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

  • Authors:

  • A. Vaccari;R. Pontalti;C. Malacarne;L. Cristoforetti

  • Affiliations:

  • Centro per la Ricerca Scientifica e Tecnologica, Istituto Trentino di Cultura, Division FCS, Trento I-38050, Italy;Centro per la Ricerca Scientifica e Tecnologica, Istituto Trentino di Cultura, Division FCS, Trento I-38050, Italy;Centro per la Ricerca Scientifica e Tecnologica, Istituto Trentino di Cultura, Division FCS, Trento I-38050, Italy;Centro per la Ricerca Scientifica e Tecnologica, Istituto Trentino di Cultura, Division FCS, Trento I-38050, Italy

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2004

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Abstract

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 subregions 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 nonrecursive 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.