On the use of conformal grids for propagation and scattering problems in finite-difference time-domain computations

The authors examine the use of grids that are conformal with the geometry of the material boundaries and, consequently, reduce the discretization errors introduced by the stair-stepped approximation. However, it is found that the introduction of the nonuniformity in the grid gives rise to at least two difficulties in the implementation of the finite-difference time-domain algorithm. The first is the loss of accuracy in the computation of finite-difference derivatives when the field points are distributed nonuniformly. The second is implementation of the appropriate boundary conditions at the material interfaces. The authors address these problems and suggest some means for eradicating them. A scheme is presented that has the attractive feature that it reduces to the conventional finite-difference time-domain method if a uniform grid is used. To illustrate the proposed algorithm the authors consider a parallel plate waveguide which supports a single propagating mode.