The paper considers the computation of non-stationary radiation in electrodynamic stuctures with circular symmetry using the finite-difference time-domain (FDTD) method. There is proposed a new kind of exactly absorbing boundary condition (ABC) at a spherical boundary which is usable in Cartesian coordinates. Realization and testing of this ABC were carried out in a problem of radiation of the axisymmetric pulse antenna fed by a coaxial cable.
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