In-out decomposition of boundary integral equations
In-out decomposition of boundary integral equations
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边界积分方程的输入输出分解
DOI：
10.1088/1751-8113/46/43/435203
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Creagh S
中科院分区：
文献类型：
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作者：
Creagh S
我们提出了一个新的边界积分方程的亥姆霍兹方程在一个域的传入和传出的边界波。我们得到的传输算子的描述是准确的，因此将功能，如衍射和倏逝波耦合，这些影响是不存在的，在著名的半经典传输运营商的意义上的Bogomolny。在半经典近似下，转移算子与边界积分方法是等价的。精确的处理一直局限于特定的边界条件（如狄利克雷或诺依曼）。我们提出的方法是独立的边界条件，事实上，允许一个完全解耦的问题，传播波在内部的反射波在边界上的问题。作为一个应用程序，我们展示了如何分解可用于计算古斯-汉兴位移的射线动力学在台球可变边界条件和电介质腔。
We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features such as diffraction and evanescent coupling; these effects are absent in the well-known semiclassical transfer operators in the sense of Bogomolny. It has long been established that transfer operators are equivalent to the boundary integral approach within semiclassical approximation. Exact treatments have been restricted to specific boundary conditions (such as Dirichlet or Neumann). The approach we propose is independent of the boundary conditions, and in fact allows one to decouple entirely the problem of propagating waves across the interior from the problem of reflecting waves at the boundary. As an application, we show how the decomposition may be used to calculate Goos–Hänchen shifts of ray dynamics in billiards with variable boundary conditions and for dielectric cavities.