The Maxwell–Klein–Gordon equation describes the interaction of a charged particle with an electromagnetic field. Solving this equation in the non-relativistic limit regime, i.e. the speed of light cc formally tending to infinity, is numerically very delicate as the solution becomes highly-oscillatory in time. In order to resolve the oscillations, standard numerical time integration schemes require severe time step restrictions depending on the large parameter c2c2.#R##N##R##N#The idea to overcome this numerical challenge is to filter out the high frequencies explicitly by asymptotically expanding the exact solution with respect to the small parameter c−2c−2. This allows us to reduce the highly-oscillatory problem to its corresponding non-oscillatory Schrodinger–Poisson limit system. On the basis of this expansion we are then able to construct efficient numerical time integration schemes, which do NOT suffer from any cc-dependent time step restriction.
['Patrick Krämer', 'Katharina Schratz']
Efficient time integration of the Maxwell–Klein–Gordon equation in the non-relativistic limit regime