3D sub-gridding algorithm for FDTD

Describes an algorithm that provides mesh refinements in space and time, and its implementation in 2D as well as 3D. The authors have place greatest emphasis on providing a smooth transition between the coarse and fine meshes. To achieve this, extrapolation in time and interpolation in time and space are used, both accurate to the second order. The boundary of the two grids is usually positioned in a homogeneous region of the structure where the field components and its derivatives have smooth behavior. The second order interpolation and extrapolation provides sufficient accuracy as documented by the test results.