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New Energy-Conserved Identitiesand Super-Convergence of the Symmetric Ec-S-Fdtd Scheme for Maxwell’s Equations in 2D

Published online by Cambridge University Press:  20 August 2015

Liping Gao  and
Dong Liang
Liping Gao*
Affiliation:
Department of Computational and Applied Mathematics, School of Sciences, China University of Petroleum, Qingdao, 266555, P.R. China
Dong Liang*
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J1P3, Canada
*
Corresponding author.Email:l.gao@upc.edu.en
Email:dliang@mathstat.yorku.ca
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Abstract

The symmetric energy-conserved splitting FDTD scheme developed in 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 uncondi-tionally 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.

Keywords

65N0665N1265N15Symmetric EC-S-FDTDenergy-conservedunconditional stabilitysuper convergenceMaxwell’s equationssplitting
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 5 , May 2012 , pp. 1673 - 1696
Copyright
Copyright © Global Science Press Limited 2012

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