Slanted Walls in the FDTD Method

In the finite-difference time-domain (FDTD) method, the spatial step is usually chosen to be between 5% and 12.5% of the minimal wavelength of interest. If the boundaries cannot be positioned at integer multiples of the chosen spatial step, one usually reduces the spatial step or uses a nonuniform grid. Reported methods for treating such offset metal boundaries require substantial changes in the FDTD code, as well as changes in the grid and the time step. Recently, we proposed an alternative method (Rickard, Y.S. and Nikolova, N.K., 2004), whereby an off-grid perfect electric conductor (PEC) and magnetic boundaries may be modeled without disturbing the original grid. The method employs extrapolation of adjacent field values from the internal computational domain to obtain exterior field values ensuring off-grid virtual boundaries in-between. As only the outer boundary values are modified, the conventional FDTD code and the grid remain unchanged. Time step reduction is unnecessary, thus the high computation speed is preserved. To validate the method, we compare the calculated frequencies of the first few resonant modes of a rectangular resonator to their analytical values when the resonator has off-grid wall(s) in parallel with and slanted to the existing grid. We investigate the accuracy the stability with off-grid BCs and give recommendations for their use.