An upwinding embedded boundary method for Maxwell’s equations in media with material interfaces: 2D case

We propose a new upwinding embedded boundary method to solve time dependent Maxwell’s equations in media with material interfaces. A global second order finite difference method is obtained by combining central difference schemes away from the interfaces and upwinding technique with jump conditions near the interfaces. The proposed finite difference method allows time step based on a uniform mesh independent of the locations and shapes of the interfaces. Moreover, the scheme is simple to implement in multidimensional cases. Numerical tests of wave equations with various types of material interfaces and electromagnetic scattering of 2D cylinders confirm the stability, uniform accuracy and ease of implementation of the method.