Origin of Parasitic Solutions With Holland and Simpson Thin Wires in the FDTD Grid

The Holland and Simpson thin wire formalism permits arbitrarily thin wires to be accounted for in the finite-difference time-domain (FDTD) method. However, it is known that a parasitic solution may be added to the physical solution when the wires are not parallel to the axes of coordinates. In this paper, we show that the spurious parasitic solutions originate in the distribution of the currents of the wires in the FDTD grid, which may produce nonphysical deposit of electric charges. A condition not to produce spurious solutions is derived, and an implementation of oblique wires that satisfies the condition is presented. Numerical experiments demonstrate the absence of parasitic solution.