Homogenization of the Maxwell Equations at Fixed Frequency
Homogenization of the Maxwell Equations at Fixed Frequency
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DOI：
10.1137/s0036139902403366
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
G. Kristensson;N. Wellander
中科院分区：
文献类型：
--
作者：
G. Kristensson;N. Wellander
本文讨论了固定频率下麦克斯韦方程组的均匀化问题。具有周期性微观结构的材料的整体（均质）电磁性能是用合适的平均值从单元胞上的局部问题求解得到的。材料可以是各向异性的，并且满足矫顽力条件。激发场是由被研究材料外部的入射场产生的。对内部问题定义了合适的半线性形式，并利用外部Calder ' on算子求解外部辐射场。采用双尺度收敛的概念来解决均匀化问题。证明了一种新的先验估计，并在校正器上得到了新的结果。(少)
The homogenization of the Maxwell equations at fixed frequency is addressed in this paper. The bulk (homogenized) electric and magnetic properties of a material with a periodic microstructure are found from the solution of a local problem on the unit cell by suitable averages. The material can be anisotropic, and satisfies a coercivity condition. The exciting field is generated by an incident field from sources outside the material under investigation. A suitable sesquilinear form is defined for the interior problem, and the exterior Calder´on operator is used to solve the exterior radiating fields. The concept of two-scale convergence is employed to solve the homogenization problem. A new a priori estimate is proved as well as a new result on the correctors. (Less)