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Namiki, T. and Ito, K. (2000) Investigation of Numerical Errors of the Two-Dimensional ADI-FDTD Method [for Maxwell’s Equations Solution]. IEEE Transactions on Microwave Theory and Techniques, 48, 1950-1956.
http://dx.doi.org/10.1109/22.883876

has been cited by the following article:

• TITLE: Energy Identities of ADI-FDTD Method with Periodic Structure

  AUTHORS: Rengang Shi, Haitian Yang

  KEYWORDS: Stability, Energy Conservation, ADI-FDTD, Maxwell Equations

  JOURNAL NAME: Applied Mathematics, Vol.6 No.2, February 4, 2015

  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.