  We present an algorithm to calculate the linear response of periodic systems
in the time-dependent density functional thoery, using a real-space
representation of the electron wave functions and calculating the dynamics in
real time. The real-space formulation increases the efficiency for calculating
the interaction, and the real-time treatment decreases storage requirements and
the allows the entire frequency-dependent response to be calculated at once. We
give as examples the dielectric functions of a simple metal, lithium, and an
elemental insulator, diamond.
