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Energy Identities of ADI-FDTD Method with Periodic Structure

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http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53792#.VNMhYSzQrzE

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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 L2 and H1 norms. Experiments are provided and the numerical results confirm the theoretical analysis on stability and energy conservation.
 
Cite this paper
Shi, R. and Yang, H. (2015) Energy Identities of ADI-FDTD Method with Periodic Structure. Applied Mathematics, 6, 265-273. doi: 10.4236/am.2015.62025.
 
References
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[2]Zheng, F., Chen, Z. and Zhang, J. (2000) Toward the Development of a Three-Dimensional Unconditionally Stable Finite-Difference Time-Domain Method. IEEE Transactions on Microwave Theory and Techniques, 48, 1550-1558.
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http://dx.doi.org/10.1016/S0252-9602(12)60184-2                                                        eww150205lx
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