On the nature of solutions produced by finite difference schemes in time domain

This paper is a review discussing properties of field solutions produced by various finite difference schemes in the time domain. Considered algorithms include standard FDTD as well as its modifications based on different sets of electromagnetic equations and/or different discretization in space. By developing their complete dispersion relations, conclusions are drawn regarding divergence, curl, and energy conserva tion by each of the emulated eigenmodes separately. This is in extension to previous works which were concerned with the total solution, and permits to formulate conditions for restricting the total solutions to physical uncoupled solenoidal and potential modes. Original classification of spurious modes for the time domain finite difference modelling is also proposed. It is shown that spurious compensating modes can propagate over the mesh in the case of penalty schemes with p≠0, and that spurious degenerate modes at high- and low-frequencies appear in the case of condensed node discretization.