Hyperboloidal layers for hyperbolic equations on unbounded domains

We show how to solve hyperbolic equations numerically on unbounded domains by means of compactification, thereby avoiding the introduction of an artificial outer boundary. The essential ingredient is a suitable transformation of the time coordinate in combination with compactification. Based on this idea, we present a new layer method, called hyperboloidal layers. Accuracy and efficiency of this method is demonstrated by numerical tests including the one dimensional Maxwell equations using finite difference methods, and the three dimensional scalar wave equation with and without nonlinear source terms using spectral methods.