A new ADI-FDTD analysis in electromagnetic scattering

This paper proposes a new set of alternative direction implicit finite-difference time-domain (ADI-FDTD) equations. In conventional ADI-FDTD, the update equation is related to several field components in cells nearby, which will lead to some difficulties in two regions: 1) around the boundary region between the perfectly matched layer (PML) and the scattering field; 2) around the adjacent boundary. Especially, in the region around the adjacent boundary, owing to the incident wave, we should make a judgment about the situation of every component and modify the update equation. It is potential to make a solution to one-dimensional or two-dimensional problem. However, in three-dimensional (3D) analysis, one equation concerns with eleven components and there exist several tens of cases to be modified. This makes the scheme very tedious and impossible to realize. This paper adopts the split field difference formation in the whole computation regime to analyse the scattering problem. Because the equations in the scattering field region have the same expressions as those in PML absorber except for some coefficients, the boundary in the region mentioned above can be ignored. Due to simplicity of the split field equation, the new ADI-FDTD formula in 3D problem has only five components to be considered and four modifications at the adjacent boundary to be made. Finally I we utilize this new method to compute some electromagnetic scattering numerical examples, and the results are in excellent agreement with those obtained with other algorithm and the measured data. Moreover, the new method have 6-7 times higher efficiency in terms of the CPU time.