Abstract
A new discrete non-reflecting boundary condition for the time-dependent Maxwell equations describing the propagation of an electromagnetic wave in an infinite homogenous lossless rectangular waveguide with perfectly conducting walls is presented. It is derived from a virtual spatial finite difference discretization of the problem on the unbounded domain. Fourier transforms are used to decouple transversal modes. A judicious combination of edge based nodal values permits us to recover a simple structure in the Laplace domain. Using this, it is possible to approximate the convolution in time by a similar fast convolution algorithm as for the standard wave equation.
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Hiptmair, R., Schädle, A. Non-Reflecting Boundary Conditions for Maxwell’s Equations. Computing 71, 265–292 (2003). https://doi.org/10.1007/s00607-003-0026-2
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DOI: https://doi.org/10.1007/s00607-003-0026-2