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Ray based finite difference method for time domain electromagnetics

Çiydem, Mehmet
In this study, novel Ray Based finite difference method for Time Domain electromagnetics(RBTD) has been developed. Instead of solving Maxwell̕s hyperbolic partial differential equations directly, Geometrical Optics tools (wavefronts, rays) and Taylor series have been utilized. Discontinuities of electromagnetic fields lie on wavefronts and propagate along rays. They are transported in the computational domain by transport equations which are ordinary differential equations. Then time dependent field solutions at a point are constructed by using Taylor series expansion in time whose coefficients are these transported distincontinuties. RBTD utilizes grid structure conforming to wave fronts and rays and treats all electromagnetic problems, regardless of their dimensions, as one dimensional problem along the rays. Hence CFL stability condition is implemented always at one dimensional eqaulity case on the ray. Accuracy of RBTD depends on the accuracy of grid generation and numerical solution of transport equations. Simulations for isotropic medium (homogeneous/inhomogeneous) have been conducted. Basic electromagnetic phenomena such as propagation, reflection and refraction have been implemented. Simulation results prove that RBTD eliminates numerical dispersion inherent to FDTD and is promising to be a novel method for computational electromagnetics.