Markel Vadim A, Schotland John C
Department of Radiology and Graduate Group in Applied Mathematics and Computational Science, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066603. doi: 10.1103/PhysRevE.85.066603. Epub 2012 Jun 4.
We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half space and derive and implement a computationally efficient continued-fraction expansion for the effective permittivity. Our results are illustrated by numerical computations for the case of two-dimensional systems. The homogenization theory of this paper is designed to predict various physically measurable quantities rather than to simply approximate certain coefficients in a partial differential equation.
我们考虑周期性复合材料麦克斯韦方程组的均匀化问题。分析基于布洛赫 - 弗洛凯理论。我们明确计算了半空间的反射系数，并推导并实现了有效介电常数的一种计算高效的连分数展开式。通过二维系统情形的数值计算对我们的结果进行了说明。本文的均匀化理论旨在预测各种物理可测量量，而非仅仅近似偏微分方程中的某些系数。
