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Developing finite element methods for Simulating Transformation Optics Devices with Metamaterials

Communications in Computational Physics 2019年第1期25卷 135-154页

作者： Wei Yang Jichun Li Yungqing Huang Bin He Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105P.R.China Department of Mathematical Sciences University of Nevada Las VegasLas VegasNevada 89154-4020USA

In this paper,we first develop the mathematical modeling equations for wave propagation in several transformation optics devices,including electromagnetic concentrator,rotator and *** we propose the corresponding finite element time-domain methods for simulating wave propagation in these transformation optics *** implement the proposed algorithms and our numerical results demonstrate the effectiveness of our modeling *** our best knowledge,this is the first work on time-domain finite element simulation carried out for the electromagnetic concentrator,rotator and splitter.

关键词： Maxwell’s equations finite element time-domain methods edge elements transfor-mation optics

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time-domain finite element method and analysis for modeling of surface plasmon polaritons

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COMPUTER methods IN APPLIED MECHANICS AND ENGINEERING 2020年 372卷 113349-113349页

作者： Yang, Wei Li, Jichun Huang, Yunqing Xiangtan Univ Hunan Key Lab Computat & Simulat Sci & Engn Xiangtan Peoples R China Univ Nevada Dept Math Sci Las Vegas NV 89154 USA

In this paper, we formulate a time-dependent model for simulating surface plasmon polaritons (SPPs) in graphene. The stability for the governing equations of the model is established. Then we propose a time-domain finite element method for solving the system of the governing equations. The discrete stability similar to the continuous level is proved. Numerical results are presented to demonstrate the effectiveness of our model for simulating SPPs along graphene slabs. To the best of our knowledge, this is the first time-domain finite element analysis and simulation obtained for SPPs in graphene. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Maxwell's equations finite element time-domain methods Edge elements Surface plasmon polaritons Graphene

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A new time-domain finite element method for simulating surface plasmon polaritons on graphene sheets

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2023年第1期142卷 268-282页

作者： Li, Jichun Zhu, Li Arbogast, Todd Univ Nevada Dept Math Sci Las Vegas NV 89154 USA Univ Texas Austin Dept Math Austin TX 78712 USA

In this paper, we develop a new variational form to simulate the propagation of surface plasmon polaritons on graphene sheets. Here the graphene is treated as a thin sheet of current with an effective conductivity, and modeled as a lower-dimensional interface. A novel time-domain finite element method is proposed for solving this graphene model, which coupled an ordinary differential equation on the interface with Maxwell's equations in the physical domain. Discrete stability and error estimate are proved for our proposed method. Numerical results are presented to demonstrate the effectiveness of this graphene model for simulating the surface plasmon polaritons propagating on graphene sheets.

关键词： Maxwell's equations finite element time-domain methods Edge elements Graphene

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Development and analysis of two new finite element schemes for a time-domain carpet cloak model

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ADVANCES IN COMPUTATIONAL MATHEMATICS 2022年第3期48卷 1-30页

作者： Li, Jichun Shu, Chi-Wang Yang, Wei Univ Nevada Dept Math Sci Las Vegas NV 89154 USA Brown Univ Div Appl Math Providence RI 02912 USA Xiangtan Univ Hunan Key Lab Computat & Simulat Sci Engn Xiangtan Peoples R China

In this paper, we are concerned about a time-domain carpet cloak model, which was originally derived in our previous work Li et al. (SIAM J. Appl. Math., 74(4), pp. 1136-1151, 2014). Some finite element schemes have been developed for this model and used to simulate the cloaking phenomenon in Li et al. (SIAM J. Appl. Math., 74(4), pp. 1136-1151, 2014) and Li et al. (methods Appl. Math., 19(2), pp. 359-378, 2019). However, numerical stabilities for those proposed explicit schemes are only proved under the time step constrain tau = O(h(2)), which is impractical and too restricted. To overcome this disadvantage, we propose two new finite element schemes for solving this carpet cloak model: one is the implicit Crank-Nicolson (CN) scheme, and another one is the explicit leap-frog (LF) scheme. Inspired by a totally new energy developed for the continuous model, we prove the unconditional stability for the CN scheme and conditional stability for the LF scheme under the usual CFL constraint tau = O(h). Both numerical stabilities inherit the exact form as the continuous stability. Optimal error estimate is also established for the LF scheme. Finally, numerical results using the LF scheme are presented to support our analysis and demonstrate the cloaking phenomenon.

关键词： Maxwell's equations finite element time-domain methods Edge elements Cloaking Metamaterial

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Developing and analyzing a finite element method for simulating wave propagation in graphene-based absorber

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2022年 122卷 76-92页

作者： Huang, Yunqing Li, Jichun Yang, Wei Xiangtan Univ Hunan Key Lab Computat & Simulat Sci & Engn Xiangtan Peoples R China Univ Nevada Dept Math Sci Las Vegas NV 89154 USA

In this paper, we are concerned about a graphene-based absorber model, which incorporates both the interband conductivity and intraband conductivity of the graphene. We first establish an energy identity and stability for the continuous model. Then we propose a finite element time-domain method for solving the model by edge elements. Numerical stability and optimal error estimate are proved for the scheme. Numerical results are presented to justify the error estimate and demonstrate the wave absorbing phenomenon by graphene slab.

关键词： Maxwell?s equations finite element time-domain methods Edge elements Graphene

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Two new finite element schemes and their analysis for modeling of wave propagation in graphene

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RESULTS IN APPLIED MATHEMATICS 2021年 9卷

作者： Li, Jichun Univ Nevada Dept Math Sci Las Vegas NV 89154 USA

In this paper, we investigate a system of governing equations for modeling wave propagation in graphene. Compared to our previous work (Yang et al., 2020), here we re-investigate the governing equations by eliminating two auxiliary unknowns from the original model. A totally new stability for the model is established for the first time. Since the finite element scheme proposed in Yang et al. (2020) is only first order in time, here we propose two new schemes with second order convergence in time for the simplified modeling equations. Discrete stabilities inheriting exactly the same form as the continuous stability are proved for both schemes. Convergence error estimates are also established for both schemes. Numerical results are presented to justify our theoretical analysis. (C) 2020 The Author(s). Published by Elsevier B.V.

关键词： Maxwell's equations finite element time-domain methods Edge elements Surface plasmon polaritons Graphene

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