we convert the source strength identification problem into the parameter inversion problems by using interpolation method first; then we identify the source strength on the numerical inversion through the differential evolution method combining with the best perturbation method. The result shows the feasibility and effectiveness of the proposed algorithm.

关 键 词：热源 有限元 插值方法 微分进化算法 最佳摄动量方法 

分 类 号：O242.2[理学—计算数学]