热传导方程点源源强反演的数值方法  

NUMERICAL METHOD FOR POINT SOURCE STRENGTH INVERSION OF HEAT CONDUCTION EQUATION

作　　者：闵涛[1] 吴兰兰 Min Tao;Wu Lanlan(School of Science,Xi’an University of Technology,Xi’an 710054,China)

机构地区：[1]西安理工大学理学院,西安710054

出　　处：《数值计算与计算机应用》2023年第2期138-149,共12页Journal on Numerical Methods and Computer Applications

摘　　要：利用分离变量法给出了含点源的一维热传导方程的积分解,在此基础上,研究了一维热传导方程点源源强的反演问题,将源强反演问题转化为优化问题,利用变分伴随法得到了梯度表达式,借助Broyden族算法对其反演,并给出数值模拟,结果表明Broyden族算法可行且有效.Using the method of separation of variables is given including integrated solution of one-dimensional heat conduction equation of point source,on this basis,study the one-dimensional heat conduction equation of point source strength inversion problem,the source strength inversion problem is transformed into optimization problem,the variational adjoint method are used to get the gradient expression,with the aid of Broyden class algorithm for the inversion,and the numerical simulation is given,The results show that the Broyden algorithm is feasible and effective.

关 键 词：热传导 点源 反演 变分伴随法 Broyden族算法 

分 类 号：O241.8[理学—计算数学]