Embedding formulae for scattering in a waveguide containing polygonal obstacles
Embedding formulae for scattering in a waveguide containing polygonal obstacles
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包含多边形障碍物的波导中散射的嵌入公式
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
N. Biggs
中科院分区：
文献类型：
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作者：
N. Biggs
对于某些波散射问题，可以导出嵌入公式，用有限个其他相关问题的相应量表示任意平面波入射角的解或解的远场行为。到目前为止，它们的范围仅限于R^2的散射，以及较小程度的R^3；本文导出了一类二维波导中波散射的嵌入公式。波导在有限长度区域外是直的，宽度均匀，在有限长度区域内的边界是分段线性的，波导可以包含多边形障碍物，限制是波导和障碍物的所有边界必须与波导的轴线以合理的角度倾斜。一旦确定了一组有限的入射传播模式的解，嵌入公式就提供了反射和传输的表达式
For certain wave scattering problems embedding formulae can be derived, which express the solution, or far-field behaviour of the solution, for arbitrary plane wave incident angle in terms of the corresponding quantities for a finite number of other related problems. Their scope has so far been limited to scattering in R^2, and to a lesser extent R^3; in this paper we derive embedding formulae for wave scattering in a class of two-dimensional waveguide. The waveguide is straight and of uniform width outside a finite length region within which the boundaries are piecewise-linear and the waveguide can contain polygonal obstacles, a restriction being that all boundaries of the waveguide and obstacles must be inclined at a rational angle to the axis of the waveguide. Once solutions are determined for a finite set of incident propagating modes, the embedding formulae provide expressions for reflection and transmission
coefficients for all remaining incident propagating modes. The precise number of solutions required is a function of the number and nature of the corners of the
boundaries and obstacles. The formulae are illustrated for a particular waveguide geometry for which the problem can be formulated as an integral equation and approximate numerical solutions determined using the Galerkin method.