Maxwell's curl equations in the time domain are solved using an explicit linear finite–element approach implemented on unstructured tetrahedral meshes. For the simulation of scattering problems, a perfectly matched layer is added at the artificial far–field boundary, created by the truncation of the physical domain prior to the numerical solution. The complete solution procedure is parallelized. The computational challenges that are encountered when attempting simulations at higher frequencies suggest that the implementation of a hybrid algorithm could have certain advantages. The hybrid approach adopted uses a combination of the finite–element procedure and the well–known low operation count/low storage finite–difference time–domain method. Examples are included to demonstrate the numerical performance of the techniques that are described.