Diffusive fields in three-dimensional cases, e.g., voluminous inclusions, voids, and cracks in planar metal slabs and conductive orebodies and other obstacles in a half-space earth subsoil, can be modeled via rigorous vector integral formulations that require Green dyads. The latter contain most of the complexity of the embedding environment whilst many situations can be attacked from precalculated discrete sets of such dyads. However, exact models remain computationally costly, and inversion problems (nondestructive evaluation of made structures and geo-electromagnetic probing of the earth) might require faster yet accurate models. Those provided by application of several so-called extended Born approximations are considered herein and their efficiency is illustrated from a number of numerical simulations whose results are compared to existing datasets