A tilted subgrid for two dimensional FDTD

Although the Finite Difference Time Domain (FDTD) method is well established for addressing a wide variety problems including the characterization of antenna arrays, a long standing challenge is to reduce discretization errors while avoiding the use of impractically large numbers of cells, particularly when the structure is large and contains regions of fine detail. One solution is to use subgrids. In most published work, Cartesian subgrids are proposed which are in the same orientation as the main grid. However there is considerable benefit to allowing for the subgrid to be tilted. In this work, a method for introducing a tilted subgrid into the 2D FDTD mesh is presented and its effectiveness, accuracy and stability is demonstrated using examples. The method is readily extendable to a full 3D implementation.