Determination of electromagnetic Bloch variety in a medium with frequency-dependent coefficients

被引：7
|
作者：
Lackner, C. [1 ]
Meng, S. [2 ]
Monk, P. [3 ]
机构：
[1] Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria
[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 358卷
基金：
奥地利科学基金会; 美国国家科学基金会;
关键词：
Bloch variety; Quadratic eigenvalue; Composite materials; Frequency-dependent materials; BAND-STRUCTURE CALCULATIONS; FINITE-ELEMENTS; APPROXIMATION;
D O I：
10.1016/j.cam.2019.03.027
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We provide a functional framework and a numerical algorithm to compute the Bloch variety for Maxwell's equations when the electric permittivity is frequency dependent. We incorporate the idea of a mixed formulation for Maxwell's equations to obtain a quadratic eigenvalue for the wave-vector in terms of the frequency. We reformulate this problem as a larger linear eigenvalue problem and prove that this results in the need to compute eigenvalues of a compact operator. Using finite elements, we provide preliminary numerical examples of the scheme for both frequency independent and frequency dependent permittivity. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码：359 / 373
页数：15
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