Stability of the FDTD Method With Holland and Simpson Thin Wires

The Holland and Simpson thin wire formalism, published in 1981, permits arbitrarily thin wires to be accounted for in the FDTD method. Implementations of oblique wires published later enlarged the interest of the formalism. This article addresses the question of the numerical stability. First, a sufficient stability condition ensuring stability of calculations is derived for the original explicit implementation of the formalism and its extensions to oblique wires. Second, a new implicit implementation is proposed for the special case where the wires are parallel to the axes of coordinates. It permits the CFL stability condition of the FDTD method to be left unchanged whatever may be the wires present in the FDTD domain.