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Rotated Subgrids in the FDTD Method

Although the finite-difference time-domain (FDTD) method is well established for addressing a wide variety of 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 subgrids, but in most of the published works, Cartesian subgrids are proposed, which are constrained to have the same orientation as the main grid. However, there is considerable benefit to allowing for the subgrid to be rotated. In this paper, a method for introducing a rotated subgrid into the FDTD mesh is presented, and its effectiveness, accuracy, and stability are demonstrated by means of some simple examples.