Seamless integration of elliptic Dirichlet-to-Neumann boundary condition and high order spectral element method for scattering problem
Seamless integration of elliptic Dirichlet-to-Neumann boundary condition and high order spectral element method for scattering problem
复制标题
椭圆狄利克雷-诺伊曼边界条件与高阶谱元法的无缝集成解决散射问题
DOI：
10.1007/s13160-019-00383-1
复制
发表时间：
2019
影响因子：
0.9
通讯作者：
Xie Ziqing
中科院分区：
文献类型：
--
作者：
Zhang Rui;Wang Bo;Xie Ziqing
本文提出了一种半解析方法，将椭圆型Dirichlet-to-Neumann（DtN）边界条件与高阶谱元方法相结合，求解细长散射体的散射问题。通过在谱元离散化过程中采用适当的元素映射，得到了计算整体DtN算子中Mathieu展开系数的半解析公式。此外，提出了一种半解析方法来计算谱元离散化中的整体边界积分项。所提出的半解析公式也可用于计算谱元网格上给定值函数的Mathieu展开系数。数值算例表明，谱元法与半解析法相结合，可以得到细长散射体散射问题的高阶数值解。
In this paper, we present a semi-analytic approach to enhance the integration of elliptic Dirichlet-to-Neumann (DtN) boundary condition and high order spectral element method in solving scattering problem with slender scatterer. By using appropriate elemental mapping in the spectral element discretization, semi-analytic formulas are obtained for the computation of Mathieu expansion coefficients involved in the global DtN operator. Further, a semi-analytic approach is proposed for the computation of global boundary integral terms in the spectral element discretization. The proposed semi-analytic formulas can also be used to calculate Mathieu expansion coefficients for functions given values on spectral element grids. Numerical examples show that spectral element method with the proposed semi-analytic approach can produce high order numerical solution for scattering problem with slender scatterer.