云南师范大学学报（自然科学版）2023，Vol.43Issue(6)：10-17,8.DOI:10.7699/j.ynnu.ns-2023-074
Poisson方程系数识别的有限元反演方法
Finite Element Inversion Method for Coefficient Identification of Poisson Equation
摘要
Abstract
The coefficient identification problem of the Poisson equation has important applications in many fields such as medical imaging and telemetry exploration.Due to its ill-posed nature and noisy sampling in practical applications,it is often difficult to solve.Therefore,a finite element inversion method is proposed to solve this problem.Firstly,the weak solution form of the boundary value prob-lem for the Poisson equation is given,and the boundary value problem is approximated in finite ele-ment space.Based on the triangulation grid,an optimization model for coefficient identification prob-lem is established,and a linear equation system for coefficient identification problem is obtained.Then,a higher-order Tikhonov regularization model is used to reduce the ill-posed effect of the inverse problem.Finally,numerical inversion experiments are conducted on the diffusion coefficients with smooth and piecewise smooth surfaces,and the effectiveness of this method is verified.关键词
系数识别/Poisson方程/有限元反演/高阶Tikhonov正则化Key words
Coefficient identification/Poisson equation/Finite element inversion/Higher-order Tikhonov regularization分类
数理科学引用本文复制引用
吴洁,杨凤莲..Poisson方程系数识别的有限元反演方法[J].云南师范大学学报（自然科学版）,2023,43(6):10-17,8.基金项目
国家自然科学基金资助项目(12271140) （12271140）
河海大学中央高校基本科研业务费资助项目(B220202081). （B220202081）
