Efficient computation of transient diffusive electromagnetic fields

When dealing with electromagnetic fields in configurations where the conductivity does not vanish and where one confines oneself to low frequencies, e.g. in many geophysical applications, it is reasonable to neglect the displacement currents in Maxwell´s equations. The resulting set of equations describes the behavior of the diffusive electromagnetic field. Computing transient diffusive electromagnetic fields by means of an explicit time-stepping method can be very time consuming since the Courant stability condition is very restrictive in this case. Druskin and Knizhnerman (1994) have proposed a much more efficient approach for these type of problems called the spectral Lanczos decomposition method (SLDM). Their approach is based on a second-order differential equation for either the electric field strength or the magnetic field strength. In this paper we propose to compute the transient diffusive electromagnetic field by considering Maxwell´s equations as a system of first-order partial differential equations and by carrying out a Lanczos algorithm with this system in a fashion similar to the one presented for electromagnetic wave fields by Remis and van den Berg (1996).