Galerkin Boundary Element Methods for High-Frequency Multiple-Scattering Problems
Galerkin Boundary Element Methods for High-Frequency Multiple-Scattering Problems
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DOI：
10.1007/s10915-020-01189-x
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发表时间：
2020-03
影响因子：
2.5
通讯作者：
F. Ecevit;A. Anand;Y. Boubendir
中科院分区：
文献类型：
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作者：
F. Ecevit;A. Anand;Y. Boubendir
我们考虑二维光滑散射体外部的高频多次散射问题，这些散射体由有限个紧凑的、不相交的和严格凸的障碍物组成。为了解决这一问题，我们提出了Galerkin边界元方法，即频率适配的Galerkin边界元方法和变量随频率变化产生的Galerkin边界元方法。对于这两种新算法，对于每一次多次散射迭代，我们证明了自由度数需要随着波数的增加而增加，以达到与频率无关的误差容限。我们通过各种数值实现来支持我们的理论发展。
We consider high-frequency multiple-scattering problems in the exterior of two-dimensional smooth scatterers consisting of finitely many compact, disjoint, and strictly convex obstacles. To deal with this problem, we propose Galerkin boundary element methods, namely thefrequency-adapted Galerkin boundary element methodsandGalerkin boundary element methods generated using frequency-dependent changes of variables. For both of these new algorithms, in connection with each multiple-scattering iterate, we show that the number of degrees of freedom needs to increase as(for any) with increasing wavenumberkto attain frequency-independent error tolerances. We support our theoretical developments by a variety of numerical implementations.