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.
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页码：359 / 373
页数：15
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