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

Abstract

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/sup -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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>