A frequency-independent boundary element method for scattering by two-dimensional screens and apertures
A frequency-independent boundary element method for scattering by two-dimensional screens and apertures
复制标题
用于二维屏幕和孔径散射的与频率无关的边界元方法
DOI：
10.1093/imanum/dru043
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发表时间：
2014
影响因子：
2.1
通讯作者：
S. Chandler
中科院分区：
文献类型：
--
作者：
D. Hewett;S. Langdon;S. Chandler
本文提出并分析了一种数值-渐近混合边界元法（BEM），用于求解平面波在任意共线声软二维屏阵列上的时谐散射问题。我们的方法使用了一个近似空间丰富的振荡基函数，选择捕获的解决方案的高频渐近。我们提供了一个严格的频率显式误差分析，证明了该方法的收敛指数的自由度N的数量增加，并达到任何所需的精度，它是足够的增加N的对数的平方成比例的频率增加（标准边界元法要求N增加至少与频率线性保持精度）。我们的数值结果表明，固定的精度，实际上可以实现在任意高的频率与频率无关的计算成本，实施所需的振荡积分时，使用Filon正交计算。我们还展示了如何我们的方法可以应用到互补的“防波堤”问题的传播通过一个光圈在一个无限的声音硬屏幕。
We propose and analyse a hybrid numerical–asymptotic hp boundary element method (BEM) for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high-frequency asymptotics of the solution. We provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom N increases, and that to achieve any desired accuracy it is sufficient to increase N in proportion to the square of the logarithm of the frequency as the frequency increases (standard BEMs require N to increase at least linearly with frequency to retain accuracy). Our numerical results suggest that fixed accuracy can in fact be achieved at arbitrarily high frequencies with a frequency-independent computational cost, when the oscillatory integrals required for implementation are computed using Filon quadrature. We also show how our method can be applied to the complementary ‘breakwater’ problem of propagation through an aperture in an infinite sound-hard screen.
平面屏幕声散射中的波数显式连续性和矫顽力估计
影响因子：
0.8
作者：
Chandler-Wilde S
通讯作者：
Chandler-Wilde S