Differencing schemes for detached interfaces in a regular FDTD grid

The FDTA algorithm models EM fields in continuous media. The Taylor series method of analyzing the accuracy of a scheme is adapted for use across material interfaces. Conventional differencing across the interface was found to be first-order accurate, and a method was developed which retained second-order accuracy across the interface. Results showed that the first-order differencing was the limiting factor in a standard FDTD (finite-difference-time-domain) analysis with a coarse grid, while the second-order method was not. The minimal computational overhead of the boundary-difference methods compared to the cost of refining the mesh justifies implementation.<>