各向异性标量共振问题的径向复标度
Radial complex scaling for anisotropic scalar resonance problems
摘要：
复尺度/完全匹配层方法是一种广泛应用于模拟开域中波传播问题的方法。该方法是非常流行的，因为它的实施是非常容易的，不需要一个基本解的知识。然而，对于各向异性介质，该方法可能会产生非物理的辐射条件，导致错误和不稳定的结果。在这篇文章中，我们认为，径向缩放（相对于carbohydrated缩放）不遭受这个缺点，并产生所需的辐射条件。这一结果是非常重要的，因为它恢复复尺度方法的各向异性介质的应用。为了更详细地介绍，我们考虑了标量各向异性共振问题的径向复标度法。我们证明了相应的算子是Fredholm算子，并证明了由同时的区域截断和有限元离散所产生的逼近的收敛性。我们目前的计算研究，巩固我们的理论结果。
英文摘要：
The complex scaling/perfectly matched layer method is a widely spread technique to simulate wave propagation problems in open domains. The method is very popular, because its implementation is very easy and does not require the knowledge of a fundamental solution. However, for anisotropic media the method may yield an unphysical radiation condition and lead to erroneous and unstable results. In this article we argue that a radial scaling (opposed to a cartesian scaling) does not suffer from this drawback and produces the desired radiation condition. This result is of great importance as it rehabilitates the application of the complex scaling method for anisotropic media. To present further details we consider the radial complex scaling method for scalar anisotropic resonance problems. We prove that the associated operator is Fredholm and show the convergence of approximations generated by simulateneous domain truncation and finite element discretization. We present computational studies to undergird our theoretical results.
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