In this paper, we present a novel Transformation Optics based Finite-difference time-domain (TO-FDTD) algorithm with Square Transformed Region, which is suitable for fast electromagnetic analysis of small structures in a large computational domain. A small structure can be solved with coarse grids in a transformed region, since it is enlarged by transformation optics. No fine grid is applied for the small structure so that computational efficiency can be improved greatly. In addition, the TO-FDTD algorithm can also avoid time-space field interpolations and the late-time instability of the subgridding algorithm. To eliminate the staircasing errors introduced by curved boundaries of its transformed region, we propose the square transformed region instead of the circular one. We parameterize the square boundary in polar coordinates so that it is easy to be implemented. Through coordinate transformation, new anisotropic permittivity and permeability can be obtained in the transformed region. Then we develop a stable anisotropic FDTD algorithm to solve the transformed Maxwell's Equations. Numerical results on diffraction and scattering of small structures show that our proposed TO-FDTD algorithm has high computational efficiency and accuracy.INDEX TERMS Finite-difference time-domain (FDTD), staircasing errors, transformation optics.
A novel numerical approach is developed to analyze electromagnetic scattering properties of a moving conducting object based on the finite-difference time-domain (FDTD) algorithm. Relativistic boundary conditions are implemented into the FDTD algorithm to calculate the electromagnetic field on the moving boundary. An improved technique is proposed to solve the scattered field in order to improve the computational efficiency and stability of solutions. The time-harmonic scattered field from a one-dimensional moving conducting surface is first simulated by the proposed approach. Numerical results show that the amplitude and frequency of the scattered field suffer a modulation shift. Then the transient scattered field is calculated, and broadband electromagnetic scattering properties of the moving conducting surface are obtained by the fast Fourier transform (FFT). Finally, the scattered field from a two-dimensional moving square cylinder is analyzed. The numerical results demonstrate the Doppler effect of a moving conducting object. The simulated results agree well with analytical results.
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