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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >The DtN nonreflecting boundary condition for multiple scattering problems in the half-plane
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The DtN nonreflecting boundary condition for multiple scattering problems in the half-plane

机译：半平面中多重散射问题的DtN非反射边界条件

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摘要

The multiple-Dirichlet-to-Neumann (multiple-DtN) non-reflecting boundary condition is adapted to acoustic scattering from obstacles embedded in the half-plane. The multiple-DtN map is coupled with the method of images as an alternative model for multiple acoustic scattering in the presence of acoustically soft and hard plane boundaries. As opposed to the current practice of enclosing all obstacles with a large semicircular artificial boundary that contains portion of the plane boundary, the proposed technique uses small artificial circular boundaries that only enclose the immediate vicinity of each obstacle in the half-plane. The adapted multiple-DtN condition is simultaneously imposed in each of the artificial circular boundaries. As a result the computational effort is significantly reduced. A computationally advantageous boundary value problem is numerically solved with a finite difference method supported on boundary-fitted grids. Approximate solutions to problems involving two scatterers of arbitrary geometry are presented. The proposed numerical method is validated by comparing the approximate and exact far-field patterns for the scattering from a single and from two circular obstacles in the half-plane.
机译：多重Dirichlet-Neumann（multiple-DtN）非反射边界条件适用于来自嵌入半平面的障碍物的声散射。多重DtN映射与图像方法相结合，作为存在声学软平面和硬平面边界的多重声学散射的替代模型。与当前的做法是，将所有障碍物都包含一个包含平面边界一部分的大半圆形人造边界，而所提出的技术则使用较小的人造圆形边界，该边界仅将每个障碍物紧邻在半平面内。适应的多重DtN条件同时施加在每个人工圆形边界中。结果，显着减少了计算量。通过在边界拟合网格上支持的有限差分方法在数值上解决了具有计算优势的边界值问题。提出了涉及两个任意几何形状散射体的近似解决方案。通过比较从半平面中单个障碍物和两个圆形障碍物散射的近似和精确远场模式，验证了所提出的数值方法。

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