  A methodology to reduce the computational cost of time domain computations of
eddy currents problems is proposed and implemented in a parallel computing
environment. It is based on the modal decomposition of the current density and
it is applicable even in presence of injected currents into the electrodes of a
conducting domain. Using a theta-method integration algorithm, the performances
of the the proposed approach are compared against those of a classical method
based on the Cholesky factorization, for a case of interest from eddy current
nondestructive testing. For this large eddy current problem (number of unknowns
greater than 100k, number of time steps of interest equal to 100k) the proposed
solution method is shown to be much faster than those based on standard time
integration schemes.
