An Extended FDTD Scheme for the Wave Equation: Application to Multiscale Electromagnetic Simulation

An algorithm for the application of the mesh refinement technique to finite-difference calculation of the wave equation is presented via the introduction of a new “extended” FDTD scheme. This scheme can be viewed as an extension of the Yee scheme using a new set of variables relating to the direction of propagation of the waves along an axis. Because of this additional information, this scheme allows a more natural implementation of the mesh refinement technique. The extended scheme is presented for both a one-dimensional and a multidimensional system. The mesh refinement algorithm is given in one dimension, and the performances are compared to other proposed schemes.