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

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.