A study of dispersion and anisotropy effects for FDTD in non-orthogonal coordinate

The FDTD method in non-orthogonal coordinate has been applied to electromagnetic problems including scattering, discontinuities in transmission structures and three-dimensional cavities. However, the dispersion and anisotropy effect of the FDTD method arise in non-orthogonal coordinate as well as in Cartesian coordinate so that the propagating velocity of time-varying electromagnetic wave depends on the frequency, propagating direction in discrete cells and the size of numerical meshes. It is important in the FDTD method to study the numerical dispersion characteristics on certain discrete meshes in order to reduce the numerical error. The numerical dispersion equation for the FDTD method in a non-orthogonal coordinate is presented. The dispersion, anisotropy effects and the numerical computational criterion are investigated. It is concluded that the size of oblique discrete cell should be equal to or less than 0.05 wavelength to ensure the numerical accuracy in any deformation mesh.