Characteristics theory and Maxwell's equations in anisotropic media

The authors describe an algorithm for solving Maxwell's equations in anisotropic media in the framework of the finite volume - time domain approach using the theory of characteristics. They obtained compact analytical expressions for fluxes at interfaces between two anisotropic media from Riemann invariants. The interface itself can be a plain interface or may consist of a thin penetrable or impenetrable layer of anisotropic dielectric and magnetic properties. A new physical insight into the underlying approximations involving applications of the theory of characteristics in two and three dimensions has also been obtained.<>