论文标题
周期性表面散射的波浪的不均匀网格法
A nonuniform mesh method for wave scattered by periodic surfaces
论文作者
论文摘要
在本文中，我们提出了一种新的非均匀网格方法，以模拟具有数值非周期性入射场的二维周期性结构中的声学散射问题。由于现有方法难以扩展到更高的维度，因此我们已经考虑了新方法，并考虑了此类扩展。借助Floquet-Bloch变换，解决原始散射问题的解决方案被写成是准周期性问题家族的组成部分。这些定义在有界间隔变化的Floquet参数的每个值中定义。我们方法中的关键步骤是通过正交规则对积分的数值近似，该规则适合于准周期溶液的规律性。我们设计了一个不均匀的网格，该网格具有应用于每个子间隔的高斯正交规则。我们证明，数值方法相对于子间隔数和高斯正交点的数量呈指数收敛。提供了一些数值实验来说明结果。
In this paper, we propose a new nonuniform mesh method to simulate acoustic scattering problems in two dimensional periodic structures with non-periodic incident fields numerically. As existing methods are difficult to extend to higher dimensions, we have designed the new method with such extensions in mind. With the help of the Floquet-Bloch transform, the solution to the original scattering problem is written as an integral of a family of quasi-periodic problems. These are defined in bounded domains for each value of the Floquet parameter which varies in a bounded interval. The key step in our method is the numerical approximation of the integral by a quadrature rule adapted to the regularity of the family of quasi-periodic solutions. We design a nonuniform mesh with a Gaussian quadrature rule applied on each subinterval. We prove that the numerical method converges exponentially with respect to both the number of subintervals and the number of Gaussian quadrature points. Some numerical experiments are provided to illustrate the results.
