JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY, cilt.29, ss.121-129, 2014 (SCI İndekslerine Giren Dergi)
Numerical methods in space-time have long been used to solve Maxwell's partial differential equations (PDEs) accurately. Finite Difference Time Domain (FDTD), one of the most widely used method, solves Maxwell's PDEs directly in computational grid. In FDTD, grid spacings (Delta x, Delta y, Delta z) are selected to properly sample field quantities to avoid aliasing and maximum allowable time-step (Delta t) is determined to ensure numerical stability of algorithm. Due to discretization of PDEs, FDTD inherently suffers from numerical dispersion, which results in numerical velocity errors and anisotropy in the grid. Anisotropy and different velocities result in numerical phase errors in the solution and it accumulates within the grid. Moreover, some modes in the grid propagate faster than light. In this study, contrary to FDTD, Geometrical Optic methods have been utilized and a new computational method called as Ray-Based Finite Difference (RBFD) method has been proposed for computational electromagnetics. Discontinuities in the fields and their successive time derivatives can only exist on the wavefronts and propagate along the rays. They are transported in computational domain by transport equations that are ordinary differential equations (ODEs). In isotropic media, energy flows in ray direction, which is perpendicular to the wavefronts. RBFD mainly utilizes directional energy flow property for grid generation and ODE nature of transport equations for numerical computations. Simulation results show that RBFD can be exploited to eliminate disadvantges of FDTD.