Integral equation solution for the transient electromagnetic response of a three-dimensional body in a conductive half-space

The time‐domain integral equation for the three‐dimensional vector electric field is formulated as a convolution of the scattering current with the tensor Green’s function. The convolution integral is divided into a sum of integrals over successive time steps, so that a numerical scheme can be formulated with a time stepping approximation of the convolution of past values of the solution with the system impulse response. This, together with spatial discretization, leads to a matrix equation in which previous solution vectors are multiplied by a series of matrices and fed back into the system by adding to the primary field source vector. The spatial discretization, based on a modification of the usual pulse basis formulation in the frequency domain, includes an additional subset of divergence‐free basis functions generated by integrating the Green’s function around concentric closed rectangular paths. The inductive response of the body is more accurately modeled with these additional basis functions, and a...