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Energy Identities of ADI-FDTD Method with Periodic Structure
Department of Applied Mathematics, Dalian University of Technology, Dalian, China
Department of Engineering Mechanics, Dalian University of Technology, Dalian, China
College of Science, China University of Petroleum, Qingdao, China
- 1 Department of Applied Mathematics, Dalian University of Technology, Dalian, China
- 2 Department of Engineering Mechanics, Dalian University of Technology, Dalian, China
- 3 College of Science, China University of Petroleum, Qingdao, China
Applied Mathematics·Volume 06 (2015)·Pages 265–273·Published 3 February 2015·DOI10.4236/am.2015.62025
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Abstract
In this paper, a new kind of energy identities for the Maxwell equations with periodic boundary conditions is proposed and then proved rigorously by the energy methods. By these identities, several modified energy identities of the ADI-FDTD scheme for the two dimensional (2D) Maxwell equations with the periodic boundary conditions are derived. Also by these identities it is proved that 2D-ADI-FDTD is approximately energy conserved and unconditionally stable in the discrete L 2 and H 1 norms. Experiments are provided and the numerical results confirm the theoretical analysis on stability and energy conservation.
KeywordsStabilityEnergy ConservationADI-FDTDMaxwell Equations
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