A high accuracy FDTD algorithm to solve microwave propagation and scattering problems on a coarse grid

If the spatial variation of electric permittivity and magnetic permeability is “small” Maxwell´s equations can be approximated by the scalar wave equation in each field component. We introduce a new high-accuracy second order finite-difference time-domain (FDTD) algorithm to solve the scalar wave equation on a coarse grid with a solution error less than 10^-4 that of the conventional one. The computational load at each grid point is greater, but it is more than offset by a large reduction in the number of grid points needed, as well as by a reduction in the number of iterations. Also boundaries can be more accurately characterized at the subgrid level. Although optimum performance is achieved at a fixed frequency, the accuracy is still much higher than that of a conventional FDTD algorithm over “moderate” bandwidths