An upwinding boundary condition capturing method for Maxwell’s equations in media with material interfaces

By using ghost points on either side of the interfaces, a global second-order accurate upwinding boundary condition capturing method for time-domain Maxwell’s equations in media with material interfaces is proposed. The equations are discretized on a uniform Cartesian grid and the interfaces are allowed to intersect the grid in an arbitrary fashion. The method is then obtained by combining central finite difference schemes with applicable nodes being replaced by the ghost points and upwinding technique with jump conditions across the interfaces being captured in a manner that the upwind property is always satisfied. The resulting discretization has the desirable property that the allowed time step size is independent of the locations and the shapes of the interfaces. Numerical examples are then given to demonstrate the second-order accuracy as well as the stability of the method, where it is used to study wave equations with various types of material interfaces, including electromagnetic scattering of a plane incident wave by a dielectric circular cylinder.