论文标题
光谱Galerkin边界元素方法用于高频声音散射问题
Spectral Galerkin boundary element methods for high-frequency sound-hard scattering problems
论文作者
论文摘要
本文涉及两种不同类别的Galerkin边界元素方法的设计，用于解决二维平滑凸散射器外部高频声音散射问题的解决方案。两种方法都需要在自由度的$ k^ε$（对于任何$ε> 0 $中）的订单略有增加，以保证频率独立精确度，并增加vavenumber $ k $。另外，如果在渐近扩展中足够多的术语纳入了积分方程公式，则数值解的准确性与频率无关。数值结果验证了我们的理论发现。
This paper is concerned with the design of two different classes of Galerkin boundary element methods for the solution of high-frequency sound-hard scattering problems in the exterior of two-dimensional smooth convex scatterers. Both methods require a small increase in the order of $k^ε$ (for any $ε>0$) in the number of degrees of freedom to guarantee frequency independent precisions with increasing wavenumber $k$. In addition, the accuracy of the numerical solutions are independent of frequency provided sufficiently many terms in the asymptotic expansion are incorporated into the integral equation formulation. Numerical results validate our theoretical findings.
