Modeling Lumped Sources in the Finite-Difference Time-Domain Method of the Scattered-Field Formulation

This paper presents the development and the validation of a scheme for modeling a lumped element in the finite-difference time-domain (FDTD) method that uses the scattered-field formulation. The proposed scheme is an adaptation of the scheme for modeling a lumped element in the FDTD method that uses the total-field formulation. The proposed scheme is presented in two different versions, one that uses a semi-implicit scheme and another one that uses a fully explicit scheme. The numerical experiments show the semi-implicit scheme to be slightly more accurate than the fully-explicit scheme, based on comparing the values of the plane-wave scattering coefficients obtained numerically with those obtained analytically. The proposed scheme is both accurate and stable in treating both dielectric and perfect electrical conductor, in the presence of a lumped source and/or an incident field.