Characteristic-based algorithms for solving the Maxwell equations in the time domain

Several numerical algorithms, developed in the computational-fluid-dynamics community for solving the Euler equations, are found to be equally effective for solving the Maxwell equations in the time domain. The basic approach of these numerical procedures is to achieve the Riemann approximation to the time-dependent, three-dimensional problem in each spatial direction. The three-dimensional equations are then solved by a sequence of one-dimensional problems. This approach is referred to as a characteristic-based method. The basic algorithm can be implemented for both finite-difference and finite-volume procedures, and has the potential to eliminate the spurious-wave reflections from the numerical boundaries of the computational domain. The formulation and relative merit of the finite-difference and the finite-volume approximations are presented, together with numerical results from these procedures.<
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