Volume 11, Issue 1
Nodal Discontinuous Galerkin Method for Time-Domain Lorentz Model Equations in Meta-Materials

Shanghui Jia, Changhui Yao & Shuai Su

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 30-48.

Published online: 2018-11

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  • Abstract

In this paper, Nodal discontinuous Galerkin method is presented to approximate Time-domain Lorentz model equations in meta-materials. The upwind flux is chosen in spatial discrete scheme. Low-storage five-stage fourth-order explicit Runge-Kutta method is employed in time discrete scheme. An error estimate of accuracy $\mathcal{O}(τ^4+h^n)$ is proved under the $L^2$-norm, specially $\mathcal{O}(τ^4+h^{n+1})$ can be obtained. Numerical experiments for transverse electric (TE) case and transverse magnetic (TM) case are demonstrated to verify the stability and the efficiency of the method in low and high wave frequency.

  • Keywords

Time-domain Lorentz model, meta-materials, Runge-Kutta method, nodal discontinuous, Galerkin method.

  • AMS Subject Headings

35L05 76M10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-11-30, author = {}, title = {Nodal Discontinuous Galerkin Method for Time-Domain Lorentz Model Equations in Meta-Materials}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {1}, pages = {30--48}, abstract = {

In this paper, Nodal discontinuous Galerkin method is presented to approximate Time-domain Lorentz model equations in meta-materials. The upwind flux is chosen in spatial discrete scheme. Low-storage five-stage fourth-order explicit Runge-Kutta method is employed in time discrete scheme. An error estimate of accuracy $\mathcal{O}(τ^4+h^n)$ is proved under the $L^2$-norm, specially $\mathcal{O}(τ^4+h^{n+1})$ can be obtained. Numerical experiments for transverse electric (TE) case and transverse magnetic (TM) case are demonstrated to verify the stability and the efficiency of the method in low and high wave frequency.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2018.m1607}, url = {http://global-sci.org/intro/article_detail/nmtma/10642.html} }
TY - JOUR T1 - Nodal Discontinuous Galerkin Method for Time-Domain Lorentz Model Equations in Meta-Materials JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 30 EP - 48 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.2018.m1607 UR - https://global-sci.org/intro/article_detail/nmtma/10642.html KW - Time-domain Lorentz model, meta-materials, Runge-Kutta method, nodal discontinuous, Galerkin method. AB -

In this paper, Nodal discontinuous Galerkin method is presented to approximate Time-domain Lorentz model equations in meta-materials. The upwind flux is chosen in spatial discrete scheme. Low-storage five-stage fourth-order explicit Runge-Kutta method is employed in time discrete scheme. An error estimate of accuracy $\mathcal{O}(τ^4+h^n)$ is proved under the $L^2$-norm, specially $\mathcal{O}(τ^4+h^{n+1})$ can be obtained. Numerical experiments for transverse electric (TE) case and transverse magnetic (TM) case are demonstrated to verify the stability and the efficiency of the method in low and high wave frequency.

Shanghui Jia, Changhui Yao & Shuai Su. (2020). Nodal Discontinuous Galerkin Method for Time-Domain Lorentz Model Equations in Meta-Materials. Numerical Mathematics: Theory, Methods and Applications. 11 (1). 30-48. doi:10.4208/nmtma.2018.m1607
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