High-order time-stable numerical boundary scheme for the temporally dependent Maxwell equations in two dimensions

High-order time-stable boundary operators for perfectly electrically conducting (PEC) surfaces are presented for a 3 × 3 hyperbolic system representing electro-magnetic fields T E to z. First a set of operators satisfying the summation-by-parts property are presented for a 2 × 2 hyperbolic system representing one-dimensional electromagnetic propagation in a PEC cavity. Boundary operators are then developed for two-dimensional electromagnetic propagation in the xy-plane. This procedure leads to a time-stable scheme for a 3 × 3 hyperbolic system and concurrently shows how to eliminate the ambiguity associated with tangential and normal electromag-netic field components at corners and edges of PEC scatterers when using colocated computational electromagnetic schemes. A numerical comparison to the popular Yee scheme is included, and this comparison suggests that the fourth-order (in space and time) scheme derived herein does effectively compute the Maxwell equations in tw