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

页码：359 / 373

页数：15

共 31 条

[21] Highly accurate closed form approximation for frequency-dependent line impedance of a lossy silicon substrate IC interconnect [J].

Ymeri, H ;

Nauwelaers, B ;

Maex, K ;

De Roest, D ;

Stucchi, M .

MICROELECTRONIC ENGINEERING, 2002, 60 (1-2) :31-37

[22] Frequency-dependent mutual resistance and inductance formulas for coupled IC interconnects on an Si-SiO2 substrate [J].

Ymeri, H ;

Nauwelaers, B ;

Maex, K .

INTEGRATION-THE VLSI JOURNAL, 2001, 30 (02) :133-141

[23] Efficiency of room acoustic simulations with time-domain FEM including frequency-dependent absorbing boundary conditions: Comparison with frequency-domain FEM [J].

Okuzono, Takeshi ;

Yoshida, Takumi ;

Sakagami, Kimihiro .

APPLIED ACOUSTICS, 2021, 182

[24] A new approximation to the reflection coefficient of the diffusive-viscous wave equation and its evaluation for frequency-dependent AVA inversion [J].

Wang, Zhiqiang ;

Gao, Jinghuai ;

Zhao, Haixia ;

Chen, Hongling .

JOURNAL OF APPLIED GEOPHYSICS, 2022, 201

[25] Numerical analysis of the frequency-dependent Jiles-Atherton hysteresis model using the example of Terfenol-D material [J].

Zhang, Cheng ;

Xue, Guangming .

AIMS MATHEMATICS, 2024, 9 (11) :31532-31552

[26] An imperfection of time-dependent diffusion models for a determination of scattering medium optical properties [J].

Tereshchenko, S. A. ;

Dolgushin, S. A. ;

Titenok, S. A. .

OPTICS COMMUNICATIONS, 2013, 306 :26-34

[27] Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel [J].

Rebolini, Elisa ;

Toulouse, Julien .

JOURNAL OF CHEMICAL PHYSICS, 2016, 144 (09)

[28] Application of Extended Matrix Pencil Method in Multiport Frequency-Dependent Network Equivalent and the Transient Analysis of Multiconductor Transmission Line System [J].

Zhang, Yin ;

Liao, Cheng ;

Shang, Yuping ;

Feng, Ju ;

Du, Wei ;

Zhong, Xuanming .

IEEE TRANSACTIONS ON POWER DELIVERY, 2023, 38 (01) :95-104

[29] A Unified Gas-Kinetic Particle Method for Frequency-Dependent Radiative Transfer Equations with Isotropic Scattering Process on Unstructured Mesh [J].

Hu, Yuan ;

Liu, Chang ;

Shen, Huayun ;

Zou, Shiyang ;

Tian, Baolin .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2024, 35 (01) :181-211

[30] A time-domain seismic SSI analysis method for inelastic bridge structures through the use of a frequency-dependent lumped parameter model [J].

Lesgidis, Nikolaos ;

Kwon, Oh-Sung ;

Sextos, Anastasios .

EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, 2015, 44 (13) :2137-2156

← 1 2 3 4 →