A novel transformation optics-based FDTD algorithm for fast electromagnetic analysis of small structures in a large scope

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.