A robust and efficient subgridding algorithm for finite-difference time-domain simulations of Maxwell’s equations

Mesh refinement is desirable for an advantageous use of the finite-difference time-domain (FDTD) solution method of Maxwell’s equations, because higher spatial resolutions, i.e., increased mesh densities, are introduced only in sub-regions where they are really needed, thus preventing computer resources wasting. However, the introduction of high density meshes in the FDTD method is recognized as a source of troubles as far as stability and accuracy are concerned, a problem which is currently dealt with by recursion, i.e., by nesting meshes with a progressively increasing resolution. Nevertheless, such an approach unavoidably raises again the computational burden. In this paper we propose a non-recursive three-dimensional (3-D) algorithm that works with straight embedding of fine meshes into coarse ones which have larger space steps, in each direction, by a factor of 5 or more, while maintaining a satisfactory stability and accuracy. The algorithm is tested against known analytical solutions.