摘要
格林函数在时域声学正反散射问题的分析和求解中应用广泛,其性质研究对求解各类正反散射问题有重要意义.在时域声学点源反演问题中,正问题解的表示包含波动算子格林函数和信号函数的卷积,在此基础上可以构造求解反问题的修正基本解方法和抽样法;在时域声学点状散射体反演问题中,正问题的解可以用格林函数近似表示,进而可以构造抽样法反演散射体的位置.
Green′s function is widely used in the analysis of acoustic forward and inverse scattering problems in time domain.The study of the Green′s function is of great significance for solving all kinds of scattering and inverse scattering problems.In the reconstruction of time domain acoustic point sources,the representation of the solution to the forward problem depends on the time convolution of the Green′s function and the signal function.On this basis,the modified method of fundamental solutions and a sampling method can be constructed to solve the inverse problems.For the reconstruction of a point-like scatterer in time domain,the solution of the forward scattering problem can be approximated by Green′s function,and then the sampling method can be constructed to reconstruct the position of the point-like scatterer.
作者
李娜
陈博
LI Na;CHEN Bo(School of Science,Civil Aviation University of China,Tianjin 300300,China)
出处
《高师理科学刊》
2023年第3期26-30,共5页
Journal of Science of Teachers＇College and University
基金
国家自然科学基金项目(12101603)
中国民航大学大学生创新创业训练计划项目(202210059085)
中央高校基本科研业务费项目中国民航大学专项(3122021072)
中国民航大学国家自然科学基金配套专项(3122022PT19)。
关键词
格林函数
时域
散射问题
反散射问题
Green′s function
time domain
scattering problem
inverse scattering problem
