An absorbing boundary condition for FDTD truncation using multiple absorbing surfaces

On the Huygens absorbing boundary conditions for electromagnetics

“…We derive theoretical properties of the Huygens ABCs in continuous spaces as well as in the discrete FDTD space. This permits results and observations in [1][2][3] to be interpreted. Especially, we show that the residual field radiated outside the Huygens surface is the time derivative of the outgoing field, while the field reflected towards the inner domain is integrated on time as it passes back through the Huygens surface.…”

“…These ABCs are the multiple absorbing surfaces (MAS) condition [1], and the re-radiating boundary condition (rRBC) [2,3]. They were developed independently and formulated in slightly different manners, but both rely on the same basic principle that consists of cancelling the outgoing field leaving the domain by means of equivalent currents that radiate a field equal in magnitude and opposite in sign to the field to be cancelled.…”

“…This is true for both traveling and evanescent waves. From this, methods [1][2][3], and more generally any HABC, cannot be viewed as novel ABCs. They are only alternative implementations of ABCs based on use of operators, for example alternative implementations of Higdon operator ABCs [5,6].…”

“…They are only alternative implementations of ABCs based on use of operators, for example alternative implementations of Higdon operator ABCs [5,6]. In consequence, ABCs [1][2][3] suffer from the same drawbacks as the operator ABCs. The most important is the strong reflection of the evanescent waves present in many problems of electromagnetics solved with numerical methods.…”

“…As shown in [1][2][3], high-order HABCs can be easily implemented by juxtaposing several one-order HABCs, without the stability problems faced when implementing high-order operator ABCs. However, the operators used in [1][2][3] are only designed to absorb traveling waves, they reflect in totality evanescent waves, so that the domain of application of the MAS [1] and rRBC [2,3] is probably narrow. We suggest two alternative ways to apply Huygens ABCs in an effective manner in realistic applications of numerical electromagnetics.…”