FDTD local grid with material traverse

Many problems in the FDTD require a relatively higher mesh resolution in only small sub-volumes of the total mesh space. By locally applying finer grids (local grids) to these volumes, the necessary resolution for these volumes can be obtained. The computational time and memory requirements may be far less than for an FDTD space with the smaller mesh resolution throughout. In many situations it is important that these local grids function when materials traverse the main grid-local grid boundary surface, since the volumes that require local grids may not be isolated in a homogeneous medium. A local grid method which allows materials to traverse its boundaries is developed. For an example result it is applied to calculate the input impedance of a monopole on a conducting box where the conductor crosses the local grid boundary. The results are compared with uniform mesh FDTD solutions.