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Complementary operators method for ADI-FDTD open-region simulations

The alternating direction implicit finite-difference time-domain (ADI-FDTD) method has been introduced as an unconditionally stable FDTD algorithm. It was shown through numerous works that the ADI-FDTD algorithm is stable both analytically and numerically even when the Courant-Friedrich-Levy (CFL) limit is exceeded. In this paper the complementary operators method (COM), which has been shown to be an effective mesh terminator when solving open-region scattering and radiation problems, has been applied in the ADI-FDTD method. Numerical experiments show the effectiveness of COM in predicting accurate time-domain responses. It is found that the accuracy of COM in the ADI-FDTD method depends on the selected order of applied absorbing boundary conditions (ABC). Furthermore, when high-order ABC are applied in the ADI-FDTD method, the simultaneous linear equations cannot be written in tri-diagonal matrix form, thus, it is not possible to achieve the computational cost efficiency of ADI-FDTD method when applied in conjunction with low-order mesh-truncation techniques.