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Non-reflecting boundary conditions for Maxwell’s equations. (English) Zbl 1042.78010
Authors’ abstract: A new discrete non-reflecting boundary condition for the time-dependent Maxwell equations describing the propagation of an electromagnetic wave in an infinite homogeneous 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.

78A50 Antennas, waveguides in optics and electromagnetic theory
65N06 Finite difference methods for boundary value problems involving PDEs
65R99 Numerical methods for integral equations, integral transforms
44A10 Laplace transform
44A35 Convolution as an integral transform
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