多连通域间稳定FDTD相互作用的离散格林函数对光

B. P. de Hon, J. Arnold
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引用次数: 7

摘要

我们建立了基于离散格林函数对光的时域有限差分边界条件。相应的z域边界算子是对称的,其虚部在复z平面上的单位圆上半部分可以证明为正半定。通过Schwarz的外部公式,得到了该算子在单位圆外解析的积分表示。基于正交规则的算子有理逼近对应于离散时域的自洽有限回溯格式。这种方案显然是稳定的,因为只有长期的、不增长的、无源的解存在,这些解可能被抑制。
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Discrete Green's function diakoptics for stable FDTD interaction between multiply-connected domains
We have developed FDTD boundary conditions based on discrete Green's function diakoptics for arbitrary multiply-connected 2D domains. The associated Z-domain boundary operator is symmetric, with an imaginary part that can be proved to be positive semi-definite on the upper half of the unit circle in the complex Z-plane. Through Schwarz' exterior formula an integral representation of this operator is obtained that is analytic outside that unit circle. A quadrature-rule based rational approximation of the operator corresponds to a self-consistent finite-lookback scheme in the discretised time domain. This scheme is demonstrably stable, in that only secular, non-growing, source-free solutions remain, which may be suppressed.
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