Symmetric Energy-Conserved S-FDTD Scheme for Two-Dimensional Maxwell’s Equations in Negative Index Metamaterials

Li, Wan-Shan; Dong, Liang

doi:10.1007/s10915-016-0214-9

Cited by 11 publications

(6 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In , we proved the identity of electromagnetic energy for Maxwell's equations in metamaterials, which is listed in Theorem 2.1. Let

‖ \cdot ‖

represent the

L_{2} (Ω)

‐norm and

‖ \cdot ‖_{normalX}

the

normalX

‐weighted

L_{2} (Ω)

‐norm, that is,

‖ V ‖_{normalX}^{2} = \int_{Ω} V^{τ} X V

dv.…”

Section: The Three‐dimensional Drude Models Of Maxwell's Equations Inmentioning

confidence: 96%

“…In [36], we proved the identity of electromagnetic energy for Maxwell's equations in metamaterials, which is listed in Theorem 2.1. Let · represent the L 2 ( )-norm and · X the X-weighted…”

Section: The Three-dimensional Drude Models Of Maxwell's Equationmentioning

confidence: 99%

“…However, for the metamaterial electromagnetic problems, there is few work on the study of the energy conservation properties and the energy‐preserving schemes. In metamaterials with negative refraction index, we obtained an identity of energy conservation for electromagnetic waves in two dimensional metamaterials and proposed and analyzed a time first‐order energy‐conserved S‐FDTD scheme in two dimensions in .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global energy‐tracking identities and global energy‐tracking splitting FDTD schemes for the Drude Models of Maxwell's equations in three‐dimensional metamaterials

Li¹,

Dong²,

Lin

2017

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

In this article, we study the Drude models of Maxwell's equations in three‐dimensional metamaterials. We derive new global energy‐tracking identities for the three dimensional electromagnetic problems in the Drude metamaterials, which describe the invariance of global electromagnetic energy in variation forms. We propose the time second‐order global energy‐tracking splitting FDTD schemes for the Drude model in three dimensions. The significant feature is that the developed schemes are global energy‐preserving, unconditionally stable, second‐order accurate both in time and space, and computationally efficient. We rigorously prove that the new schemes satisfy these energy‐tracking identities in the discrete form and the discrete variation form and are unconditionally stable. We prove that the schemes in metamaterials are second order both in time and space. The superconvergence of the schemes in the discrete H1 norm is further obtained to be second order both in time and space. Their approximations of divergence‐free are also analyzed to have second‐order accuracy both in time and space. Numerical experiments confirm our theoretical analysis results. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 763–785, 2017

show abstract

“…In , we proved the identity of electromagnetic energy for Maxwell's equations in metamaterials, which is listed in Theorem 2.1. Let

‖ \cdot ‖

represent the

L_{2} (Ω)

‐norm and

‖ \cdot ‖_{normalX}

the

normalX

‐weighted

L_{2} (Ω)

‐norm, that is,

‖ V ‖_{normalX}^{2} = \int_{Ω} V^{τ} X V

dv.…”

Section: The Three‐dimensional Drude Models Of Maxwell's Equations Inmentioning

confidence: 96%

Section: The Three-dimensional Drude Models Of Maxwell's Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Global energy‐tracking identities and global energy‐tracking splitting FDTD schemes for the Drude Models of Maxwell's equations in three‐dimensional metamaterials

Li¹,

Dong²,

Lin

2017

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

show abstract

“…Lanteri and Scheid [12] conducted a complete study of a DGTD method for Maxwell's equations in dispersive media. Li et al [13] proposed an energy-conserved splitting type FDTD scheme for Maxwell's equations in metamaterials. Mu et al [14] extended the weak Galerkin method to solve the time-harmonic Maxwell's equations.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and numerical analysis of a non-local dispersion model for light interaction with metallic nanostructures

Huang¹,

Li²,

Yang³

2016

Computers & Mathematics with Applications

View full text Add to dashboard Cite

Available online xxxx Keywords:Maxwell's equations Non-local dispersion model Nédélec finite elements a b s t r a c tIn this paper, we discuss the time-domain Maxwell's equations coupled to another partial differential equation, which arises from modeling of light and structure interaction at the nanoscale. One major contribution of this paper is that the well-posedness is rigorously justified for the first time. Then we propose a fully-discrete finite element method to solve this model. It is interesting to note that we need use curl conforming, divergence conforming, and L 2 finite elements for this model. Numerical stability and optimal error estimate of the scheme are proved. Numerical results justifying our theoretical convergence rate are presented.

show abstract

“…Of course, there exist many excellent results on the existence, uniqueness and FEMs for solving Maxwell's equations in other media (e.g., [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and references therein). The mathematical analysis and development of our FETD method for solving the ferrite model is original.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis and finite element simulation of a magnetized ferrite model

Huang

Yang

2016

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

MSC: 65N30 35L15 78-08 Keywords: Maxwell's equations Magnetized ferrite model Edge element Perfectly matched layer a b s t r a c tMicrowave scattering by obstacles made of ferrite materials has been studied for a long time because of its important applications in radar, satellite, optical imaging system, signal processing, atmospheric science, and even cloaking device design. In this paper, we present for the first time the rigorous mathematical analysis of a magnetized ferrite model widely used by engineers. The well-posedness of the model is established first. Then we develop a finite element time-domain method for solving this model. Numerical stability similar to the continuous stability is proved for our scheme, and the optimal error estimate in the L 2 norm is obtained. Numerical results are consistent with our theoretical analysis and show how wave propagates in the ferrite material.

show abstract

Symmetric Energy-Conserved S-FDTD Scheme for Two-Dimensional Maxwell’s Equations in Negative Index Metamaterials

Cited by 11 publications

References 31 publications

Global energy‐tracking identities and global energy‐tracking splitting FDTD schemes for the Drude Models of Maxwell's equations in three‐dimensional metamaterials

Global energy‐tracking identities and global energy‐tracking splitting FDTD schemes for the Drude Models of Maxwell's equations in three‐dimensional metamaterials

Theoretical and numerical analysis of a non-local dispersion model for light interaction with metallic nanostructures

Mathematical analysis and finite element simulation of a magnetized ferrite model

Contact Info

Product

Resources

About