论文标题
高频散射迭代的渐近膨胀，以解决声音硬散射问题
Asymptotic expansions of high-frequency multiple scattering iterations for sound hard scattering problems
论文作者
论文摘要
我们考虑在有限的脱节，紧凑，光滑的，严格凸出的二维高频平面波散射问题的情况下，具有诺伊曼边界条件。使用积分方程式公式，我们确定了Hörmander类，并得出了与散射障碍物边界上多个散射迭代相对应的总场的高频渐近膨胀。这些渐近膨胀用于获得对多个散射总场的衍生物的尖锐依赖性估计值，而这些散射总场又允许对Galerkin边界元素方法的最佳设计和数值分析，以实现高效（频率独立）声音硬散射回报的有效（频率独立）近似值。提出了支持这些扩展有效性的数值实验。
We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth, strictly convex obstacles with Neumann boundary conditions. Using integral equation formulations, we determine the Hörmander classes and derive high-frequency asymptotic expansions of the total fields corresponding to multiple scattering iterations on the boundaries of the scattering obstacles. These asymptotic expansions are used to obtain sharp wavenumber dependent estimates on the derivatives of multiple scattering total fields which, in turn, allow for the optimal design and numerical analysis of Galerkin boundary element methods for the efficient (frequency independent) approximation of sound hard multiple scattering returns. Numerical experiments supporting the validity of these expansions are presented.
