A discontinuous Galerkin method to solve Liouville’s equation of geometrical optics

Abstract

We present an alternative method to ray tracing that is based on a phase space description of light propagation. Liouville’s equation of geometrical optics describes the evolution of the basic luminance on phase space. At an optical interface, the laws of optics describe non-local boundary conditions for the basic luminance. A discontinuous Galerkin method is employed to solve Liouville’s equation for a dielectric total internal reflection concentrator.