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Volume 10, Issue 4
A New Energy-Conserved S-FDTD Scheme for Maxwell's Equations in Metamaterials

W. Li, D. Liang & Y. Lin

Int. J. Numer. Anal. Mod., 10 (2013), pp. 775-794.

Published online: 2013-10

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  • Abstract

In this paper, we develop a new energy-conserved S-FDTD scheme for the Maxwell's equations in metamaterials. We first derive out the new property of energy conservation of the governing equations in metamaterials, and then propose the energy-conserved S-FDTD scheme for solving the problems based on the staggered grids. We prove that the proposed scheme is energy-conserved in the discrete form and unconditionally stable. Based on the energy method, we further prove that the scheme for the Maxwell's equations in metamaterials is first order in time and second order in space. Numerical experiments are carried out to confirm the energy conservation and the convergence rates of the scheme. Moreover, numerical examples are also taken to show the propagation features of electromagnetic waves in the DNG metamaterials.

  • Keywords

Maxwell's equations, metamaterials, energy-conserved, splitting, FDTD, convergence.

  • AMS Subject Headings

65M10, 65M15, 65N10, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-10-775, author = {W. Li, D. Liang and Y. Lin}, title = {A New Energy-Conserved S-FDTD Scheme for Maxwell's Equations in Metamaterials}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {4}, pages = {775--794}, abstract = {

In this paper, we develop a new energy-conserved S-FDTD scheme for the Maxwell's equations in metamaterials. We first derive out the new property of energy conservation of the governing equations in metamaterials, and then propose the energy-conserved S-FDTD scheme for solving the problems based on the staggered grids. We prove that the proposed scheme is energy-conserved in the discrete form and unconditionally stable. Based on the energy method, we further prove that the scheme for the Maxwell's equations in metamaterials is first order in time and second order in space. Numerical experiments are carried out to confirm the energy conservation and the convergence rates of the scheme. Moreover, numerical examples are also taken to show the propagation features of electromagnetic waves in the DNG metamaterials.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/595.html} }
TY - JOUR T1 - A New Energy-Conserved S-FDTD Scheme for Maxwell's Equations in Metamaterials AU - W. Li, D. Liang & Y. Lin JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 775 EP - 794 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/595.html KW - Maxwell's equations, metamaterials, energy-conserved, splitting, FDTD, convergence. AB -

In this paper, we develop a new energy-conserved S-FDTD scheme for the Maxwell's equations in metamaterials. We first derive out the new property of energy conservation of the governing equations in metamaterials, and then propose the energy-conserved S-FDTD scheme for solving the problems based on the staggered grids. We prove that the proposed scheme is energy-conserved in the discrete form and unconditionally stable. Based on the energy method, we further prove that the scheme for the Maxwell's equations in metamaterials is first order in time and second order in space. Numerical experiments are carried out to confirm the energy conservation and the convergence rates of the scheme. Moreover, numerical examples are also taken to show the propagation features of electromagnetic waves in the DNG metamaterials.

W. Li, D. Liang and Y. Lin. (2013). A New Energy-Conserved S-FDTD Scheme for Maxwell's Equations in Metamaterials. International Journal of Numerical Analysis and Modeling. 10 (4). 775-794. doi:
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