A nearly exact second-order finite-difference time-domain wave propagation algorithm on a coarse grid

Abstract

We introduce a new second-order finite-difference time-domain (FDTD) algorithm to solve the wave equation on a coarse grid with a solution error less than 10−4 that of the conventional one. Although the computational load per time step is greater, it is more than offset by a large reduction in the number of grid points needed, while maintaining high accuracy, as well as by a reduction in the number of iterations. In addition, boundaries can be more accurately characterized at the subgrid level. This algorithm is based on a second-order finite-difference Laplacian that is nearly isotropic with respect to the wave propagation direction. 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.