The electromagnetic (EM) measurements obtained by using one transmitter and one receiver antenna in a borehole environment are simulated. The measurements are used to assess electrical properties of rock formations. First, logging instruments as well as rock formation properties are assumed to exhibit axial symmetry around the axis of a vertical borehole. The optimal mesh for axially symmetric problem is obtained by a 2D self-adaptive goal-oriented hp-Finite Element Method (FEM) that delivers exponential convergence rates in terms of the quantity of interest against the CPU time. The 3D mesh is obtained by full revolution of the generated 2D mesh. The computations are then performed for angles of formation layers deviated by 30, 45 and 60 degrees. The concurrent engineering infrastructure that solves the problem automatically in parallel is presented. The 3D code has been verified by comparison of numerical results with the known exact solution of the problem of antenna radiating into a homogenous space, and by comparison of results of 2D and 3D code for the problem with axially symmetric layers in formation.