A fictitious domain method for conformal modeling of the perfect electric conductors in the FDTD method

We present a fictitious domain method to avoid the staircase approximation in the study of perfect electric conductors (PEC) in the finite-difference time-domain (FDTD) method. The idea is to extend the electromagnetic field inside the PEC and to introduce a new unknown, the surface electric current density to ensure the vanishing of the tangential components of the electric field on the boundary of the PEC. This requires the use of two independent meshes: a regular three-dimensional (3-D) cubic lattice for the electromagnetic field and a triangular surface-patching for the surface electric current density. The intersection of these two meshes gives a simple coupling law between the electric field and the surface electric current density. An interesting property of this method is that it provides the surface electric current density at each time step. Furthermore, this method looks like FDTD with a special model for the PEC. Numerical results for several objects are presented.