Volume 11, Issue 5
New Energy-Conserved Identities and Super-Convergence of the Symmetric EC-S-FDTD Scheme for Maxwell's Equations in 2D

Liping Gao & Dong Liang

Commun. Comput. Phys., 11 (2012), pp. 1673-1696.

Published online: 2012-11

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  • Abstract

The symmetric energy-conserved splitting FDTD scheme developed in [1] is a very new and efficient scheme for computing the Maxwell's equations. It is based on splitting the whole Maxwell's equations and matching the x-direction and y-direction electric fields associated to the magnetic field symmetrically. In this paper, we make further study on the scheme for the 2D Maxwell's equations with the PEC boundary condition. Two new energy-conserved identities of the symmetric EC-S-FDTD scheme in the discrete H1-norm are derived. It is then proved that the scheme is unconditionally stable in the discrete H1-norm. By the new energy-conserved identities, the super-convergence of the symmetric EC-S-FDTD scheme is further proved that it is of second order convergence in both time and space steps in the discrete H1-norm. Numerical experiments are carried out and confirm our theoretical results.

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@Article{CiCP-11-1673, author = {}, title = {New Energy-Conserved Identities and Super-Convergence of the Symmetric EC-S-FDTD Scheme for Maxwell's Equations in 2D}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {5}, pages = {1673--1696}, abstract = {

The symmetric energy-conserved splitting FDTD scheme developed in [1] is a very new and efficient scheme for computing the Maxwell's equations. It is based on splitting the whole Maxwell's equations and matching the x-direction and y-direction electric fields associated to the magnetic field symmetrically. In this paper, we make further study on the scheme for the 2D Maxwell's equations with the PEC boundary condition. Two new energy-conserved identities of the symmetric EC-S-FDTD scheme in the discrete H1-norm are derived. It is then proved that the scheme is unconditionally stable in the discrete H1-norm. By the new energy-conserved identities, the super-convergence of the symmetric EC-S-FDTD scheme is further proved that it is of second order convergence in both time and space steps in the discrete H1-norm. Numerical experiments are carried out and confirm our theoretical results.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.121110.030611a}, url = {http://global-sci.org/intro/article_detail/cicp/7429.html} }
TY - JOUR T1 - New Energy-Conserved Identities and Super-Convergence of the Symmetric EC-S-FDTD Scheme for Maxwell's Equations in 2D JO - Communications in Computational Physics VL - 5 SP - 1673 EP - 1696 PY - 2012 DA - 2012/11 SN - 11 DO - http://dor.org/10.4208/cicp.121110.030611a UR - https://global-sci.org/intro/article_detail/cicp/7429.html KW - AB -

The symmetric energy-conserved splitting FDTD scheme developed in [1] is a very new and efficient scheme for computing the Maxwell's equations. It is based on splitting the whole Maxwell's equations and matching the x-direction and y-direction electric fields associated to the magnetic field symmetrically. In this paper, we make further study on the scheme for the 2D Maxwell's equations with the PEC boundary condition. Two new energy-conserved identities of the symmetric EC-S-FDTD scheme in the discrete H1-norm are derived. It is then proved that the scheme is unconditionally stable in the discrete H1-norm. By the new energy-conserved identities, the super-convergence of the symmetric EC-S-FDTD scheme is further proved that it is of second order convergence in both time and space steps in the discrete H1-norm. Numerical experiments are carried out and confirm our theoretical results.

Liping Gao & Dong Liang. (2020). New Energy-Conserved Identities and Super-Convergence of the Symmetric EC-S-FDTD Scheme for Maxwell's Equations in 2D. Communications in Computational Physics. 11 (5). 1673-1696. doi:10.4208/cicp.121110.030611a
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