Solution of 3D non-stationary problems of impulse electric prospecting

This paper considers some aspects of modeling non-stationary electromagnetic fields for the 3D domains, including inhomogeneous conducting media. The source of such fields is an underground power line. To describe the fields in conducting media, a vector magnetic potential and a scalar electric potential are used, while a magnetic field in non-conducting media is described by a scalar magnetic potential. Systems of equations in conducting media are integrated by the Krank–Nickolson scheme. The conjugation conditions of the vector and the scalar magnetic potentials on the interfaces between the conducting and the nonconducting media hold with mean time steps. The scalar equations are solved by a scalar finite element method of second order, and the vector equations – by the Nedelek vector finite element method of second order of the second kind. The vector variation statements of the problems include the Lagrange factors, governing the divergent properties of vector values.