次扩散方程的分数阶参数优化算法  

A FRACTIONAL PARAMETER OPTIMIZATION ALGORITHM FOR SUB-DIFFUSION EQUATIONS

作　　者：汪韬 厉井钢 Wang Tao;Li Jinggang(China Nuclear Power Technology Research Institute Co.Ltd.,Shenzhen 518000,China)

机构地区：[1]中广核研究院有限公司,深圳518000

出　　处：《数值计算与计算机应用》2023年第3期272-284,共13页Journal on Numerical Methods and Computer Applications

摘　　要：本文考虑一个次扩散方程的反问题,即根据某个时刻解在空间区域上的积分反向优化方程中的分数阶参数.本文说明了当初值为0时,以上问题可能有多个解.基于时空有限元法,我们提出了一个参数优化算法,并利用离散Laplace变换技巧证明了该算法的全局收敛性.另外针对球形区域,利用-△算子的谱分解,我们还提出了一个快速算法.最后两个数值算例验证了算法的有效性.In this paper,we consider a inverse problem of sub-diffusion equations,i.e.the fractional parameter in the equation is optimized according to the spatial integral of the solution at a certain time.This paper shows that the inverse problem may have multiple solutions,when the initial value is O.Based on the space-time finite element method,we propose a parameter optimization algorithm,and proved the global convergence of the algorithm by using the discrete Laplace transform technique.In addition,for the spherical region,we propose a fast algorithm by using the spectral decomposition of -△ operator.Finally,two numerical examples verify the effectiveness of the algorithm.

关 键 词：次扩散方程 参数优化 时空有限元 

分 类 号：O241.82[理学—计算数学]