Elimination of FDTD Numerical Dispersion by using Geometrical Optics

The ray based time domain (RBTD) method for the computation of time-dependent electromagnetic fields is introduced. RBTD deals with discontinuities of field quantities, transports them along the rays and then constructs time-dependent field by using Taylor series with coefficients being discontinuities at the point of interest. The presented theory of RBTD handles propagation, reflection and refraction of finite jump discontinuities but not diffraction. Transport equations are 1D and RBTD implements xutri=nuxutrit along the ray. Hence in effect, RBTD reduces all higher dimensional problems to 1D along the ray. Honoring directional signal propagation and ODE nature of transport equations provide RBTD to eliminate numerical dispersion and superluminal effect of FDTD, which result from discretization of PDEs