积分方程方法在层状散射问题中的应用研究  

Integral Equation Methods Applied in a Layered Medium Scattering Problem

作　　者：邓霞 向建立 叶建国 DENG Xia;XIANG Jianli;YE Jianguo(School of Mathematical Sciences,Changsha Normal University,Changsha 410100,China;School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China;School of Mathematics and Statistics,Kashi University,Kashi 844006,China)

机构地区：[1]长沙师范学院数学科学学院,湖南长沙410100 [2]华中师范大学数学与统计学学院,湖北武汉430079 [3]喀什大学数学与统计学学院,新疆喀什844006

出　　处：《应用数学》2020年第4期836-846,共11页Mathematica Applicata

基　　金：国家自然科学基金项目(11571132);湖南省教育厅科学研究项目(17C0111)复杂散射体的混合散射问题的研究。

摘　　要：本文研究声波在分层均匀介质中碰到不可穿透障碍物产生的混合边值散射问题.应用边界积分方程法将原问题转化为与之等价的边界积分方程组,通过分析积分算子的Fredholm性质,得到正问题解的适定性.应用Nystr?m方法将积分算子离散,给出远场模式的计算方法,并利用具体的数值实验验证方法的有效性,为进一步展开反问题的研究奠定理论基础.In this paper,we consider an acoustic scattering problem in inhomogeneous medium with mixed type boundary conditions.In order to show the well posedness of the direct scattering problem,the boundary integral equation method is used,that is,we transform the original problem into an equivalent boundary integral systems and investigate the Fredholm properties of the corresponding integral operators.Furthermore,with the Nystr?m method,these integral operators are discretized and the far field pattern can be computed which makes a theory foundation for further study of inverse problem.Finally,we present some numerical experiments to show the validity of the method.

关 键 词：HELMHOLTZ方程 边界积分方程 NYSTROM方法 

分 类 号：O175.5[理学—数学]