An efficient contour integral based eigensolver for 3D dispersive photonic crystal

Tsung Ming Huang; Weichien Liao; Wen Wei Lin; Weichung Wang

doi:10.1016/j.cam.2021.113581

An efficient contour integral based eigensolver for 3D dispersive photonic crystal

Tsung Ming Huang, Weichien Liao, Wen Wei Lin, Weichung Wang^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Numerical simulations play a significant role in studying the properties of dispersive metallic photonic crystals. The dispersive photonic crystals are modeled by the Maxwell equations, and the equations are then discretized by the widely-used Yee's scheme. After applying certain similarity transformations to the discretized system, the original simulation problem becomes a non-Hermitian eigenvalue problem with clustered eigenvalues. An efficient contour integral (CI) based eigensolver is developed to overcome the difficulties of applying existing methods to solve eigenvalues in designated regions. This efficient method combines the contour integral, the fast matrix–vector multiplication, and efficient linear system solver. The numerical results illustrate the efficiency of our algorithm.

Original language	English
Article number	113581
Journal	Journal of Computational and Applied Mathematics
Volume	395
DOIs	https://doi.org/10.1016/j.cam.2021.113581
Publication status	Published - 2021 Oct 15

Keywords

Contour integral based eigensolver
Discrete single-curl operator
Dispersive photonic crystal
Fast matrix–vector multiplication
The Maxwell equations

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2021.113581

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title = "An efficient contour integral based eigensolver for 3D dispersive photonic crystal",

abstract = "Numerical simulations play a significant role in studying the properties of dispersive metallic photonic crystals. The dispersive photonic crystals are modeled by the Maxwell equations, and the equations are then discretized by the widely-used Yee's scheme. After applying certain similarity transformations to the discretized system, the original simulation problem becomes a non-Hermitian eigenvalue problem with clustered eigenvalues. An efficient contour integral (CI) based eigensolver is developed to overcome the difficulties of applying existing methods to solve eigenvalues in designated regions. This efficient method combines the contour integral, the fast matrix–vector multiplication, and efficient linear system solver. The numerical results illustrate the efficiency of our algorithm.",

keywords = "Contour integral based eigensolver, Discrete single-curl operator, Dispersive photonic crystal, Fast matrix–vector multiplication, The Maxwell equations",

author = "Huang, {Tsung Ming} and Weichien Liao and Lin, {Wen Wei} and Weichung Wang",

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year = "2021",

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doi = "10.1016/j.cam.2021.113581",

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T1 - An efficient contour integral based eigensolver for 3D dispersive photonic crystal

AU - Huang, Tsung Ming

AU - Liao, Weichien

AU - Lin, Wen Wei

AU - Wang, Weichung

PY - 2021/10/15

Y1 - 2021/10/15

N2 - Numerical simulations play a significant role in studying the properties of dispersive metallic photonic crystals. The dispersive photonic crystals are modeled by the Maxwell equations, and the equations are then discretized by the widely-used Yee's scheme. After applying certain similarity transformations to the discretized system, the original simulation problem becomes a non-Hermitian eigenvalue problem with clustered eigenvalues. An efficient contour integral (CI) based eigensolver is developed to overcome the difficulties of applying existing methods to solve eigenvalues in designated regions. This efficient method combines the contour integral, the fast matrix–vector multiplication, and efficient linear system solver. The numerical results illustrate the efficiency of our algorithm.

AB - Numerical simulations play a significant role in studying the properties of dispersive metallic photonic crystals. The dispersive photonic crystals are modeled by the Maxwell equations, and the equations are then discretized by the widely-used Yee's scheme. After applying certain similarity transformations to the discretized system, the original simulation problem becomes a non-Hermitian eigenvalue problem with clustered eigenvalues. An efficient contour integral (CI) based eigensolver is developed to overcome the difficulties of applying existing methods to solve eigenvalues in designated regions. This efficient method combines the contour integral, the fast matrix–vector multiplication, and efficient linear system solver. The numerical results illustrate the efficiency of our algorithm.

KW - Contour integral based eigensolver

KW - Discrete single-curl operator

KW - Dispersive photonic crystal

KW - Fast matrix–vector multiplication

KW - The Maxwell equations

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An efficient contour integral based eigensolver for 3D dispersive photonic crystal

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