An Energy Conservative hp-method for Liouville’s Equation of Geometrical Optics

Abstract Liouville’s equation on phase space in geometrical optics describes the evolution of an energy distribution through optical system, which is discontinuous across interfaces. The Galerkin spectral element method conservative and can achieve higher order convergence locally, making it a suitable for this equation. When dealing with interfaces space, non-local boundary conditions arise. Besides being difficulty itself, these must also satisfy conservation constraints. To end, we introduce treatment Numerical experiments are performed to prove that obeys conservation. Furthermore, compared industry standard ray tracing. numerical show outperforms tracing by reducing computation time up three orders magnitude error $$10^{-6}$$ 10 - 6 .