Rotated sub-grids in the FDTD Method

Although the Finite Difference Time Domain (FDTD) method is well established for addressing a wide variety problems, 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 sub-grids but in most published work, Cartesian sub-grids are proposed which are constrained to have the same orientation as the main grid. However there is considerable benefit to allowing for the sub-grid to be rotated. In this work, a method for introducing a rotated sub-grid into the FDTD mesh is presented and its effectiveness, accuracy and stability is demonstrated by means of some simple examples.