  In this paper we introduce a novel 3D Lattice-Boltzmann model that recovers
in the continuous limit the Maxwell equations in materials. In order to build
conservation equations with antisymmetric tensors, like the Faraday law, the
model assigns four auxiliary vectors to each velocity vector. These auxiliary
vectors, when combined with the distribution functions, give the
electromagnetic fields. The evolution is driven by the usual BGK collision
rule, but with a different form for the equilibrium distribution functions.
This LBGK model allows us to consider for both dielectrics and conductors with
realistic parameters, and therefore it is adequate to simulate the most diverse
electromagnetic problems, like the propagation of electromagnetic waves (both
in dielectric media and in waveguides), the skin effect, the radiation pattern
of a small dipole antenna and the natural frequencies of a resonant cavity, all
with 2% accuracy. Actually, it shows to be one order of magnitude faster than
the original FDTD formulation by Yee to reach the same accuracy. It is,
therefore, a valuable alternative to simulate electromagnetic fields and opens
lattice Boltzmann for a broad spectrum of new applications in electrodynamics.
In this paper we develop a 3D Lattice-Boltzmann model that recovers in the
continuous limit the Maxwell equations for macroscopic mediums. The model can
sucessfully reproduces the propagation of the electromagnetic waves in
dielectric mediums and waveguide, the skin effect, the electrical dipole
radiation and the electromagnetic response of a resonant cavity.
