A higher order a-stable Maxwell solver using successive convolution

Summary form only given. We develop a numerical scheme for solving Maxwell´s equations to high accuracy in both space and time, without incurring the traditional Courant-Friedrichs-Lewy (CFL) stability limit on the time step. Our scheme utilizes a novel technique, successive convolution, to achieve order 2P in time at N spatial points, with a cost of O(P^dN) in d spatial dimensions. The speed and efficiency of the solver is due to the dimensional splitting we employ, which means that spatial convolution is performed line-by-line, making it logically Cartesian. However, the spatial points can be adjusted without affecting the stability, and so we can freely embed smooth non-rectangular domains into the grid, thereby preserving accuracy.