Modal decomposition in numerical modelling of eddy current problems

A methodology to reduce the computational cost of time domain computations of eddy currents problems is proposed. It is based on the modal decomposition of the current density. In particular, a convenient strategy to perform the modal decomposition even in presence of injected currents into the electrodes of a conducting domain is proposed and implemented in a parallel computing environment. Using a theta-method integration algorithm, the performances of the proposed approach are compared against those of a classical method based on the Cholesky factorization, for a case of interest in the framework of 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.