A novel HE-coupling for explicit multigrid-FDTD

In this paper we put forward a novel coupling method that directly ties both the field variables, electric (E) and magnetic (H), in the multigrid-FDTD algorithm. Conventional leapfrog multigrid-FDTD or subgridding only directly couples one field variable between the grids, either the E or the H field, and the one that is not coupled is indirectly linked with the first by the FDTD equations. The FDTD method staggers the E and H fields. This means a strong numerical coupling for the directly connected field but only a weak coupling for the second field for multigrid-FDTD. There is nothing to prevent the weakly connected field from disengaging from each other in different grids, and if it does, it leads to instability. This can happen because there is nothing explicit that ties them together. Finally, a new and coherent approximation has been derived using the divergence and Green´s theorems for the spatial derivative terms in the FDTD equations to enhance stronger coupling in multigrid-FDTD.