Based on realistic numerical simulations of the three-dimensional time-dependent Schrödinger equation describing a hydrogen atom interacting with a strong electromagnetic field, the influence of the magnetic component is studied. The same computational techniques can be applied to the case of strong field photoionization as well as to the case of ionization by an incident relativistic heavy ion. One of the main consequences, in the strong-laser-field case, is the presence of true even harmonics of the incoming field. In the heavy ion impact, the asymmetry of the wave function reveals the importance of the nondipole nature of the interaction.